Charge order from orbital-dependent coupling evidenced by NbSe2

Abstract

Niobium diselenide has long served as a prototype of two-dimensional charge ordering, believed to arise from an instability of the electronic structure analogous to the one-dimensional Peierls mechanism. Despite this, various anomalous properties have recently been identified experimentally, which cannot be explained by Peierls-like weakcoupling theories. Here, we consider instead a model with strong electron-phonon coupling, taking into account both the full momentum and orbital dependence of the coupling matrix elements. We show that both are necessary for a consistent description of the full range of experimental observations. We argue that NbSe 2 is typical in this sense, and that any chargeordered material in more than one dimension will generically be shaped by the momentum and orbital dependence of its electron-phonon coupling as well as its electronic structure. The consequences will be observable in many charge-ordered materials, including cuprate superconductors.

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.…”

“…The low effective dimensionality of TPT suggests its CDW transition will be preceded by significant fluctuations over a range of temperatures [22,23]. The absence of evidence of CDW order in bulk probes of TPT -resistivity, heat capacity, thermal conductivity [6,7,29], and arguably Raman spectroscopy [30] -as well as our quantum oscillation measurements showing no Fermi surface reconstruction between 300 K and 1.5 K, suggest that the CDW seen by STM at 4 K could be stabilized by the surface, corresponding in the bulk to the fluctuating regime rather than true CDW order.…”

“…The transition we see at 20 K could be the turning-on of these fluctuations. A sharp turn-on of CDW fluctuations has previously been proposed to account for a resistivity bump in the q2D transition metal oxide bronze P 4 W 10 O 38 [31,32] and has been predicted in the q2D transition metal dichalcogenide NbSe 2 [23,33]. Despite the fluctuating CDW order being along the b-direction chains it would not necessarily give a strong resistivity boost in this direction.…”

Charge order inNbSe2

“…In addition to the nature of the pseudogap phase, puzzling aspects of the NbSe 2 phenomenology include the question of why only one band develops a CDW gap; uncertainty over the size of the CDW gap, with estimates ranging from 0 meV 25 to 35 meV 29 ; and an observed asymmetry in the particle and hole states near the CDW gap 14 , leading to an offset of the gap with respect to E F 30 . The present authors recently outlined a model based on a strongly momentum-and orbital-dependent electron-phonon coupling to explain all of these unusual features of the NbSe 2 CDW state, as well as providing a quantitative explanation of how the wave vectors of the 3Q and 1Q CDW instabilities are selected 15,16 . The present paper extends the results of this previous work as well as providing details of the calculations involved.…”

“…In the absence of nesting, understanding the influence of electron-phonon coupling is paramount to understanding both the origin of charge order, and the competition between different geometries of CDW states. In two recent papers, the present authors outlined a model describing the charge-ordered phases of niobium diselenide 15,16 . The present paper extends these results and provides the calculational details of the model, showing how both the momentum and orbital dependence of the electron-phonon coupling co-operate to drive the onset of charge order in NbSe 2 , and how their interplay with the electronic structure directs the competition between single-Q and multi-Q CDWs.…”