저작자표시-비영리-변경금지 2.0 대한민국 이용자는 ... - S-Space

저작자표시-비영리-변경금지 2.0 대한민국 이용자는 아래의 조건을 따르는 경우에 한하여 자유롭게 l. 이 저작물을 복제, 배포, 전송, 전시, 공연 및 방송할 수 있습니다.. 다음과 같은 조건을 따라야 합니다:. 저작자표시. 귀하는 원저작자를 표시하여야 합니다.. 비영리. 귀하는 이 저작물을 영리 목적으로 이용할 수 없습니다.. 변경금지. 귀하는 이 저작물을 개작, 변형 또는 가공할 수 없습니다.. l l. 귀하는, 이 저작물의 재이용이나 배포의 경우, 이 저작물에 적용된 이용허락조건 을 명확하게 나타내어야 합니다. 저작권자로부터 별도의 허가를 받으면 이러한 조건들은 적용되지 않습니다.. 저작권법에 따른 이용자의 권리는 위의 내용에 의하여 영향을 받지 않습니다. 이것은 이용허락규약(Legal Code)을 이해하기 쉽게 요약한 것입니다. Disclaimer. 이학박사 학위논문. Electronic structure studies of nematic phases in iron based superconductors 철기반 초전도체 네마틱 상에 대한 전자구조 연구. 2021 년 8 월. 서울대학교 대학원 물리학과 허순상. Electronic structure studies of nematic phases in iron based superconductors Soonsang Huh Supervised by Professor Changyoung Kim. A Dissertation Submitted to the Faculty of Seoul National University in the partial fulfillment of the requirements for the degree of Doctor of Philosophy. The graduate school Seoul National University Department of Physics and Astronomy. June 2021. ABSTRACT. Electronic structure studies of nematic phases in iron based superconductors. Soonsang Huh Department of Physics and Astronomy The Graduate School, Seoul National University, Seoul, Korea. Iron based superconductors have a nematic phase in which the rotational symmetry is broken in the electronic structure. This nematic phase has attracted attention because it is expected to be related to the pairing mechanism of superconductivity in iron based superconductors and is a novelty in itself. Therefore, understanding the origin of nematic phases is considered an important research task, and a number of studies have been conducted to find the mechanism. However, there is still no precise understanding of how exactly the nematic phase is formed. In order to understand the nematic phase accurately, it is necessary to directly observe how the rotational symmetry of the electronic structure is broken. For this reason, angle resolved photoemission spectroscopy (ARPES), which allows direct observation of the electronic structure, was conducted. FeSe has unique properties of the nematic phase compared to other iron based superconductors. The most peculiar aspect is the absence of long range magnetic order, which always coexists with orbital order in the iron pnictides nematic phase. Furthermore, it was reported that the resistivity anisotropy of FeSe has the opposite sign to that of iron pnictides. For this reason, the electronic structure study of FeSe was considered to provide important clue for understanding the nematic phase. Accordingly, ARPES and an X-ray absorption experiments were performed to investigate the electronic structure of the FeSe nematic phase. Through the analysis of the orbital character of the band dispersion, it was confirmed that one pocket disappeared in the 1 Fe Brillouin zone. In addition, the occupancy imbalance between the dxz and dyz orbitals was opposite compared to that of. other iron based superconductors. Through these results, it was possible to understand the peculiar characteristics of the FeSe nematic phase. Furthermore, it was revealed that ferro orbital order is not the origin of the nematic phase. Finally, the relationship between the nematic phase and superconductivity has been addressed through the experimentally identified electronic structure. Through the previous results, it was confirmed that the splitting between the dxz and dyz bands has momentum dependence in the nematic phase. Moreover, this finding was found not only in FeSe but also in other iron based superconductors. However, information about LaFeAsO, one of the representative iron based superconductor with nematic phase, was insufficient. Therefore, an electronic structure study was performed on the LaFeAsO nematic phase. It was found that the momentum dependent dxz/yz hole band splitting exist in the LaFeAsO nematic phase. Through this study, it was confirmed that the momentum dependent dxz/yz hole band splitting exist universally in the iron based superconductors. We propose that the instability for the observed universal momentum dependent band splitting should be the true origin of the nematic phase.. Key words : Iron based superconductor, Nematic phase, Angle-resolved photoemission spectroscopy, X-ray Absorption spectroscopy, Electronic structure, FeSe, LaFeAsO.. Contents. Abstract List of Figures. iv. 1 Introduction. 1. 1.1. 1.2. 1.3. Overview of iron based superconductors (IBSs) . . . . . . . . . . . . . . . .. 2. 1.1.1. Background of IBSs . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2. 1.1.2. Phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. 1.1.3. Electronic structure . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5. Nematic phase in IBSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7. 1.2.1. Nematic phase in IBSs . . . . . . . . . . . . . . . . . . . . . . . . . .. 7. 1.2.2. Evidence of nematic phase . . . . . . . . . . . . . . . . . . . . . . . .. 9. 1.2.3. Origin of nematic phase . . . . . . . . . . . . . . . . . . . . . . . . . 10. Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13. 2 Experimental Methods 2.1. 14. Angle resolved photoemission spectroscopy (ARPES) . . . . . . . . . . . . . 15 2.1.1. Introduction of ARPES . . . . . . . . . . . . . . . . . . . . . . . . . 15. 2.1.2. Polarization dependent ARPES . . . . . . . . . . . . . . . . . . . . . 18. 2.2. X-ray absorption spectroscopy (XAS) . . . . . . . . . . . . . . . . . . . . . 19. 2.3. Detwin process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21. 2.4. 2.3.1. Twin domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21. 2.3.2. Detwin process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. 2.3.3. Piezo based detwin device . . . . . . . . . . . . . . . . . . . . . . . . 24. Sample growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29. i. 2.4.1. Chemical vapor transport (CVT) method . . . . . . . . . . . . . . . 29. 2.4.2. Growth of FeSe crystal . . . . . . . . . . . . . . . . . . . . . . . . . . 30. 2.4.3. Sample characterization . . . . . . . . . . . . . . . . . . . . . . . . . 33. 3 Results I : Investigation of FeSe nematic phase 3.1. 36. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.1.1. Introduction of FeSe nematic phase . . . . . . . . . . . . . . . . . . . 37. 3.1.2. Previous electronic structure studies of FeSe nematic phase . . . . . 38. 3.2. Experimental detail. 3.3. Electronic structure in the nematic phase . . . . . . . . . . . . . . . . . . . 41. 3.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41. 3.3.1. Fermi surface topology . . . . . . . . . . . . . . . . . . . . . . . . . . 41. 3.3.2. Band dispersion. 3.3.3. Orbital characterization . . . . . . . . . . . . . . . . . . . . . . . . . 45. 3.3.4. Temperature evolution of electronic structure . . . . . . . . . . . . . 54. 3.3.5. Orbital occupation measurement . . . . . . . . . . . . . . . . . . . . 57. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.4.1. Orbital selective hybridization. . . . . . . . . . . . . . . . . . . . . . 60. 3.4.2. Unique characteristic of nematic phase . . . . . . . . . . . . . . . . . 62. 3.4.3. Understanding mechanism of nematic phase . . . . . . . . . . . . . . 63. 3.4.4. Relation to the superconductivity . . . . . . . . . . . . . . . . . . . . 64. 4 Results II : Investigation of LaFeAsO nematic phase 4.1. 67. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.1.1. Momentum dependent band splitting in the nematic phase . . . . . 68. 4.1.2. Introduction of LaFeAsO nematic phase . . . . . . . . . . . . . . . . 70. 4.2. Experimental detail. 4.3. Electronic structure in the nematic phase . . . . . . . . . . . . . . . . . . . 72. 4.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72. 4.3.1. Electronic structure of LaFeAsO nematic phase . . . . . . . . . . . . 72. 4.3.2. Temperature evolution of the electronic structure . . . . . . . . . . . 75. 4.3.3. Electronic structures of twinned and detwinned LaFeAsO . . . . . . 79. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 ii. 5 Other result : Electronic structure of Cu doped FeSe 5.1. 82. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.1.1. Chemical substitution on FeSe . . . . . . . . . . . . . . . . . . . . . 83. 5.2. Experimental detail. 5.3. Evolution of the electronic structure through doping . . . . . . . . . . . . . 86. 5.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86. 5.3.1. Evolution of the Fermi surface topology . . . . . . . . . . . . . . . . 86. 5.3.2. Evolution of the band dispersion . . . . . . . . . . . . . . . . . . . . 88. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91. 6 Summary. 92. Bibliography. 93. 국문 초록. 103. iii. List of Figures 1.1. Phase diagrams of Cuprates and IBSs . . . . . . . . . . . . . . . . . . . . .. 2. 1.2. Crystal structures of IBSs . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. 1.3. Lattice and magnetic structure of IBSs . . . . . . . . . . . . . . . . . . . . .. 4. 1.4. General electronic structure of IBSs . . . . . . . . . . . . . . . . . . . . . .. 5. 1.5. Bonding angle dependent electronic structure . . . . . . . . . . . . . . . . .. 6. 1.6. Nematic phase in IBSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7. 1.7. Phase diagram of nematic susceptibility . . . . . . . . . . . . . . . . . . . .. 8. 