Charge-density wave

(solid-state physics) The ground state of a metal in which the conduction-electron charge density is sinusoidally modulated in space.

A possible ground state of a metal in which the conduction-electron charge density is sinusoidally modulated in space. The periodicity of this extra modulation is unrelated to the lattice periodicity. Instead, it is determined by the dimension of the conduction-electron Fermi surface in momentum space. See also Fermi surface.

In a quasi-one-dimensional metal, for which conduction electrons are mobile in one direction only, a charge-density wave can be caused by a Peierls instability. This mechanism involves interaction between the electrons and a periodic lattice distortion having a wave vector Q parallel to the conduction axis. The linear-chain metal niobium triselenide (NbSe₃) is prototypical.

For isotropic metals, and quasi-two-dimensional metals, Coulomb interactions between electrons are the cause of a charge-density wave instability. The exchange energy, an effect of the Pauli exclusion principle, and the correlation energy, an effect of electron-electron scattering, both act to stabilize a charge-density wave. However, the electrostatic energy attributable to the charge modulation would suppress a charge-density wave were it not for a compensating charge response of the positive-ion lattice. See also Exchange interaction; Exclusion principle.

A wavelike displacement of this lattice will generate a positive-ion charge density that almost cancels the electronic charge modulation of the charge-density wave. A typical value of the displacement amplitude is about 1% of the lattice constant. Ion-ion repulsive interactions must be small in order to permit such a distortion. Consequently, charge-density waves are more likely to occur in metals having small elastic moduli. See also Band theory of solids; Crystal structure; Spin-density wave.