Itinerant density wave instabilities at classical and quantum critical points

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

“…Commensurate CDW (CCDW) systems are generically expected to develop via the evolution of the wave vector of an incommensurate CDW (ICDW) taking advantage of lattice lock-in energy at lower temperatures [24,39]. The evolution is continuous over a range of temperatures before jumping discontinuously at the transition, as seen for example in (q2D) 2H-TaSe 2 (T ICDW = 122.3 K, T CCDW = 92 K) and (q1D) TTF-TCNQ (T ICDW = 54 K, T CCDW = 38 K) [25,32,36,40]. This proposal naturally accounts for the discrepancy be-tween the quantum oscillation data with DFT, as well as the lack of Fermi surface reconstruction at 20 K, since the band structure is already reconstructed at higher temperatures by the ICDW.…”

“…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

“…Figure 6 shows the resulting renormalized phonon frequency, when setting the overall magnitude g of the electronphonon coupling such that a CDW instability develops at the experimentally-observed transition temperature of 33.5 K. The plot across the Brillouin zone shows that the phonon mode first softens to zero along ΓM. The momentum-space cut in this direction, whose evolution with temperature is displayed in figure 7, reveals that the instability in fact occurs precisely at the known ordering vector of the 3Q CDW state, as seen for example in neutron scattering 17,19 , or X-ray diffraction experiments 20,23,24 . The presence of a broad plateau of partially-softened phonon frequencies surrounding the CDW wave vector, similar to that seen experimentally 23,24 , is a direct result of the strong electron-phonon coupling in NbSe 2 , or, equivalently, of the absence of a truly nested electronic structure.…”

“…The large anisotropy, signaled by a small ratio of interlayer to intralayer coupling, suggests that quasi-two dimensional models can be expected to capture the important physics 3,18 . NbSe 2 undergoes a phase transition to a 3Q incommensurate CDW state at 33.5 K. From neutron diffraction and high-resolution X-ray scattering the CDW wave vectors are known to sit along the ΓM directions at Q CDW = (1 − δ) 2 3 ΓM, with δ ≈ 0.014 17,19,20 . The 1Q CDW phases found in locally-strained regions by recent scanning tunneling microscopy (STM) experiments have a slightly modified wave number of Q CDW = (1 − δ) mechanisms underlying the CDW formation, including nested saddle-points in the electronic dispersion 21 , local field effects 22 , or a combination of weak nesting with strongly momentum-dependent electron-phonon coupling 18,23 .…”

Charge ordering geometries in uniaxially strainedNbSe2

“…We find that the 1Q phase transitions are second-order, whereas the 3Q transitions are weakly-first-order. With increasing temperature we predict a shortening CDW wavevector in the locally-fluctuating, short-range-ordered, pseudogap regime above the CDW transition, analogous to the recently-observed non-monotonic evolution of the CDW wavevector within the ordered state [14].Model -niobium diselenide consists of hexagonal layers of niobium atoms sandwiched between layers of selenium atoms, displaced so that they lie above and below half of the Nb interstitial locations. The crystal structure and bandstructure are depicted in Fig.…”