1.8. Experimental evidence of nematic pahse . . . . . . . . . . . . . . . . . . . .. 9. 1.9. Lattice distortion of IBSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. 1.10 Ferro orbital order in IBSs nematic phase . . . . . . . . . . . . . . . . . . . 11 1.11 Spin excitation anisotropy in IBSs nematic phase . . . . . . . . . . . . . . . 12 2.1. Schematic figure of ARPES . . . . . . . . . . . . . . . . . . . . . . . . . . . 15. 2.2. ARPES system at SNU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17. 2.3. In − situ ARPES cluster system . . . . . . . . . . . . . . . . . . . . . . . . 18. 2.4. Experimental geometry for identifying orbital parity . . . . . . . . . . . . . 19. 2.5. Schematic figure of XAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20. 2.6. Schematic of twin domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21. 2.7. Polarized microscope image of twinned and detwinned domain. 2.8. Detwin effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23. 2.9. Schematic image of the piezo based detwin device . . . . . . . . . . . . . . . 24. . . . . . . . 22. 2.10 Strain measurement of the piezo based detwin device . . . . . . . . . . . . . 25 2.11 Polarized image of twinned and detwinned FeSe . . . . . . . . . . . . . . . . 26 2.12 Image of piezo holder for ARPES and XAS . . . . . . . . . . . . . . . . . . 28. iv. 2.13 Schematic process of CVT method . . . . . . . . . . . . . . . . . . . . . . . 29 2.14 Binary phase diagram of Fe and Se . . . . . . . . . . . . . . . . . . . . . . . 30 2.15 Corn shape sealed quart tube . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.16 3 Steps for the CVT method . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.17 Single crystal of FeSe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.18 Laue diffraction pattern of FeSe . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.19 Resistivity of FeSe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.1. Phase diagram of FeSe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37. 3.2. Resistivity anisotropy of FeSe and BaF e2 As2 . . . . . . . . . . . . . . . . . 38. 3.3. previous ARPES studies of FeSe . . . . . . . . . . . . . . . . . . . . . . . . 39. 3.4. previous STM studies of FeSe . . . . . . . . . . . . . . . . . . . . . . . . . . 40. 3.5. Fermi surface of twinned and detwinned sample . . . . . . . . . . . . . . . . 42. 3.6. Piezo bias on/off fermi surface. 3.7. Schematic Fermi surface maps in the 2 Fe BZ and 1 Fe BZ . . . . . . . . . . 44. 3.8. Band dispersion above and below nematic phase transition. 3.9. Schematic of 1 Fe BZ and 2 Fe BZ . . . . . . . . . . . . . . . . . . . . . . . 46. . . . . . . . . . . . . . . . . . . . . . . . . . 43. . . . . . . . . . 45. 3.10 Relative orientations of orbital in real space for the following orbital of the reciprocal space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.11 Orbital character determination of MX point. . . . . . . . . . . . . . . . . . 48 3.12 Orbital character determination of MY point. . . . . . . . . . . . . . . . . . 49 3.13 Fermi surface in 1 Fe BZ scheme . . . . . . . . . . . . . . . . . . . . . . . . 51 3.14 Orbital character determination of Γ point . . . . . . . . . . . . . . . . . . . 52 3.15 Summary of orbital characterization . . . . . . . . . . . . . . . . . . . . . . 53 3.16 Temperature evolution of dxz electron band . . . . . . . . . . . . . . . . . . 54 3.17 Temperature evolution of dxz/yz hole band . . . . . . . . . . . . . . . . . . . 55 3.18 Schematic illustration of the band reconstruction at the BZ corner across the nematic phase transition in 1-Fe BZ scheme . . . . . . . . . . . . . . . . 56 3.19 Fe L edge spectra with different polarization. . . . . . . . . . . . . . . . . . 57. 3.20 Temperature dependent XLD result . . . . . . . . . . . . . . . . . . . . . . 58. v. 3.21 Structure contribution of XLD . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.22 Comparison of FeSe and BaFe2 As2 XLD data . . . . . . . . . . . . . . . . . 60 3.23 Evolution of the energy level diagram . . . . . . . . . . . . . . . . . . . . . 61 3.24 Scenario for the weak coupling picture and experimental result . . . . . . . 62 3.25 Orbital configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.26 S doped FeSe phase diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . 64. 3.27 S doped FeSe phase diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . 65. 3.28 Phase diagram with Lifshitz transition . . . . . . . . . . . . . . . . . . . . . 66 4.1. Electronic structure with and without ferro orbital order . . . . . . . . . . . 68. 4.2. Temperature dependence of dxz and dyz band in FeSe . . . . . . . . . . . . 69. 4.3. Momentum dependent dxz /dyz splitting in FeSe, NaFeAs and BaFe2 As2 . . . 70. 4.4. Phase diagram of Co doped LaFeAsO. . . . . . . . . . . . . . . . . . . . . . 70. 4.5. Phase diagram of nematic susceptibility in Co doped LaFeAsO. . . . . . . . 71. 4.6. Electronic structure of LaFeAsO nematic phase. . . . . . . . . . . . . . . . . 73. 4.7. Tight binding calculation result. . . . . . . . . . . . . . . . . . . . . . . . . 74. 4.8. Temperature evolution of the electronic structure near Γ point. . . . . . . . 75. 4.9. Temperature dependent EDC near Γ point . . . . . . . . . . . . . . . . . . . 76. 4.10 Temperature evolution of the electronic structure near M point. . . . . . . . 77 4.11 Temperature dependent EDC near M point . . . . . . . . . . . . . . . . . . 78 4.12 electronic structure of twinned and detwinned sample . . . . . . . . . . . . 79 4.13 Universal momentum dependent dxz /dyz splitting in IBS nematic phase . . 80 5.1. Phase diagram of FeSe1−x Sx and FeSe1−x Tex . . . . . . . . . . . . . . . . . 83. 5.2. Bardeen-Cooper-Schrieffer Bose-Einstein condensation crossover and topological superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84. 5.3. Transport properties of Fe1−x Cux Se . . . . . . . . . . . . . . . . . . . . . . 85. 5.4. Fermi surface of Fe1−x Cux Se . . . . . . . . . . . . . . . . . . . . . . . . . . 87. 5.5. Doping evolution of the band dispersion near Γ point . . . . . . . . . . . . . 88. 5.6. Fermi surface of Fe1−x Cux Se . . . . . . . . . . . . . . . . . . . . . . . . . . 89. 5.7. Doping evolution of the band dispersion near M point . . . . . . . . . . . . 90. vi. Chapter 1. Introduction This chapter provides a brief overview of iron based superconductors (IBSs). The background of this material, general phase diagram and its electronic structure are described. Then, nematic phase of IBSs is introduced. Importance of nematic phase due to the possible relation with superconductivity and effort to find the origin of the nematic phase is provided. After discussing the limitation of understanding the origin of the nematic phase, I will discuss the research motivation of the thesis.. 1. 1.1 1.1.1. Overview of iron based superconductors (IBSs) Background of IBSs. In 2008, iron based superconductors (IBSs) were discovered with relatively high superconducting transition temperature (TC ) [1]. This discovery was a big surprise for the research field, as there was a preconception that superconductivity can not exists in magnetic material like Fe compound. Since the first discovery, numerous materials have been synthesized. As result, TC achieved near 55 K in single crystal form [2] and TC near 100 K in thin film form [3]. These materials immediately drew a lot of attention because of their similarity to Copper based superconductors (here after Cuprate). It is also a multi orbital system, which is different compared to single orbital system of cuprate. In particular, similarity of the phase diagram compared to that of Cuprate raised some hope that IBSs may lead to gain the new clue to the microscopic theory for the high TC materials [4].. Figure 1.1: General phase diagram of Cuprates (left) and IBSs (right) [4].. With these reason, intensive and extensive researches has been conducted in IBSs. Numerous experiment and theoretical studies have been performed on various materials as shown in Figure 1.2 [5]. Up to now, more than 100,000 research papers on IBSs have been published since 2008. Even some phenomena emergent in IBSs have been understood, 2. still numerous physics including the mechanism of the high TC have remained uncovered issue.. Figure 1.2: Crystal structures of IBS families [5].. 1.1.2. Phase diagram. To understand superconductivity and related phenomena, it is essential to understand the phase diagram. This section introduces various phases that appears in IBSs through phase diagram. First of all, superconductivity appears when chemical substitution or hydrostatic pressure is applied. Above the TC , there are two other phases. There is a structural phase transition in which tetragonal phase changes to orthorhombic phase as the temperature decreases. As illustrated in Figure 1.3 (middle), a axis becomes longer than b axis in the orthorhombic phase. As can be seen in Figure 1.1, doping or pressure lowers the transition temperature (TS ) and suppresses it near by optimal doping level. In addition, there is magnetic transition. As the temperature decreases, paramagnetic phase goes to the antiferromagnetic (AF) phase. Generally, it is known that magnetic transition temper-. 