1.3 Charge Density Wave
1.3.2 Coexistence of Superconductivity and the Charge Density Wave
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]].
1.3.2 Coexistence of Superconductivity and the Charge Density
coupling. A number of CDW-bearing materials are also superconducting, and the idea that superconductivity and CDW states are competing electronic states at low tempera- tures is one of the fundamental concepts of condensed matter physics [51, 52, 53, 54].
There is an extensive experimental evidence for the coexistence of SC and CDW order. The ever increasing group of CDW superconductors includes the layered transition metal dichalcogenides (2H-TaSe2, 2H-TaS2, 2H-NbSe2 and 2H-NbS2) and NbSe3. The high-TC cuprate superconductors and also the recently discovered iron-based class of su- perconductors exhibit CDW and SC together. It is a well known fact that CDW leads to a reconstruction of the band structure where the FS is nested [55]. Depending on the underlying band structure, the formation CDW can change the number of bands crossing the Fermi level. Therefore, even in one-band systems the formation of CDW order can result in two bands crossing the Fermi level. Thus, as mentioned earlier, one will have to deal with multi-band superconductivity. In this case, a CDW can coexist with SC. In those material where coexistence of CDW and SC transition found, it is observed that the CDW transition occur at a much higher temperature than that of the superconduct- ing transition. It is also important to mention that the dielectric gap due to the CDW phase transition is much larger than the superconducting gap. Therefore, the question of interest is whether the gapping of the FS due to the CDW phase transition is favorable or destructive to the superconductivity which occurs at low temperatures.
Recently, it has been shown that certain materials known for exhibiting CDW or- dering can also show SC simply by tuning the concentration of specific dopants or by application of external pressure. These tuning parameters modify the Fermi surface or the electron-phonon coupling, and thus tip the balance in favour of one or the other state as the choice of ground state, indicative of the competition between them. There are a variety of compounds which have established well the competition between SC and CDW.
NbSe2, TaS2, (TaSe2)2I and NbSe2 (pressure) [52, 56], TaS2 (doping) [57] and Lu5Ir4Si10 (pressure+doping) [18] are the best known examples for the competition that are being talked about in the present context. To certain extent there is some consensus on the sta- bility of superconducting transition in the presence of density wave order. A strong case for the above scenario was observed in 2H-NbSe2, exhibiting the coexistence of CDW and SC, which undergoes a CDW transition (TCDW) at 33 K and a superconducting transition (TSC) at 7.2 K. Figure 1.9 shows variation ofTCDW andTSC in 2H-NbSe2 as a function of pressure. The resistivity measurement in presence of a hydrostatic pressure upto 35 kbar showed that the CDW transition decreases linearly and above a pressure of 36 kbar the CDW transition completely disappears. Besides, it has clearly been observed that the
Figure 1.9: Pressure dependence of the CDW ordering, TCDW and SC transition tem- perature,TSC in 2H-NbSe2 [courtesy [58]].
superconducting transition increases rapidly with pressure TSC(P) (5×10−5 K/bar) upto about 35 kbar, above which it remains nearly constant for high pressure upto 140 kbar, and thus this results gave the first clear evidence that the enhancement of superconduc- tivity in 2H-NbSe2 (and presumably in other MX2 compounds) was due to the progressive removal of the CDW by the application of pressure.
However, there is also an opposite viewpoint [59, 60]. The superconducting tran- sition temperature is theoretically shown to rise as a result of presence of the Peierls instability within a simple incomplete-nesting model in two dimensions. The implication of this is discussed for the high-TC superconductors La2−xMxCuO4. Such a situation has not been experimentally verified yet. The recently discovered iron based (pnictides) su- perconductors, (representatives of the quasi 2D systems), have renewed the interest to do a study exploring the competition between CDW/SDW and SC [10, 21, 61]. The interesting fact that the pnictide parent compound (for example, RFeAsO, AFe2As2) un- dergoes SDW transition at high temperatures along with a structural transition and the superconductivity in iron pnictides appears only after substituting the parent compounds with charge carriers [22, 62]. This type of competition of both kind of order ranging from concurrence to mutual cooperation has opened a new route for the materials that exhibit interplay of DW and SC behavior in addition to high TC cuprates, so far considered as one of the greatest puzzles of contemporary solid state physics.
Thus the question about the interplay and competition between superconductiv- ity and charge-density ordering remains of immense interest to both theoreticians and experimentalists alike.