Dielectric function of the semiconductor hole liquid: Full frequency and wave vector dependence

TL;DR

This paper provides a comprehensive analysis of the dielectric function of p-doped semiconductor hole liquids, revealing complex plasmon behaviors and Friedel oscillations by considering full frequency and wave vector dependence within the RPA framework.

Contribution

It introduces a detailed calculation of the full dielectric function for hole liquids in semiconductors, including analytical expressions and exploration of plasmon and Friedel oscillation phenomena.

Findings

Identification of two plasmon branches influenced by hole mass differences.

Analytical expressions for the imaginary part of the dielectric function.

Observation of beating Friedel oscillations in the static limit.

Abstract

We study the dielectric function of the homogeneous semiconductor hole liquid of p-doped bulk III-V zinc-blende semiconductors within random phase approximation. The single-particle physics of the hole system is modeled by Luttinger's four-band Hamiltonian in its spherical approximation. Regarding the Coulomb-interacting hole liquid, the full dependence of the zero-temperature dielectric function on wave vector and frequency is explored. The imaginary part of the dielectric function is analytically obtained in terms of complicated but fully elementary expressions, while in the result for the real part nonelementary one-dimensional integrations remain to be performed. The correctness of these two independent calculations is checked via Kramers-Kronig relations. The mass difference between heavy and light holes, along with variations in the background dielectric constant, leads to dramatic alternations in the plasmon excitation pattern, and generically, two plasmon branches can be identified. These findings are the result of the evaluation of the full dielectric function and are not accessible via a high-frequency expansion. In the static limit a beating of Friedel oscillations between the Fermi wave numbers of heavy and light holes occurs.