3. ature (TN ) is same or slightly lower than TS . In this AF phase, spins are ordered antiferro magnetically along a axis while it orders ferro magnetically along b axis as shown in Figure 1.3 (bottom). This stripe type AF order appears in most IBSs except the FeTe [6], which shows bi-collinear AF. Similar to the structural transition, TN decreases with doping or pressure. It was believed that fluctuation of magnetism could be the pairing glue for the Cooper pair, as the tendency of TN and TC are similar to the Cuprate case.. Figure 1.3: Lattice and magnetic structure of IBSs.. 4. 1.1.3. Electronic structure. Figure 1.4: Electronic structure (above) and Fermi surface (below) of IBSs [7].. Electronic structure is a key for understanding the noble physics emerging in IBSs. As mentioned above, there are numerous system in IBSs, but overall electronic structure is similar. As shown in Figure 1.4 above, the electronic structure mostly consists of Fe 3d characters (dxz , dyz and dxy orbital). This multi orbital/band system is the most discrepancy point compared to Cuprate, known as single band system (mostly dx2 −y2 orbital). The detailed electronic structure is explained as follows. Near Γ points, dxz , dyz and dxy hole bands locates. Meanwhile dxz , dyz and dxy crosses Fermi level (EF ) near M point and hole bands locates below EF . As a consequence, there are several pockets exists in the Fermi surface (see Figure 1.4 below). Near Γ points, there are usually two hole pockets while there are electron pockets near M point. It is noteworthy that relative energy level of the hole band near Γ point depend varies system to system, resulting 5. different Fermi surface topology (i.e. FeSe 1 monolayer on SrTiO3 [9], Csx Fe2 Se2 [10]). Figure 1.5: Calculated Fermi surface and electronic structure depend on the bonding angle. [8].. As mentioned above, electronic structure may vary depending on the material. One of the reasons for this dependence is its crystal structure. IBSs is known to be sensitive to the bonding angle or As (Se) height. As shown in Figure 1.5, calculation result of electronic structure reported that if bonding angle (α) is larger than 110 degree dxy band located upper position while it locates lower position as bonding angle is smaller than 110 degree. The energy difference between (0,0) and (π,π) point (Γ point and M point) is proportional to the nearest hopping parameter. When the bonding angle is relatively small, the hopping through Fe - As (Se) - Fe reduced, other means nearest hopping reduced. It result energy difference of the (0,0) and (π,π) point. We note that other bands are also affected by the crystal structure. However, the reason why dxz orbital is sensitive to the bonding angle is that dxy is in plane orbital while dxz/yz are out of plane orbital.. 6. 1.2 1.2.1. Nematic phase in IBSs Nematic phase in IBSs. Figure 1.6: (a) Nematic liquid crystal. (b) Schematic Fermi surface topology of normal state (left) and nematic state (right). (c) Nematic phase in IBSs [11].. Several phases were introduced in the previous section. There is additional phase, nematic phase. The word nematic comes from the liquid crystal. The nematic liquid crystal is shown in Figure 1.6 (a). This crystal have elliptical shape, in other words it is a C2 symmetric crystal. In IBSs, the nematic phase refers to a state with broken rotational symmetry (C4 to C2 ) in the electronic structure. As shown in Figure 1.6 (b), Fermi surface 7. of normal state has 4 fold symmetry. Meanwhile, in the nematic phase, it clearly shows the 2 fold symmetry Fermi surface. At the M point, there is only one elliptical pocket while there are two cross shaped elliptical pocket in the normal state. This nematic phase is indicated as blue region in the phase diagram shown in Figure 1.6 (c) [11]. Nematic phase transition occurs near TS . In addition, similar to TS and TN , it is suppressed where TC appears.. Figure 1.7: Phase diagram of nematic susceptibility measured by resistivity anisotropy [11].. The nematic phase has been center of the research due to its possible relationship with superconductivity. It has been suggested that nematic fluctuation could be the glue for the Cooper pairs. Indeed, several experimental result have revealed nematic fluctuation and suggested relation to the superconductivity. As shown in Figure 1.7 [11], the phase diagram of nematic susceptibility shows that nematic fluctuation appears over a wide range of doping levels and diverges near the optimal doping level. Similar result have been reported with several materials [12], which indicates that nematic fluctuation could be universal paring glue in the IBSs. Note that nematic susceptibility is measured from resistivity anisotropy along a and b axis by controlling uniaxial strain. 8. 1.2.2. Evidence of nematic phase. Evidence of the nematic phase has been observed with various experimental tools. Transport studies show that electrical resistivity along b axis (ferromagentic direction) is greater than that of along a axis (AF direction) in Ni doped BaFe2 As2 [13] as shown in Figure 1.8 (a). This result is unexpected because conductivity is larger along ferromagnet direction than along AF direction in most of the case. It is observed to be exist over wide range of doping and temperature, as shown in Figure 1.8 (a). It is noteworthy that direction of the resistivity anisotropy changes in the K doped BaFe2 As2 [14] and FeSe [15]. The mechanism was difficult to understand due to the diversity of the direction of the resistivity anisotropy but they all believed to be the evidence of the nematic phase.. Figure 1.8: Experimental evidence of nematic phase measured by (a) resistivity anisotropy (b) STM (c) NMR (d) magnetic torque measurement.. 9. Inelastic neutron scattering study for CaFe2 As2 reported large anisotropy in magnetic exchange coupling [16] (Figure 1.8 (b)). The magnitude of J1a and J1b are different, which implies electronic anisotropy. This anisotropy was also reported in scanning tunneling microscopy studies on Co doped CaFe2 As2 [17] and FeSe [18]. The unidirectional pattern in quasi particle interference indicates C2 symmetric of electronic structure. In addition, NMR spectra of As and Se [19,20] (Figure 1.8 (c)), magnetic torque measurement (Figure 1.8 (d)) reported electronic nematicity [21].. 1.2.3. Origin of nematic phase. Figure 1.9: Lattice distortion of Co doped BaFe2 As2 [22].. The relationship between nematic phase and superconductivity was mentioned in the previous section. In this regard, researchers believed that understanding the origin of the nematic phase may provide clues for the elucidating the superconductivity mechanism. Extensive and intensive research has been conducted to find the mechanism of the nematic phase. Since nematic phase exists with structural and magnetic transition, it is believed that lattice, spin and orbital degree of freedom can drive the nematic phase. However,. 10. about 1 % lattice distortion [22, 23] is not sufficient to explain the experimental evidence of nematic phase (see Figure 1.9). For this reason, it is believed that the nematic phase stems from spin or orbital degree of freedom, in other words electronic origin. Candidate for the nematic phase will be discussed in below.. Figure 1.10: (a) Schematic picture of Ferro orbital order [24]. (b) phase diagram of Ferro obital order [25].. For the orbital degree of freedom case, Ferro orbital order is mostly believed to be a candidate. Ferro orbital order in IBSs is defined as dxz orbital is more occupied than dyz orbitals in every Fe site as shown in Figure 1.10 (a). [24]. Several electronic structure studies. 11. have reported anisotropic band structure that implies nxz (occupation of dxz orbital) > nyz (occupation of dyz orbital) [26–32]. In addition, X-ray linear absorption on Co doped BaFe2 As2 directly revealed the existence of ferro orbital order and its fluctuation [25].. Figure 1.11: Spin excitation anisotropy of Ni doped BaFe2 As2 [33]. For the spin degree of freedom case, inelastic neutron scattering experiment result shows that there is anisotropic spin fluctuation between [1,0,1] and [0,1,1] direction (see Figure 1.11) [33]. Both excitation exist above the nematic phase transition temperature, but one of them suppressed when system enters the nematic phase. This result implies that anisotropic spin excitation is strongly coupled with the nematic phase, which means spin fluctuation could be the origin of the nematic phase.. 12. 1.3. Motivation. Evidence of nematic phase has been studied with various experimental techniques and materials. These results suggested a possible relationship between superconductivity and nematic phase. For this reason, it has been important issue to figure out how the nematic phase was formed. However, there is still not sufficient research on the origin of the nematic phase. To address the issue more directly, exact electronic structure of the nematic phase required. Since the definition of nematic phase is rotational symmetry broken state in the electronic structure. Despite the importance of the electronic structure, studies were not seriously done. Moreover, it is conducted on the few specific systems. Thus, comprehensive studies are needed to provide the precise and wide understanding of the nematic phase. In this sense, we made effort to understand the exact electronic structure of the nematic phase of FeSe and LaFeAsO. From the result, we were able to resolve many unique phenomena occuring in the nematic phase, and also we address the universal mechanism for the origin of the nematic phase. Detailed result will be described in the result section.. 