Charge Density Wave

Introduction

Charge Density Wave (CDW) is a spatial modulation of the conduction electron density in a metal and an associated modulation of the lattice atom positions. In the relation to the symmetry breaking, CDW is a broken symmetry state of metals brought by the electron-phonon interactions whose ground states are the coherent superposition of electron-hole pairs, and it displays spatial variation.

CDW states was first discussed by Frohlich in 1954 and by Peierls in 1955. The latter pointed out that a one-dimensional metal coupled to the underlying lattice is not stable at low temperatures. The ground state of the coupled electron-phonon system is characterized by a gap in the single-particle excitation spectrum and by a collective mode formed by electron-hole pairs involving a wave vector $q=2k_{F}$ with the charge density $\rho ({\vec {r}})=\rho _{0}+\rho _{1}cos(2{\vec {k_{F}}}\cdot {\vec {r}}+\phi$, where $\rho _{0}$ is the unperturbed electron density of the metal and the condensate is called the charge density wave. As with the superconductivity, CDW has a complex order parameter $\Delta e^{i\phi }$ with the magnitude of $\Delta$ determines the size of the electronic gap and the amplitude $\delta u$ of the atomic displacements. The phase $\phi$ determines the position of the CDW relative to the underlying lattice.