Alternative route to charge density wave formation in multiband systems

Abstract

Charge and spin density waves, periodic modulations of the electron, and magnetization densities, respectively, are among the most abundant and nontrivial low-temperature ordered phases in condensed matter. The ordering direction is widely believed to result from the Fermi surface topology. However, several recent studies indicate that this common view needs to be supplemented. Here, we show how an enhanced electron-lattice interaction can contribute to or even determine the selection of the ordering vector in the model charge density wave system ErTe 3 . Our joint experimental and theoretical study allows us to establish a relation between the selection rules of the electronic light scattering spectra and the enhanced electron-phonon coupling in the vicinity of band degeneracy points. This alternative proposal for charge density wave formation may be of general relevance for driving phase transitions into other brokensymmetry ground states, particularly in multiband systems, such as the iron-based superconductors.electron-phonon interactions | nonconventional mechanism | Raman spectroscopy | solid-solid phase transitions T he common view of charge density wave (CDW) formation was originally posed in the work by Kohn (1). Using Kohn's reasoning (1), the tendency to ordering is particularly strong in low dimensions, because the Fermi surface has parallel parts, referred to as nesting. This nesting leads to a divergence in the Lindhard susceptibility, determining the magnitude and direction of the ordering vector Q (2). This divergence in the electronic susceptibility is conveyed to the lattice by the electron-phonon coupling: a phonon softens to zero frequency at Q, and a static lattice distortion develops when the system enters the CDW state, a behavior known as the Kohn anomaly.However, several publications raise the question as to whether nesting alone is sufficient to explain the observed ordering direction Q (3-7), particularly in dimensions higher than 1D. A central question is whether the selection of the CDW ordering vector is always driven by an electronic instability or if the ordering vector could, instead, be determined by a lattice distortion driven by some other mechanism exploiting the role of the electron-phonon coupling. In the latter case, the selected ordering vector would not necessarily nest the Fermi surface. The importance of strongly momentum-dependent electron-phonon coupling on CDW formation was pointed out in refs. 3 and 4, where the relevance of the Fermi surface for determining the ordering vector was indeed found to decrease as the coupling strength increases. In a recent paper on inelastic X-ray scattering measurements on 2H-NbSe 2 , acoustic phonons were observed to soften to zero frequency over an extended region around the CDW ordering vector (8). The authors argue that this behavior is not consistent with a Kohn anomaly picture, where sharp dips are expected (8). Therefore, the phonon softening must be driven by another mechanism, which they identify as a wave vector-dependent e...

Charge density waves and phonon-electron coupling inZrTe3

“…In this line of thinking, it is only natural to recognize the essential role of phonon-electron coupling in the formation of CDW order, as suggested by several authors [30,32]. This idea has been explicitly tested in quasi-2D materials both theoretically [29,[33][34][35][36] and experimentally [36][37][38], and has proved quite successful in explaining the q cdw that deviates from q n . In quasi-1D materials, the importance of phonon-electron coupling relative to that of FSN has remained largely untested, as the good agreement between q n and q cdw in 1D cases might appear to render such tests unnecessary.…”

Exact solution for Bloch oscillations of a simple charge-density-wave insulator

“…Since then, CDW behavior has been seen in many different materials and in higher dimensions as well. Still, the precise origin of CDW behavior in real materials is controversial [2][3][4] -is it arising from electron-phonon interactions and a softening phonon or from a purely electronic instability in the static charge susceptibility or via an instability driven by the electron-phonon coupling? We do not investigate that question here, but instead focus on the behavior in the nonequilibrium state.…”

Classification of collective modes in a charge density wave by momentum-dependent modulation of the electronic band structure

“…One of the characteristic collective excitations in such Peierls-like CDWs is a gapped amplitude mode (AM), which modulates the magnitude ∆(t) of the order parameter 10 . Quasi-2D rare-earth tritellurides RTe 3 (R=Y, LaSm, Gd-Tm) form an incommensurate CDW along the crystallographic c-axis and have been studied extensively [11][12][13][14][15][16][17][18][19] . At low temperatures, the heaviest members of the RTe 3 series (R=Dy-Tm) additionally order with a second CDW perpendicular to the first CDW 15,19,20 .…”

“…Quasi-2D rare-earth tritellurides RTe 3 (R=Y, LaSm, Gd-Tm) form an incommensurate CDW along the crystallographic c-axis and have been studied extensively [11][12][13][14][15][16][17][18][19] . At low temperatures, the heaviest members of the RTe 3 series (R=Dy-Tm) additionally order with a second CDW perpendicular to the first CDW 15,19,20 . Angle-resolved photoemission spectroscopy (ARPES) reveals the Fermi surface (FS) topology and the momentum-dependent gap structure [20][21][22][23][24] .…”

“…Angle-resolved photoemission spectroscopy (ARPES) reveals the Fermi surface (FS) topology and the momentum-dependent gap structure [20][21][22][23][24] . Collective modes in RTe 3 were studied with Raman spectroscopy 19,25,26 , time-resolved optical reflectivity 7,27,28 , and time-resolved ARPES (trARPES) 4,29,30 . Yet even for this thoroughly investigated CDW system unambiguous identification of an AM is non-trivial.…”