Classification of charge density waves based on their nature

Abstract

The concept of a charge density wave (CDW) permeates much of condensed matter physics and chemistry. CDWs have their origin rooted in the instability of a one-dimensional system described by Peierls. The extension of this concept to reduced dimensional systems has led to the concept of Fermi surface nesting (FSN), which dictates the wave vector (q CDW ) of the CDW and the corresponding lattice distortion. The idea is that segments of the Fermi contours are connected byq CDW , resulting in the effective screening of phonons inducing Kohn anomalies in their dispersion at q CDW , driving a lattice restructuring at low temperatures. There is growing theoretical and experimental evidence that this picture fails in many real systems and in fact it is the momentum dependence of the electron-phonon coupling (EPC) matrix element that determines the characteristic of the CDW phase. Based on the published results for the prototypical CDW system 2H-NbSe 2 , we show how well theq-dependent EPC matrix element, but not the FSN, can describe the origin of the CDW. We further demonstrate a procedure of combing electronic band and phonon measurements to extract the EPC matrix element, allowing the electronic states involved in the EPC to be identified. Thus, we show that a large EPC does not necessarily induce the CDW phase, with Bi 2 Sr 2 CaCu 2 O 8+δ as the example, and the charge-ordered phenomena observed in various cuprates are not driven by FSN or EPC. To experimentally resolve the microscopic picture of EPC will lead to a fundamental change in the way we think about, write about, and classify charge density waves.charge density wave | phonon | nesting T he phrase charge density wave (CDW) was first used by Fröhlich (1, 2) but originates from Peierls' description of a fundamental instability in a one-dimensional (1D) chain of atoms equally spaced by a lattice constant a (2). Fig. 1A shows the free electron band of such a 1D chain with one electron per atomic site. The Fermi points are at k F = ±π/2a and are connected by the nesting vector q = 2k F . In 1930 Peierls asserted that this system is unstable, showing an electronic disturbance with the wave vector 2k F , changing the periodicity of the chain, and opening up a gap at the zone boundary (k = π/2a) of the new unit cell containing two atoms (1, 2). The conjecture was that the gain in electronic energy would always overwhelm the cost of restructuring the atoms (1). Consequently in the Peierls model there would be a transition from the metallic high-temperature state to the insulating-dimerized ground state at a critical temperature T CDW . Kohn (3) pointed out that there is an image of the Fermi surface in the vibrational spectrum, because the zero energy electronic excitations at 2k F will effectively screen any lattice motion with this wave vector. Fig. 1B shows the phonon dispersion for this 1D chain at different temperatures (1). Below T CDW the phonon energy at q = 2k F becomes imaginary, meaning there is a new lattice structure. Above T CDW there is a sharp dip (K...

Electron-phonon coupling in a system with broken symmetry: Surface ofBe(0001)

“…It should be pointed out that there is no possibility of EPC resulting from Fermi surface nesting (Fig. 8(b)) consistent with recent work showing that Fermi surface nesting is not relevant to charge density wave formation in quasi two dimensional materials [38].…”

“…The -dependent EPC manifests itself in changes in the phonon width and energy as a function of [7,38] and would not be reproduced in a phonon dispersion calculation.…”

“…result from a -dependent EPC matrix element as seen in the layered transition metal dichalcogenides and cuprates, not from any form of Fermi surface nesting [7,38] . The -dependent EPC manifests itself in changes in the phonon width and energy as a function of [7,38] and would not be reproduced in a phonon dispersion calculation.…”

“…These results can be summarized as: (1) The high value of found for Be(0001) is primarily a result of the electrons in the surface state coupling to the low energy surface RW; (2) The two low energy features observed in the ELF cannot be explained by the surface phonon spectra [12,25] or in fact by a calculation of the ELF [25]. These peaks must result from -dependent EPC [7,38], which is indicated by the measured change in the phonon linewidth [14].…”

Manipulating charge density waves in1T−TaS2by charge-carrier doping: A first-principles investigation

“…Above the transition temperature the phonon frequency near q CDW drops but does not go to zero. Just below the transition temperature the phonon frequency near q CDW is imaginary, meaning there is a restructuring of lattice with a superlattice vector of q CDW [36]. Therefore, phonon dispersion without imaginary frequency implies that the structure is stable compared to CDW structure.…”