1.3 Charge Density Wave
1.3.1 Charge density wave Materials and Experiments
The CDW transitions are readily observed in the materials which have chain or layered structures and transition is a second order one. This brings out the fact that low dimensional materials allow possibility of nesting of Fermi surface, as predicted theoret- ically. There are large number of organic and inorganic materials having linear chains, show a transition to a CDW phase has been discovered extensively. Such materials include (TMTSF)2PF6(Bechgaard salt), NbSe3, K0.3MoO3, (TaSe4)2I and KCP (Krogmann’s salt) or K2Pt(CN)4Br0.3.3.2H2O etc., which have a chain structure [44, 45].
For example, transition Metalchalcogenides (MX3, MX2 and (MX4)nY) form a vari- ety of linear chain compounds that host CDW transition, where M=Nb or Ta (group IV or V transition metals), X=S or Se chalcogen atoms and Y=I, Br or Cl halogen atoms.
The first inorganic linear-chain material in which CDW transition was found is NbSe3, the crystal structure of which is shown in Figure 1.5. The crystal symmetry of NbSe3 was
Figure 1.5: The schematic chain structure of the NbSe3 compounds. (a) The stacking of the prisms along the b-axis in the NbSe, structure (b) A projection of the NbSe3 structure perpendicular to the b-axis [courtesy [46]].
monoclinic and that the structure consists of infinite chains of Se trigonal prisms stacked on top of each other by sharing the triangular faces, as shown in Figure 1.5(a). The Nb atoms are located approximately at the centre of the prisms. The chains were found to be parallel to the b-axis. Figure 1.5(b) shows a projection of the structure perpendicular to the b-axis. The chain of Se trigonal prisms are linked together with Nb-Se bonds in the c direction so as to form infinite slabs parallel to bc plane, resulting in NbSe3 as a true bidimensional material. These slabs are two trigonal prisms thick and they are linked together by weak Se-Se bonds. Inside the slab, there exist two types of units, which can be grouped as a set of four chain and a set of two chain. Each chain is displaced and rotated with respect to the adjacent one by 2b and approximately 1800 respectively. The two transitions taking place in NbSe3 along b-axis are related to the four chain and two chain units, would strongly support the 1D character of NbSe3 [46].
Compared to the one dimensional materials, CDW states are also observed in quasi 2D materials: RTen and R2Ten, where R is a rare earth element [47]. These layered com- pounds can be described in terms of nominally tetragonal structure based on alternating layers of square-planar Te sheets and a corrugated RTe slab, as shown in Figure 1.6. This square Te planar layers possibly tune the properties of the CDW states. The material
Figure 1.6: The crystal structure of RTen. The axes are shown for convenience [courtesy [47]].
indicates a strongly anisotropic two dimensional Fermi surface.
But recently the 2-3-5 (R2T3X5) as well as the 5-4-10 (R5T4X10) series compounds, which are considered to have a 3D structure, have provided evidence of CDW ordering, accompanied by a first order transition. The compound Lu5Ir4Si10 where the SC and CDW coexist with that of the conventional low dimensional CDW systems like NbSe2 and NbSe3. Lu5Ir4Si10 adopts the tetragonal Sc5Co4Si10- type structure, as shown in Figure 1.7. Here, Ir and Si atoms form planar rings, which are stacked parallel to the basal planes, are connected along c-axis via Ir-Si-Ir zigzag chains. The Lu atoms form a quasi one- dimensional zigzag chain alongc-axis which are well separated from Ir-Si ring.
The distance between adjacent Lu-Lu and Ir-Ir atoms are large, whereas Ir-Si and Si-Si distances are small, indicating strong covalent interactions. The chain like structure of Lu atoms along thec-axis may not only form a quasi-one-dimensional electronic band but also achieve a CDW ground state [48].
These materials undergo a metal-to-insulator (or metal-to-semimetal) transition at temperatures below the room temperature, as evidenced by a wide range of transport, magnetic, and specific-heat studies. Furthermore, detail structural measurements, like x- ray and neutron diffraction studies, together with measurements of local properties (like
Figure 1.7: The crystal structure of Lu5Ir4Si10 [courtesy [48]].
nuclear magnetic resonance for example) lead to the examination of the structural changes which accompany the phase transitions.
As an example, Figure 1.8 displays evidence of a CDW transition in NbSe3 as ob- served in different measurements. The temperature dependence of dc resistivity along the b-axis of NbSe3 is shown in Figure 1.8(a). It shows a sharp increase in the resistivity at temperatures, TCDW1 = 149 K and TCDW2 = 59 K, where a metal to a semimetal tran- sition can be observed, unlike a metal to a insulator transition as predicted by Peierls.
This indicates partial destruction of the Fermi surface at these temperatures, which is confirmed by the Hall effect and the Magnetoresistance studies. Figure 1.8(b) shows the susceptibility across the CDW transition which decreases below TCDW and this is related to the opening up of a gap (or FS) across the CDW transition. Figure 1.8(c) depicts the heat capacity of the compound as a function of temperature. The well defined anomalies at TCDW1 = 149 K and TCDW2 = 59 K identify the CDW transition. The peaks which are observed at the transition temperatures are significantly large and the data reveal their broadness, instead of a sharp jump at TCDW, hence indicating a second-order na- ture of the transition. Further, the electron and x-ray diffraction studies provide direct
evidence for such distortions by demonstrating that both CDW states are associated with the development of incommensurate lattice distortions along the chain direction.
Figure 1.8: Signatures of a CDW transition is demonstrated (a) The temperature de- pendence of the dc resistivity of NbSe3 [46]. Note the increase ofρdc atTCDW1 = 149 K and TCDW2 = 59 K. (b) The magnetic susceptibility of NbSe3 shows a decrease below 150 K which are associated with the upper CDW transition [49]. (c) The specific heat of NbSe3 as a function of temperature: top scale for TCDW1 ; bottom scale for TCDW2 [courtesy [50]].