The electronic specific heat of a one-dimensional crystal with a sinusoidal potential

The electronic specific heat of a one-dimensional crystal with a sinusoidal potential is examined in the second quantized formulation. Two electrons per lattice site are assumed to be under the influence of the potential; electron-electron interactions via Coulomb repulsion are ignored. The Green’s function equation-of-motion technique is utilized to obtain an exact expression for the specific heat forK, the allowed linear momenta, restricted to two Brillouin ones. The specific heat shows metal, semiconductor-to-metal, or insulator-to-metal behavior as a function of temperature, dependent upon the well depth of the sinusoidal potential.