13. Chapter 2. Experimental Methods This chapter introduces the experimental method used to understand the electronic structure of the nematic phase. First, angle resolved photoemission spectroscopy (ARPES) and X-ray absorption will be introduced. Second, I will describe piezo based detwin method to obtain the single domain. Finally, growth method for the single crystal used for the experiment will be introduced.. 14. 2.1 2.1.1. Angle resolved photoemission spectroscopy (ARPES) Introduction of ARPES. Angle resolved photoemission spectroscopy (ARPES) is a direct tool for measuring the distribution of the electrons in the reciprocal space of solid. When light incidents to the sample, electrons are emitted from the sample by well known photoelectric effect (Figure 2.1). These electrons have information about kinetic energy and emitted angle. From this information, it is able to deduce the binding energy and momentum information of the electrons in the crystal. The detailed principle is explained below.. Figure 2.1: Schematic figure of ARPES.. The photoelectron have information as follows,. }kx =. p 2mEkin sinϑcosϕ. (2.1). }ky =. p 2mEkin sinϑsinϕ. (2.2). 15. }kz =. p 2mEkin cosϑ. (2.3). where Ekin is the kinetic energy of the photoelectron. In principle, the electronic structure can be obtained with the information of Ekin , ϑ and ϕ. However, the out of plane momentum (}kz ) is not conserved because there is no translational symmetry along the surface normal whereas in plane momentum is conserved. Therefore, additional task is required to determine }kz . Assuming that the dispersion of the electron final state involved in the photoemission process, one can adopt a nearly free electron description for the final bulk Bloch state as follows.. Ef (k) =. 2 }2 kk2 + }2 k⊥. 2m. − E0. (2.4). E0 corresponds to the bottom of the valence band. By using the equation follows. Ef (k) = Ekin + φ. }2 kk2. (2.5). = Ekin sinϑ2. (2.6). 1p 2mEkin cosϑ2 + V0 }. (2.7). 2m k⊥ (kz ) could be obtained as. k⊥ =. V0 (E0 + φ) referred as inner potential. Determining V0 provides information of k⊥ . It can be obtained through photon energy dependent experiment. By changing photon energy, other means changing k⊥ value, then V0 can be obtained from using the periodicity of k⊥ . Figure 2.2 is the ARPES system installed in the home lab. As shown in figure, hemisphere analyzer is attached to the main chamber. photoelectron emitted from the sample comes into the hemisphere then energy and momentum information are detected. For the. 16. light source, He and Xe discharge lamps are used. In addition, X-ray source with Ag Lα (2984.3 eV) and Al Kα (1486.6 eV) can be used for X ray photoemission spectroscopy. The temperature of the sample can be controlled from 5 K to 350 K. In general, ARPES mainly observes low energy region. In other words, it is a surface sensitive measurement. For this reason, experiment should be conducted under ultra high vacuum condition. Turbo pump, cryo pump, NEG pump and TSP are attached to achieve the vacuum below the 5 ×10−11 torr. In addition, the spin component of the band dispersion can be resolved by VLEED type detector attached to top of the hemisphere analyzer. Also low energy electron diffraction (LEED) can be used for check the quality of the sample surface.. Figure 2.2: ARPES system at SNU.. 17. Figure 2.3 shows the in − situ ARPES cluster system installed in the home lab. In addition to measuring single crystal samples, thin film grown by pulsed laser deposition (PLD) and molecular beam epitaxy (MBE) can also be measured without exposure to air by in − situ transfer system.. Figure 2.3: In − situ ARPES cluster system.. 2.1.2. Polarization dependent ARPES. The ARPES intensity is proportional to the matrix element based on perturbation theory. In this case, matrix element is given by equation 2.8.. I = | < ψf |V |ψi > |2 δ(}ν − Ef + Ei ). (2.8). Where ψi and ψf are initial and final state and V is dipole Hamiltonian with polarization vector. Since the later part acts as a constraint on the allowed conversion, the polarization dependence of the transition comes from the previous part. For example, assuming a typical cubic structure with the geometry as shown in Figure. 18. 2.4, the dxy and dyz orbital have odd parity while dxz orbital has even parity. The final state would have even parity. If s-polarized light (odd parity) incident to the sample, odd parity orbitals (dxy and dyz orbital) are observed. Meanwhile if p-polarized light (even parity) incident to the sample, even parity orbital (dxz orbital) are observed. Note that, identifying orbital character of IBSs is much more complicated than the simple case described above. It will be discussed in the result section.. Figure 2.4: Experimental geometry for identifying orbital parity.. 2.2. X-ray absorption spectroscopy (XAS). X-ray absorption spectroscopy (XAS) is one of the widely used experimental tools to determining the electronic structure. XAS provides information on the partial density of unoccupied state of the material. In this technique, when the X ray light incidents to the sample, transition of core electrons to the conduction band occurs as they absorb energy from the incident light (Figure 2.5). Each atomic element in the sample has its own characteristic binding energy for the certain core level, therefore XAS can provide element dependent information.. 19. Figure 2.5: Schematic figure of XAS. From the Beer’s law, the attenuation of the electromagnetic radiation of the material can be described as. I(x) = I0 e−µx. (2.9). where I0 is the intensity of incident radiation, I(x) is the intensity of the radiation after traversing through the absorbing, x is the depth of the material and µ is absorption or attenuation coefficient. The absorption coefficient µ is described as. µ = | < ψf |V |ψi > |2 δ(}ν − Ef + Ei ). (2.10). Where ψi is core state and ψf is an unoccupied state. It is similar to the one from the matrix element of ARPES but V is the absorption process of photon in this case.. 20. 2.3 2.3.1. Detwin process Twin domain. Figure 2.6: (a) Schematic of twin domain. (b) Polarized microscope image of BaFe2 As2 above and below TS [34, 35].. As mentioned in the introduction section, most of the IBSs have a structural transition. Below TS , the lattice constant of a and b axis are changed to form structural twin domains. These twin domains are formed perpendicularly as shown in Figure 2.6 (a) [34, 35]. In the polarized microscope image (Figure 2.6 (b)), two different domains are shown in different color due to difference in reflectance of domain. It is noteworthy that this behavior is not 21. shown above the TS . The size of the these domains is known to be few µm, which is much larger than the beam size of usual photoemission experiment. For this reason, signal in the mixed (twin) domain is measured in the transport or photoemission experiment. In this case, electronic structure with isotropic signal is obtained though we are measuring anisotropic nematic phase.. 2.3.2. Detwin process. Measurements in a single area are required to obtain information about the anisotropy of the nematic phase. Making the single domain process is called a detwin process. In the IBSs, detwin process done by applying magnetic field or uniaxial strain. Both field/strain are applied along orthorhombic a/b direction. In these case, a direction is defined by the direction of stretched and field applied. For the magnetic field detwin method, more than 10 T is required to detwin the sample [36]. For the strain detwin method, few MPa is needed to detwin [33]. In the Figure 2.7, there are 2 domains before applying the strain (left) while there is almost one domain after the applying the strain (right).. Figure 2.7: Polarized microscope image of twinned and detwinned domain [34].. It is not able to apply magnetic field during the photoemission experiment, since the electronic structure are distorted. Therefore, for the experiment, we developed a uniaxial strain device that does not generate an electric field/magnetic field. As shown in Figure 2.8 (a), strain is applied by screwing the bolt at the side of the holder [37, 38]. Using this. 22. holder, several studies have successfully observed the electronic structure of the nematic phase. In the Figure 2.8 (b), Fermi surface of twinned and detwinned FeSe shows clear difference [39]. In the twinned sample, there are 2 elliptical pocket with cross shape at the Brillouine zone (BZ) corner. Meanwhile, in the detwinned sample, there is only one elliptical pocket at BZ corner. Due to the twin domains, 4 fold shape Fermi surface is observed while it is intrinsically 2 fold shape Fermi surface. In short, detwinned sample is required to obtain exact electronic structure of the nematic phase.. Figure 2.8: (a) Mechanical detwin holder [37, 38]. (b) Fermi surface of twinned and detwinned FeSe [39].. 23. 