Charge-density waves arising from two electron bands

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 hyperbolic-sine 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.