Electron-phonon interaction in the modified tight-binding approximation

The electron-phonon interaction matrix element is examined in a modified tight-binding approximation. It is found that the matrix element is proportional to the bandwidth and therefore very small for an extremely narrow band. Paradoxically, in the usual Bloch tight-binding approximation the same matrix element which is proportional to the well-known Bloch constant C , is also found to be proportional to the bandwidth for intra-band transitions. The reasons for this equivalence are discussed. Inter-band transitions where the two matrix elements differ grossly in magnitude are also considered.