2.3.3. Piezo based detwin device. The Mechanical detwin method is most widely used method for the detwin ARPES as described in the previous section. Tensile or compressive strain can be applied by screwing the sample. There are difficulties with this method. Most of IBSs sample are less than 100 µm thick, so it is easily broken. For instance, FeSe tears or bends even when we tight the screw about few degrees. In addition, the strain direction is not accurate. For the preparing sample with mechanical detwin holder, we glue the both side of the sample with epoxy. Due to the thermal shrink of the epoxy, sample can be detwinned without screwing the bolt. Moreover, it is difficult to change the amount of the strain inside the chamber. Therefore, it is not easy to apply strain with mechanical detwin holder.. Figure 2.9: Schematic image of the piezo based detwin device.. To overcome this issues, we have developed piezo based detwin device. Piezo electric material are known to expand when the electric field is applied and vice versa. In our case, we used PbZrx Ti1−x O3 based piezo. We used Piezomechanik Pst 150/2/3/5 model, which can be usable in the ultra high vacuum and cryogenic temperature. We directly glued sample on the piezo stack then apply bias voltage to the piezo stack to apply uniaxial strain (Figure 2. 9). 200 : 7 commercial silver epoxy was used for the glue due to various purpose. First, piezo stack can not be heated up to above 120 Celsius. Therefore, low curing epoxy was needed to preparing the sample. Used commercial silver epoxy cures at 80 K in 2 hour which is able to use for preparing the sample. Second, there must be a conduction path to avoid the charging effect during the photoemission experiment. To 24. make path, conducting silver epoxy was used. Third, a conducting material is required to hide the polymer based coating on the piezo stack. Note that piezo itself is very sensitive to the scratch, therefore tweezers are not used during preparing the sample. Also, polymer coating is sensitive to the Acetone and Ethanol, so we tried to avoid to use it during preparation. Isopropanol was able to use during preparation. The next step is to check the amount of the strain we can apply. A strain gauge (Commercial product form Vishay Precision Group) was used to measure amount of the strain. By using gauge directly attach on to the piezo and the sample, it was able to determine the amount of the strain. From the measured value up to 60 V (Figure 2.10), we can deduce that strain amount of the piezo and sample at 150 V (maximum voltage we can apply at room temperature) is about 0.1 % and 0.03 % , respectively. 0.1 % strain of the piezo well agree with the known value. Note that the less value of the strain of the sample compared to the piezo may be due to the effect of silver epoxy and thickness of the sample.. Figure 2.10: Strain measurement of the piezo based detwin device at 300 K.. 25. It is known that strain value of the piezo has temperature dependence. The maximum strain value become 20 % and 4 % of the value of room temperature at 77 K and 4 K, respectively. Therefore, the amount of maximum strain of the sample at 20 K can be roughly estimated as 0.003 %. The amount of pressure could be obtained with Young’s modulus value as described in equation 2.11.. E=. σ . (2.11). Where, E is the Young’s modulus value, σ is tensile stress and is the strain value. For example, FeSe Young’s modulus value at 20 K is about 40 GPa and tensile strain applied from piezo is about 0.003 % [40]. From the equation 2.11, the amount of pressure applied to the sample is about 1.2 MPa. Since it is known that few Mpa can detwin the sample, the pressure applied from piezo is reasonable amount to detwin the sample.. Figure 2.11: Polarized image of twinned (0 V) and detwinned (150 V) FeSe. We used polarized microscope to check strain from the piezo is enough to detwin the sample. In Figure 2.11, there are pink and blue domains in twinned sample (0 V). For the detwinned sample, we applied 150 V to piezo at the 150 K, above the TS (90 K) of the. 26. FeSe, then cool down. It is clearly observed that most of the blue domains disappeared. Thus, we can deduce that the sample is nearly fully detwinned by piezo. There are reasons for applying voltage at high temperature even above the TS . First, at the high temperature we can apply more strain due to the temperature dependence of the piezo. Second, the amount of strain to detwin the sample is less required near TS . Therefore, we applied strain above the TS and cooled down. It is noteworthy that once detwinned domain does not go back to twinned domain when voltage is turned off below the TS . After confirming that it is able to detwin the sample by piezo, we developed a piezo based detwin holder for the ARPES and XAS (Figure 2.12). Figure 2.12 (a) is schematic drawing piezo based detwin holder for ARPES. Figure 2.12 (b) is the picture of the piezo based ARPES detwin holder that used for the Beamline 4 of the Advanced Light Source. Figure 2.12 (c) is the piezo based XAS detwin holder for the Beamline 2A of Pohang Light Source. To apply bias voltage inside the chamber, electrical line were attached near the manipulator. To avoid the distortion effect from the electric field generated from the piezo, additional metal piece were added near the sample. We double checked distortion effect during the experiment and found to be it is negligible.. 27. Figure 2.12: (a) Schematic image (b) picture of piezo holder for ARPES. Holder is designed for Beamline 4 of Advanced Light source. (c) picture of piezo holder for XAS. Holder is designed for Beamline 2A of Pohang light source.. 28. 2.4 2.4.1. Sample growth Chemical vapor transport (CVT) method. High-quality single crystals are a top priority for obtaining good experimental data. There are various method for growing sample such as floating zone, Bridgmann, Czochralski, Flux and chemical vapor transport (CVT) method. The latter is the method used here for single crystal growth. The term CVT refers to heterogeneous reaction, volatilization and crystallization. Transition metal (i.e. Fe) known to have high melting temperature, so it is difficult to volatilize themselves at ambient pressure. However, it is possible to turn into a gas phase when reacting with transport agent [41]. When raw material and agent containing quartz tube is heated to appropriate temperature, the material starts to volatilize due to the reaction with the agent. When a temperature gradient created by two zone furnace, the volatilized material in one end of the quartz is transported to other side, where the reverse reaction occurs. In this side, volatilized compound separated into original material and agent. At this point, it makes a seed itself and grows slowly and then becomes single crystal (Figure 2.13).. Figure 2.13: Schematic process of CVT method.. The CVT method is one of the widely accepted method to synthesize of Van der Waals materials such as metal dichalcogenides, a material that has been intensively studied for the new generation device [42]. This method is one of the easiest way to make a sample if 29. one have capability to seal the quartz tube and have multi zone furnace. In addition, for the some material, CVT is the only available method to growth. On the other hands, the crystal usually has defect due to substitution by the agent and limitation of the growing size up to few millimeter.. 2.4.2. Growth of FeSe crystal. There are two methods of grwoing single crystal of FeSe: Flux method [43,44] and CVT method [45, 46]. In the former case, the raw material (Fe and Se) heated to a temperature at which it starts to melt. Then, it is slowly cool down to the room temperature to get crystal. However, there are many phase of FeSe in the Fe-Se binary phase diagram as shown in Figure 2.14. With flux method, it is difficult to avoid phase mixing of the sample, especially hexagonal FeSe. In addition, large difference melting temperature of Fe and Se make it hard to get sample with desired ratio.. Figure 2.14: Binary phase diagram of Fe and Se.. On the other hand, the CVT method is appropriate way to grow the crystal. In order to grow single phase FeSe crystal which superconductivity, the growth temperature should 30. be lower than 400 Celsius (Figure 2.14). This temperature is much lower than melting temperature of Fe. As mentioned in the previous section, by using a transport agent (Cl2 ), it is possible to vaporize the Fe atoms at the temperature lower than 400 Celsius. Though the halogen atoms can be inserted inside the crystal and act as defects, the amount of defect is too small to alter the electrical properties of sample significantly.. Figure 2.15: Corn shape sealed quart tube. For growth, quartz tube with an inner diameter 14 mm and a length of 18 cm was used. For the starting material, Fe 0.25 g (0.0044 mol), Se 0.321g (0.004 mol), KCl 1.1g (0.0147 mol) and AlCl3 3.92g (0.0294 mol) was put into the quartz tube. Additional Fe is used for avoiding the synthesize of Fe7 Se8 phase. The reason mixture of KCl and AlCl3 used is that tis mixture starts to melt at 150 Celsius and start to evaporate Cl2 gas. Then tube was sealed as cone shape as shown in Figure 2.15. During the sealing process, Ar gas was used to keep ambient pressure then path was closed within a vacuum better than 1 ×10−5 torr. To avoid the exposure to the air, most of the process was done in the glove box which the atmosphere inside is less than 0.1 ppm of oxygen and water.. Additional process are added during the synthesis to enhance the quality of the sample. If some particles are located near the zone where the crystal grows, each particle will act as a nucleation seed for the growth. Each seed will attracts ion competitively. Therefore, they prevent themselves from growing large crystal. In order to reduce the number of particle at the growth side, back transport process (temperature reversed compared to forward transport) was used before doing forward transport (Figure 2.16). During the. 31. Figure 2.16: 3 Steps for the CVT method. back transport process, temperature gradient was set 65 Celsius per 18 cm during 24 hour. After back transport, temperature gradient was set to zero during 12 hour for the nucleation process. Then, vapor transport was processed with 240 hour. After the sequence, the samples were grown in the cold zone part. After breaking the quartz tube, samples were sonicated twice for 1 minute with deionized water and Ethanol. This process is intended to remove the remained Chloride on the sample surface. After. 