Effects on lattice fluctuations on the charge-density-wave transition in transition-metal dichalcogenides

Thermodynamic anomaly above the superconducting critical temperature in the quasi-one-dimensional superconductorTa4Pd3Te16

“…The arrival of a commensurate CDW upon cooling a lowdimensional system would normally be preceded by two events: in decreasing temperature we would first expect the onset of a fluctuating, short-range-correlated CDW regime [20][21][22][23], then second the development of an incommensurate CDW state, eventually locking into the commensurate state at a lower temperature [24][25][26]. The thermodynamic transition we see at 20 K is unlikely to be the development of true charge order along the b direction, as this would be accompanied by a significant boost in the along-chain resistivity and a more pronounced specific heat discontinuity.…”

Charge order inNbSe2

“…In some cases, such as that of spin density waves in two- dimensional metals, the presence of Landau damping can suppress a factor of g 2 in this term and put it on equal footing with the other two 42 . In the present case of CDW order, however, it is simply a sixth-order term in the electron-phonon coupling, and may be neglected 39,41 . In the bottom-left diagram of Fig.…”

“…20. Taking into account only these additional terms in the free energy expansion is known as the mode-mode coupling approximation (MMA) [39][40][41] . The bottom-right diagram in Fig.…”

Charge order from orbital-dependent coupling evidenced by NbSe2

“…To understand the properties of NbSe 2 above its CDW transition temperature, it is therefore necessary to consider the influence of phonon fluctuations beyond RPA. The so-called mode-mode coupling approximation (MMA) includes the lowest order terms of this type and has been shown to successfully describe the influence of phonon fluctuations in some of the electronic properties of related dichalcogenide materials like TaSe 2 and TiSe 2 21,22,34 . The additional terms included in the MMA fall into two categories: a vertex correction, which we neglect by appeal to Migdal's theorem because of the large momentum transfer associated with Q CDW , and self-energy corrections to the internal electron lines (indicated diagrammatically in Fig.…”

“…In the temperature range T MMA oToT RPA , the phonon fluctuations are strong enough to destroy the long-range order predicted by (mean field) RPA theory. In that regime, the amplitude of the static order parameter vanishes, hĵ Q i ¼ 0, but dynamic fluctuations of the order parameter persist, hĵ Q 2 i40 [20][21][22] . The result is a locally fluctuating short-range ordered state, characterized by the presence of a non-zero order parameter amplitude, without any long-range phase coherence 23 .…”