In this chapter, we briefly review the “one gap” and “two gap” theoretical models of the ground state excitations of cuprates and the experimental progress to date aimed at discerning between the two scenarios. Subsequently, we detail our experimental methods to perform spatially resolved STS on Y-123 as a function of temperature and magnetic field. We then present our experimental data and discuss the results in the context of the two models. The totality of results in Y123 suggest that a ground state of superconductivity alone is unable to account for all the unconventional behavior observed.
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contains superconductivity alone and that the onset of Cooper pair formation occurs at the pseudo- gap temperature, T∗, which is greater than TC [26, 133, 134, 135, 98, 8]. For T*>T>TC, these preformed pairs exhibit no global phase coherence; therefore, macroscopic superconductivity is not observed in bulk measurements. Further, the “one-gap” scenario asserts that for T<TC preformed pairs condense and then cuprates exhibit macroscopic superconductivity and global phase coherence.
Consequently, this scenario asserts that the pseudogap and the T≤TC superconducting gap share a common origin.
In contrast, a second general viewpoint supposes that the ground state of cuprates consists of coexisting superconductivity and competing orders. We discussed this scenario, which we refer to as the “two-gap” scenario, more fully in the previous chapter detailing measurements on La-112. In addition to the findings in electron-type cuprates, experimental observations in hole-type cuprates appear to favor a “two-gap” model [6, 85, 60, 4]. The “two-gap” scenario asserts that the pseudo- gap is due to competing orders other than superconductivity and that the source of unconventional temperature and magnetic-field dependent quasiparticle excitations arise from interplay of super- conductivity and competing orders [136, 31, 137, 86]. In the “two-gap” scenario, T∗ indicates the transition temperature of a competing order, and TC is the superconducting transition temperature.
The pseudogap excitation spectra may be investigated by varying temperature above TC and characterizing the quasiparticle spectra in hole-type cuprates; however, pseudogap-like spectra may also be investigated by applying a magnetic field and examining the quasiparticle spectra inside vortex cores using the same technique we used in studying the electron-type La-112 in the last chapter. Similar to the experimental situation we observed in La-112, pseudogap-like quasiparticle excitation spectra also appear inside vortices in hole-type cuprates; however, two energy scales other than the superconducting gap emerge in the vortex cores of the hole-type cuprates. Specifically, an energy gap similar to the pseudogap energy and a subgap energy smaller than the superconducting gap have been observed in the vortex cores of Y-123 [69, 138] and Bi-2212 [20] previously. Doping dependent studies show that the subgap energy decreases as doping increases and demonstrates a linear relationship with the average peak-to-peak gap, ∆pk−pk, seen in zero-field for T TC in
of any inferred relation between VP G and ∆0 and the peak-to-peak gap in Bi-2212. Namely, the quasiparticle spectra and values of ∆pk−pkin Bi-2212 are known to exhibit significant inhomogeneity over lengths scales of approximately 5nm [68]. Therefore, any inferences [115, 33] drawn by the linear relationship between the peak-to-peak gap and the VP Genergy require careful consideration of the origin of the peak-to-peak gap in zero-magnetic field, especially in underdoped Bi-2212. As we pointed out in Chapters 1 and 2, the average ∆pk−pk values of underdoped Bi-2212 do not follow the same doping behavior as the bulk superconducting TC values [33, 68]. Furthermore, careful inspection of the vortex state spectra of hole-type cuprates reveals pseudogap-like behavior at energies that differ up to∼30meV from the values of ∆pk−pkobserved in zero-magnetic field [115, 69].
Due to the fact that the pseudogap and superconducting gap are similar in energy and that there is experimental evidence of two gaps coexisting in hole-type cuprates, detailed measurements of the zero-field and vortex-state gap energies in cuprates other than Bi-2212 are required to draw further conclusions. We perform such detailed spatial measurements on Y-123 in the work presented here.
Adding to the complexity of the vortex core spectra and zero-field spectra in hole-type cuprates, measurements in Bi-2212 at H=5T revealed an energy independent checkerboard-like conductance modulation with 4a0×4a0lattice constant periodicity inside vortex cores [21] in addition to energy- dependent quasiparticle scattering interferences [68]. Herea0=0.385nm is the planar lattice constant of Bi-2212. The energy-independent 4a0 ×4a0 conductance modulations could not be accounted for by modeling quasiparticle scattering interference in Bi-2212 [78, 79]. Various competing order models purport to explain the modulations by invoking pair-density waves (PDW) [83, 84], pinned spin-density waves (SDW) [29, 86], and charge-density waves (CDW) [31, 87], and it is supposed
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Figure 5.1: Energy symmetry of the amplitude of FT-LDOS to discern a pair-density wave (PDW) and a charge-density wave (CDW). (a) Theoretical energy dependence of the amplitude of FT- LDOS for CDW and PDW using realistic bandstructures for the cuprates. Figure adapted from Ref. [84]. (b) The results of decomposing the theoretical model for CDW and PDW in (a) into symmetric and anti-symmetric components. Left panel: Symmetric components from (a). Right panel: Anti-symmetric components from (a).
that the spatial ordering of these competing orders is more readily revealed in vortices where super- conductivity is suppressed.
Fundamentally, PDWs differ from CDWs and SDWs because PDWs are particle-particle excita- tions with a finite momentum, whereas SDWs and CDWs are particle-hole excitations. Empirically, it is expected that the spatial conductance contrast of a PDW will remain the same when switching from positive to negative energy, while the spatial conductance contrast for CDW or SDW excita- tions is expected to reverse. Furthermore, a theoretical model to differentiate PDW from CDW and SDW excitations along these same lines exists [84]. The theory predicts the amplitude of diffraction modes observed in Fourier transformed local density of states (FT-LDOS) measurements will be symmetric in energy for PDW and antisymmetric in energy for CDW and SDW [84]. However, the insertion of realistic bandstructures for cuprates into the theory leads to mixing of symmetric and anti-symmetric energy dependence in the FT-LDOS for PDW, CDW, and SDW. The authors in Ref. [84] conclude, in this case, that a PDW is expected to show stronger symmetric components than anti-symmetric components, whereas a CDW or SDW will show show stronger anti-symmetric or equal symmetric/anti-symmetric components. We illustrate the theoretical scenario for realistic bandstructures in Fig. 5.1 for further clarity.
Following the observation of conductance modulations near vortices in Bi-2212, subsequent spa- tially resolved STS experiments performed in zero-magnetic field in Bi-2212 also revealed a 4a0 ×
data revealing checkerboard-modulations in Bi-2212 at H=5T [21] shows a set of seemingly energy- independent diffraction modes along the nodal direction; however, all spots along the nodal direction in the paper are attributed to supermodulations. In the context of our results in Y-123 to be pre- sented, we point out that Y-123 does not exhibit periodicity due to supermodulation because of the absence of the BiO layers, but a set of nodal energy-independent diffraction modes is eminently observed. Therefore, it is possible that at least one other conductance modulation periodicity has been observed in Bi-2212 but overlooked. To date, experiments investigating the FT-LDOS and magnetic field dependence of the quasiparticle spectra in Y-123 have not been explored, except for the work we present here.
In this chapter, we explore the FT-LDOS of Y-123 using spatially resolved STS as a function of magnetic field. Additionally, we characterize the evolution of the ∆SC, ∆ef f, VP G, and ∆0 energy scales as a function of magnetic field using spatially resolved STS and explore the implications of all our results in Y-123.