32. the process, samples were heated at 80 Celsius for 20 minute to remove the remaining water and Ethanol. Samples obtained after cleaning are shown in Figure 2.17. Silver plate sample has square shape and it size is about 1 mm × 1 mm. It is noteworthy that the sample surface turned red when exposed to air for about 1 day, which implies it is sensitive to the air. To avoid oxidation, sample is kept in the glove box.. Figure 2.17: Single crystal of FeSe. 2.4.3. Sample characterization. Figure 2.18: Laue diffraction pattern of FeSe.. 33. The quality of the sample was checked in various ways. First, as a result of measuring EDX (Energy dispersive X-ray spectroscopy), the ratio of Fe and Se was 1:1. Second, from the single crystal XRD (x-ray diffraction) measurement, lattice constant obtained as a = b = 3.773 Å c = 5.523 Å at room temperature with space group P4/nmm, 129. Obtained lattice constant value and space group well matches with previous studies. Then, crystallinity of the sample was measured by Laue diffraction (Figure 2.18). The diffraction pattern shows high quality of the crystals. From the diffraction pattern, the axis of the crystal can be deduce. Tetragonal a anb b axis are along vertical and horizontal direction while orthorhombic axis are 45 degree from tetragonal axis. It can be speculated by additional peak as marked red circle in the Figure 2.18.. Figure 2.19: Resistivity of FeSe.. The resistivity of the sample was measured by Quantum design physical property measurement system (PPMS) (Figure 2.19). Superconductivity has been shown to appear near 9 K with sharp resistivity drop. Structural transition appears near 90 K with hump of the resistivity. These observed values are consistent with previous transport result. We calculated the residual resistivity ration (RRR) of the sample, which can be used to. 34. estimate the quality of the sample. The RRR of the sample is about 34. The value is similar or higher than previous report.. 35. Chapter 3. Results I : Investigation of FeSe nematic phase In this chapter, we show the results of angle resolved photoemission and X-ray absorption spectroscopy studies on FeSe detwinned by a piezo. We fully resolved band dispersions with orbital characters near the Brillouin zone corner, and revealed an absence of any Fermi pocket at the Y point in the 1 Fe Brillouin zone scheme. In addition, the occupation imbalance between dxz and dyz orbitals was the opposite of that of iron pnictides, consistent with the identified band characters. We discuss why orbital selective hybridization happen and unique properties emerges in the nematic phase. Then, we mention mechanism of the nematic phase and relation to the superconductivity.. 36. 3.1 3.1.1. Background Introduction of FeSe nematic phase. Figure 3.1: Phase diagram of FeSe [47].. FeSe, the simplest structure among IBSs, has unique properties in the nematic phase compared to the iron pnictide. First, there is no magnetic order as shown in Figure 3.1 [47]. The magnetic susceptibility measurement results also support the it is paramagnetic even at low temperature [48]. Compared to other materials known to have structural and magnetic transition with the nematic phase (e.g. BaFe2 As2 ), FeSe has only structural transition with the nematic phase near 90 K. Note that it has been reported that there is spin fluctuation at the low temperature in pristine FeSe [19] and long range magnetism appears when hydrostatic pressure applied about more than 2 GPa. Second, in resistivity anisotropy which is one of the typical experimental evidence of the nematic phase, FeSe has opposite direction compared to other IBSs. For BaFe2 As2 case, the resistivity along a axis is larger than that of b axis [49]. However, in the case of FeSe, resistivity along a axis is 37. larger than b axis (Figure 3.2) [50]. Moreover, resistivity anisotropy tends to be disappear as the temperature lowers below 40 K. In the BaFe2 As2 case, resistivity anisotropy does not appear even at low temperature. This contrasting behavior of FeSe compared to other IBSs lead to the speculation that FeSe has a distinct nematic phase.. Figure 3.2: Resistivity anisotropy of FeSe and BaFe2 As2 [49, 50].. 3.1.2. Previous electronic structure studies of FeSe nematic phase. As mentioned in the previous section, the nematic phase of FeSe has different characteristic compared to other IBSs. Therefore, FeSe is expected to provide new information about mechanism of the nematic phase. For this reason, extensive and intensive studies have conducted to understand the electronic structure. However, there is still controversy about the electronic structure. First of all, there is controversy on the Fermi surface topology. A previous study argued that the Fermi surfaces at the BZ corner consist of elliptical and large circular pockets with dyz and dxy orbital characters, respectively [51]. Another study claimed that each BZ corner has two elliptical pockets that are elongated along the kx -directions and ky -directions with orbital characters of dxy and dyz (dxz ), respectively, but none was observed along the ky -direction [39]. Second, interpretation of the band structure differs which made more severe controversy. There is study report splitting of dxz and dyz hole band near M point that implies ferro orbital order exist [52]. Other study report that there is momentum dependent dxz and dyz hole band splitting (there is small 38. splitting near Γ point while large splitting exist near M point) which implies d wave bond order [28]. Meanwhile, other study report that there is no dxz and dyz splitting which result from unidirectional nematic bond order [39]. Also, there was other report that sign reversal of dxz and dyz order exist [51, 53].. Figure 3.3: previous ARPES studies of FeSe [39, 51].. Electronic structure was also obtained by STM studies as shown Figure 3.4. From analyzing the quasiparticle interference, It shows that there should be one elliptical pocket at X and Y point in the Fermi surface [54, 55]. However, they failed to observe the trace of Y point pocket due to reduced spectral weight of dxz orbital weight. In addition, STM experiment could not resolved a and b axis of orthorhombic phase due to its small difference (0.4 %). Thus, defining the X and Y point is not accurate. Therefore, it made more controversy on the exact electronic structure of the FeSe nematic phase.. Other experiments have been conducted to reveal the exact electronic structure of the. 39. Figure 3.4: previous STM studies of FeSe [54]. FeSe nematic phase [56,57]. However, despite these effort, it is still controversial and exact electronic structure has not been revealed. Considering previous results, we can deduce why there are still controversy. First, absence of high quality single crystal. If the crystal quality is not good, band dispersion is hardly resolved particularly dxy orbital at the M point. Second, absence of detwin experiment. Difficulty of the detwinning the sample caused absence of detwin experiment. This difficulty may comes from the thickness of the sample. The thickness of FeSe sample is less than 100 µm thus it is easily breakable even with very small amount of strain. Third, absence of the polarization dependent experiment. In order to reveal the exact electronic structure, polarization dependent ARPES with detwinned sample is required. However, there is no such a study done on FeSe and it causes controversy of the electronic structure. Therefore, we performed polarization dependent ARPES experiment on detwinned high quality FeSe crystal. The result will be presented below.. 40. 