The One-Dimensional Coulomb Glass within the Bethe-Peierls-Weiss Approximation

The authors present a new analytical approach to the Coulomb glass problem in one dimension, using the Bethe-Peierls-Weiss (BPW) approximation. The single-particle density of states (DOS) at zero temperature is calculated analytically; it has a soft Coulomb gap at the Fermi energy. The self-consistency condition used within the BPW scheme influences the calculated DOS. They discuss the two possible limiting cases for the self-consistency condition which give an upper and a lower bound of the DOS. The upper limit yields a DOS similar to that following from the self-consistent equation of Efros (g( epsilon ) approximately 1/In( epsilon ₀ / epsilon )); the lower limit gives a power-law Coulomb gap near the Fermi energy (g( epsilon ) approximately epsilon ^kappa , where kappa is proportional to the relative interaction strength).