An electron-phonon theory for a quasi-one-dimensional band of electrons forming a moving incommensurate charge-density wave (CDW) state at zero temperature is presented. A useful analytic expression for the energy gap as a function of electron-phonon coupling is found. The gap is quite a bit larger than the well-known weak-coupling result, even for modest coupling, where the mean-field approximation should still be valid. It is also shown that the form of the Hamiltonian implies that there is no spread at all in the wavevector of the CDW in the vicinity of 2k F . Comparisons of theoretical and experimental values of the energy gap and the lattice displacement amplitude are made for NbSe 3 .
The state of the electrons in a charge-density wave (CDW) sliding at arbitrary velocity and with arbitrary electron-phonon coupling constant is discussed. The mean-field framework deals directly with the quantum mechanics of a system having non-energy-eigenstate solutions. The quasiparticle approximation is replaced by a more accurate electron-hole condensate. Corrections to the uniform current, which become important at moderate electron-phonon coupling or at high CDW speed, show that the Fermi sea is swept along with a velocity slightly less than the velocity of the CDW. Corrections to the effective energy gap for photon absorption are also discussed.
A theory for a quasi-one-dimensional incommensurate charge-density wave state arising from electron-phonon (el-phon) interaction connecting electron states in two different bands is presented. An expression for the fundamental component of the energy gap as a function of the effective el-phon coupling, valid for all coupling strengths, has been found. For a single band, the expression simplifies to a reciprocal hyperbolicsine dependence on the reciprocal effective coupling. The effective coupling, although simply related to the n assumed phonon-band frequencies, is not generally expressible as a sum of independent functions of these frequencies. The theory is applied to tetrathiofulvalinium-tetracyanoquinodimethane and to potassium blue bronze.
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