Theory of negative differential conductivity in a superlattice miniband

Bloch equation conductivity perpendicular to the layers of a superlattice (period d) is evaluated using an extension of the balance-equation approach [X. L. Lei and C. S. Ting, Phys. Rev. B 32, 1112 (1985)] to narrow-band transport. The perpendicular peak drift velocity ${\mathit{v}}_{\mathit{p}}$ and the critical field ${\mathit{E}}_{\mathit{c}}$, at which the drift velocity peaks, are analyzed as functions of miniband width. Our theoretical prediction that ${\mathit{E}}_{\mathit{c}}$d increases with decreasing miniband width agrees well with the data of Sibille et al. [Phys. Rev. Lett. 64, 52 (1990)], even for the samples of narrowest miniband width in their experiment.