Band Structure of Bismuth: Pseudopotential Approach

Abstract

The electronic band structure of bismuth is studied by means of a pseudopotential approach. The Lin-Kleinman pseudopotential was adopted; its parameters were adjusted slightly to bring the band structure into agreement with two known energy differences in bismuth. With this pseudopotential, the band structure along symmetry lines and planes is calculated and the effective masses of the carriers are studied. The band structure is in good agreement with optical data and with effective-mass anisotropies, but the magnitude of the effective masses may differ from experiment by a factor of 3. Using the experimental effective masses and $g$ factor of the holes, we infer the energy-level scheme at $T$ near $E_F$. Also, we have tentatively identified a higher-lying band which has been experimentally observed. A very efficient method of calculating nonlocal and spin-orbit coupling terms in $\mathbf{k}·\mathbf{\pi }$ perturbation theory is presented.