Coulombic resonance states in zero-gap semiconductors

Abstract

We present a detailed theory of resonance states in HgTe due to charged acceptor impurities. This problem has previously been studied by Gel'mont and Dyakonov, but on the rather unrealistic assumptions of an unscreened Coulomb potential and zero electron mass. In a zero-gap (ZG) semiconductor, the screening is important and sensitive to the band parameters. Within the effective-mass formalism, we have obtained a variational solution for the lowest-order radial components in the partial-wave expansion of the wave function. Two variational methods for the phase shift are used and improved upon---the Kohn method and the Harris method, which is an interesting modification of the former and is more appropriate for the study of resonances. A simple Thomas-Fermi (TF) potential and the full random-phase approximation screened Coulomb potential have been used. We find that the resonance energy ${E}_{R}$ is very sensitive to screening, while the relative width $\frac{\ensuremath{\Gamma}}{{E}_{R}}$ is only weakly dependent upon it. The interband polarization, which is known to be substantial in a ZG semiconductor, dramatically reduces the resonance energy. Interestingly, within the reported range of band parameters, either the 0.7-meV or the 2.2-meV resonance can be reproduced, corresponding respectively to hole masses of $0.35{m}_{0}$ or $0.58{m}_{0}$. We also find that the resonance energy varies by at most 10% with the Fermi level ${E}_{F}$ in the range of interest, ${E}_{F}l{E}_{R}$.