3.2. Experimental detail. ARPES measurements were carried out at Beamline 4.0.3 of the Advanced Light Source. Linearly polarized light with photon energy of 56 eV was used. Piezo bias control ARPES measurement were performed at homelab based system at SNU with 21.2 eV photon energy. All the samples for ARPES measurement were cleaved in situ a pressure better than 6 ×10−11 torr. X-ray absorption spectroscopy (XAS) experiments were performed at the Beamline 2A of the Pohang Light Source and spectra were recorded in total electron yield (TEY) mode. All spectra were normalized by the incident photon flux intensity, as measured using a gold mesh, and calibrated with respect to the L3 absorption peak of the Fe2 O3 alloy located in front of the analysis chamber. All crystals were cleaved in situ at a pressure better than 9 ×10−11 Torr for XAS. Samples were detwinned using uniaxial strain, which was applied along the tetragonal [110] direction.. 3.3 3.3.1. Electronic structure in the nematic phase Fermi surface topology. To resolved the controversy on the Fermi surface topology, we measured Fermi surface of twinned and detwinned sample. In the twinned sample (Figure 3.5 above), there are two elliptical pocket which makes cross shape near the MX/Y point. Meanwhile, in the detwinned sample (Figure 3.5 below), there is only one elliptical pocket near the M point. If an additional pocket exists as reported from previous studies [39], it should be shown in this data because the experimental geometry (i.e., light polarization and plane of the light incidence, which was chosen to be diagonal to the orthorhombic axis) allows observation of all expected orbitals (dxz ,dyz and dxy ). Based on this experimental observation, we conclude that there is only one elliptical pocket at each BZ corner in the nematic phase. It is noteworthy that tensile strain is applied along the Γ - Mx direction to detwin the sample, which is parallel to the orthorhombic a axis.. 41. Figure 3.5: Fermi surface of twinned and detwinned sample.. 42. We also double checked of the strain direction by turning on and off the piezo bias. In this experiment, 21.2 eV photon energy was used. Figure 3.6 left shows Fermi surfaces of FeSe at MX below the nematic phase transition temperature with the bias off (twinned sample). Similar to the 56 eV measurement, a cross shaped pocket is observed. With a bias of 150 V (Figure 3.6 right), a single elliptical pocket elongated along the strain direction (detwinned) is clearly seen. The significant difference in the measured Fermi surface data, with versus without bias, indicated successful strain tunability.. Figure 3.6: Fermi surface maps around the MX point with different bias voltages to the piezo. Fermi surface maps for twinned sample with 0 V bias voltage and detwinned sample with 150 V are shown, respectively. Our observation of the Fermi surface implies that one of the two pockets in the normal state should disappear across the nematic phase transition, i.e., the pocket at the Y point in the 1 Fe BZ scheme shown in Figure 3.7 should disappear, while the pocket at the X point remains. It is noteworthy that all of the ARPES data are shown in the 2 Fe BZ scheme, whereas the 1 Fe BZ scheme is used for orbital character analysis as discussed below. To distinguish between the two cases, the BZ corners in the 2 Fe BZ scheme are labeled MX and MY , and the corresponding zone edges in the 1 Fe BZ scheme are labeled X (Y). The detailed explanation of the 1 Fe and 2 Fe BZ scheme is in the following section.. 43. Figure 3.7: Schematic Fermi surface maps in the 2 Fe BZ (above) and 1 Fe BZ (below).. 3.3.2. Band dispersion. To understand how electronic structure changes in the nematic phase, band dispersions and orbital characters should be fully identified. In this section, band dispersion will be introduced. Figure 3.8 show the overall band dispersions along the Γ − MX (along kx ) and Γ − MY (along ky ) directions from a detwinned sample in the normal and nematic states, respectively. Starting from isotropic normal state band dispersions (Figure 3.8 (a)), anisotropic band dispersions develop in the nematic phase. Particularly, the band dispersions around the BZ corner are renormalized and become those of two merged Dirac cones (possibly with small gaps at band crossing points) (Figure 3.8 (b)). The Γ − MX high-symmetry cut shows a large electron band and two split hole bands. Meanwhile, in the cut along the Γ − MY , a tiny electron band near EF , and two nearby hole bands with a higher binding energy, are observed, consistent with previous reports [39].. 44. Figure 3.8: High symmetry cut along MX - Z - MY direction and corresponded schematic three dimensional (a) above and (b) below nematic phase transition.. 3.3.3. Orbital characterization. Polarization dependent ARPES was used to precisely characterize the orbital characters. There is an additional task to take into account glide mirror symmetry before determining the orbital character. All IBSs have 2 inequivalent Fe per unit cell, as indicated in red and blue in Figure 3. 9(a) [58]. The inequivalency comes from the location of the As, which always form a tetrahedra as shown in Figure 3. 9 (b). As potential originated at the 2 inequivalent Fe sites seems to be equal, but it has an opposite symmetry with respect to out of plane direction. In the 2 Fe BZ scheme corresponding to this structural unit cell, there are 10 Fe 3d bands to consider (Figure 3. 9 (c)). To simplify, 1 Fe BZ has been adopted as in Figure 3. 9 (d), where the number of bands would be 5. It is well 45. accepted that the other bands can be obtained to a good approximation by folding with respect to the 2 Fe BZ boundaries. However, this simple 1 Fe BZ scheme has problem in understanding experimental data. Although spectral weight of folded and main band are different, they have not been considered carefully in the photoemission community.. Figure 3.9: (a) Structure of one FeSe slab. (b) Tetrahedral As environment of 1 Fe. (c) Fermi surface expected in the 2 Fe BZ scheme. (d) Fermi surface in the 1 Fe BZ scheme [58].. From now on, Spectral weight of main and folded band will be discussed. Considering 1F e (r) can be defined from atomic orbital χ(r), 1 Fe BZ scheme, Bloch function ψk,χ. 1F e ψk,χ (r) =. X. eik·r χ(r − R). (3.1). R. where χ(r) is one of the Fe 3d orbitals and summation covers over all Fe site. At the Γ point, for example dxy orbital, all orbital are in phase and a spatial representation would be shown as Figure 3.9. At the X point, there should be additional dephasing term φ = k ·r due to the Bloch term considering k=(π/a, 0). Expanding 1 Fe BZ scheme to 2 Fe BZ scheme, we need to consider folded band with new defined zone boundary. Simply, it could be considered translating the band by q = (π/a, π/a). Folded band can be described as. 46. 1F e ψkf olded (r) = ψk+q (r) =. X. eiq·r eik·r χ(r − R). (3.2). R. For the A Fe site (red circle in Figure 3.8 (a)), eiq·r term would be 1. For the B Fe site (blue circle in Figure 3.8 (a)), eiq·r term would be -1. Therefore, it can be described as. ψkf olded (r) =. X. eik·RA χ(r − RA ) −. RA. X. eik·RB χ(r − RB ). (3.3). RB. It implies that B site Fe are dephased by π compared to A site Fe. It is shown in Figure 3.10.. Figure 3.10: Relative orientations of dxy orbital in real space for the following dxy orbital of the reciprocal space.. With this description, we could determine the parity of the orbitals of the band. It is noticeable that mirror plane should be on the As atoms due to the inequivalent position of As atom. Therefore, not as the simple picture in the method section, orbital parity would be more complicated. Such as even same orbital character can have different parity whether it is from main band or folded band. With orbital parity analysis mentioned above, we analyzed orbital character of the FeSe nematic phase. We used s-polarized light, which allows detection of odd-parity orbitals only (indicated by solid lines in Figure 3.11). For the analysis, a plain 1 Fe BZ scheme should be considered. As ARPES data are usually shown in a 2 Fe BZ scheme , unfolded (ψ) and. 47. folded (ψ ∗ ) bands of the 1 Fe BZ scheme must be distinguished. In the figure, unfolded and folded bands are represented by thick and thin lines, respectively.. Figure 3.11: (a) Schematic Fermi surfaces above and below nematic phase transition. Solid lines mark bands with odd parity while dashed lines are for bands even parity. Thick (thin) lines represent unfolded (folded) bands in the plain 1Fe BZ. (b) High symmetry cuts of the bands near the MX point for the two states. Cut directions are shown in (a). 48. Figure 3.12: (a) Schematic Fermi surfaces above and below nematic phase transition. (b) High symmetry cuts of the bands near the MY point for the two states. Cut directions are shown in (a).. 49. Figure 3.11(a) represents Fermi surfaces above and below nematic phase transition in the 2 Fe BZ scheme with light polarization along the b direction. To determine orbital characters of the bands near MX point, we analyze two different cuts: cut 1 along the kx direction and cut 2 along the ky -direction. The results are shown in Figure 3.11(b). In this experimental geometry, orbital symmetries allow detection of d∗xz , dyz , and dxy orbitals. For cut 1, in comparison to the normal state data, the hole band splits into two, which can be naturally identified as dyz and dxy in the nematic phase. As the dyz hole band shifts upward as the temperature decreases, the hole band closer to EF in the nematic phase should be dyz . Because dyz hole band top and dyz electron band bottom expected to be overlapped. Meanwhile, in cut 2 data, the small electron band should be dyz , according to a previous report, and the hole band should be d∗xz . Simply rotating the sample by 90 degree, data of MY point is obtained (light polarization along the a direction). The results are shown in Figure 3.12 (a) and (b). In this geometry, dxz , d∗yz , and dxy orbitals can be observed. A similar analysis as above was performed to reveal the orbital characters at MY point. In cut 1 data, the electron band near EF has dyz character, which is the same as the electron band in cut 2 of MX . The two hole bands are identified as dxz and dxy . In cut 2, the large electron band has a dxy character, as the dxz electron band is pushed above EF when system goes in to the nematic phase. The hole band near EF is dyz , which is the same hole band seen in cut 1 at MX . The other d∗xy hole band should not be visible in this geometry, but is seen as a result of hybridization with the dxz electron band. The reason for hybridization between dxy and dxz orbital will be discussed later. Based on the above analysis, the Fermi surface in the normal state and nematic phase in the plain 1 Fe BZ scheme can be described as shown in Figure 3.13. In the nematic phase, only the dyz (dxy ) orbital Fermi surface is seen at the X (Y) point. Fermi surfaces with consideration of the glide-mirror symmetry, which is a widely accepted form in the 1 Fe BZ scheme, are shown in Figure 3.13 below. In this case, dxy orbital Fermi surfaces at the Y point in the plain 1 Fe BZ scheme are translated to the X point ((π/a, π/a) translation), and thus do not contribute to the Y pocket in the nematic phase [59].. 50. Figure 3.13: Schematic Fermi surfaces are shown in the plain 1 Fe BZ scheme (above) and 1-Fe BZ scheme with glide mirror symmetry considered (below). To determine the orbital characters of the bands near the BZ center, an analysis similar to that for the BZ corner, as described above, was performed. Figure 3. 14 above shows Fermi surfaces above and below nematic phase transition in the 2 Fe BZ scheme. Two cuts along the kx - and ky -directions were used for orbital characterization. The results are shown below of the figure. In this experimental geometry, orbital symmetries allow detection of dxz , d∗yz , and d∗xy orbitals. For cuts 1 and 2, compare with normal state data, the hole band with strong intensity is determined as dxz in the nematic phase. On the other hand, dyz and dxy hole bands should not be visible in this geometry. However, it can be observed as a result of hybridization with the dxz band. The reason for the hybridization here may be from spin orbit coupling. The results of orbital characterization are consistent. 51. with previous reports [51, 60].. Figure 3.14: Schematic Fermi surfaces above and below nematic phase transition temperature at the BZ center (above). High symmetry cuts of the bands near the Γ point for the two states (below).. The orbital characters of the bands in the 2 Fe BZ are summarized in Figure 3.15. Two peculiar features of the FeSe electronic structure in the nematic phase can be observed. First, there is a reversal behavior in the relative energy level of the dxz and dyz hole bands. In Fig 3.15 below, the dxz hole band (red, at MY ) is located below the dyz hole band (green, at MX ) at BZ corners, while the dxz hole band is located above the dyz band at the BZ. 52. center. Another, more important feature is the reduced number of electron bands at MX and MY . In the normal state, there are two electron bands at both MX and MY points–the common dxy electron band and the dxz (dyz ) electron band at MX (MY ) point. In the nematic phase, only one electron band crosses EF at each BZ zone corner point. Two other electron bands, dxz and dxy at MX and MY , respectively, were not observed. Therefore, it is reasonable to speculate that these two bands are pushed above EF across the nematic phase transition.. Figure 3.15: Schematic Fermi surfaces and band dispersion above and below nematic phase transition.. 53. 3.3.4. Temperature evolution of electronic structure. Figure 3.16: Temperature dependent ARPES data along the kx -direction near the MY point. MDCs at 5 meV above EF are overlaid on the figure. The contributions of dxy and dxz are shown as blue and red curves, respectively. Peak positions of the dxz band are indicated by red arrows.. The temperature evolution of the electronic structure across the nematic phase transition indeed confirms the speculation in the previous section. Figure 3.16 shows the temperature dependence of band dispersion along the kx -direction at MY point. Above of the each figure is momentum distribution curves (MDCs) acquired 5 meV above EF . In the normal state, the dxz electron band crosses EF and peaks in the MDC have finite momentum (indicated by red arrows). As the temperature decreases, peaks for the dxz electron band shift toward MY and disappear at low temperatures, consistent with the view that the dxz electron band shifts upward and is finally pushed above EF . In fact, a recent ARPES study on FeSe indicated the occurrence of dxz electron band shift. By alkali metal dosing, surface electron doping effect is expected, dxz electron which was located above EF pushed down to EF was observed [61].. The evolution of the hole band is also observed. The dxz (dyz ) hole band at MX (MY ) point shifts downward (upward) as the temperature decreases, as seen in the temperature-. 54. Figure 3.17: Schematic illustration of the experimental geometry (left most). Temperature dependent energy distribution curves (EDCs) at MX (along ky -direction, cut 1) and MY points (along kx -direction, cut 2), showing downward and upward shifts of the dx z and dy z band upon cooling, respectively (middle). The peak position of the dxz (red square) and dyz (green square) band as a function of temperature. dependent data shown in Figure 3.17. Cut direction is described in the left most figure. The splitting at low temperature occurs at about 60 meV and persists above the nematic phase transition temperature. Splitting above the nematic phase transition may due to the effect of strain as similar behavior is observed in the resistivity anisotropy measurement [49,50]. It is noteworthy that the two hole bands do not cross EF , and remain below EF after the shift from the effect of nematic phase transition. From now on, how the electron pocket at Y in 1 Fe BZ shifts upward and disappears, i.e., how the number of electron bands is reduced across the nematic phase transition will be described. We discussed that the observed evolution in the electronic structure can be explained by the orbital dependent band shift (or splitting) and hybridization. For the simple understanding, an 1 Fe BZ scheme with fewer bands is provided in Figure 3.18. The left and right halves of each panel indicates the band dispersions along the kx -directions and ky -directions, respectively. Starting from symmetric bands in the normal state (above panels), the dyz and dxz bands shift upward and downward at BZ corner, respectively, as the temperature decreases below nematic phase transition temperature (middle panels); we call this phenomenon nematic band shift. Then, orbital-selective hybridization occurs. For the dyz band, there is only weak mixing with dxy and thus the dispersion remains unchanged. On the other hand, the dxz band hybridizes strongly with the dxy band, thereby pushing the hole band down below EF while also raising the dxz and dxy electron bands above EF (below panels). This results in the absence of the electron pocket at Y in the 1 55. Fe BZ scheme.. Figure 3.18: Schematic illustration of the band reconstruction at the BZ corner across the nematic phase transition in 1-Fe BZ scheme.. 56. 3.3.5. Orbital occupation measurement. A new perspective on the interpretation of the previous section is that the dxz orbital should be less occupied than dyz , which is the opposite of the case with iron pnictide and is also contrast with the prediction of the ferro-orbital order scenario. The energy position of the dxz band is higher than that of dyz near the Γ point, so the dxz state is less occupied than dyz . The disappearance of the dxz electron band at the BZ corner also leads to less occupied dxz orbitals. It is noteworthy that the dxz and dyz hole bands at the BZ corner are does not contributes, as both are fully occupied. To directly obtain information on such anomalous orbital occupancy, we performed XLD measurements on detwinned samples. XLD, as local probe for orbital-selective density of states, can directly confirm any imbalance in the orbital occupancy [62].. Figure 3.19: Schematic illustration of the experimental geometry (left). Fe L-edge absorption spectra from detwinned FeSe acquired at 10 K with two different polarization (right). The XLD (black curve) represents the difference.. 57. Figure 3.19 above shows the experimental geometry. Two light polarizations, parallel and perpendicular to the direction of tensile strain, was incident to the sample. The Fe L-edge absorption spectra from detwinned FeSe, acquired with the two light polarizations at 10 K, are plotted in Figure 3.19 below. To normalize the data, intensity of gold mesh was measured. Shift of the beam energy was monitored by measuring Fe2 O3 alloy. Both gold mesh and Fe2 O3 alloy