# Dielectric and electronic properties of three-dimensional Luttinger semimetals with a quadratic band touching

## TL;DR

This paper investigates the dielectric and electronic properties of three-dimensional Luttinger semimetals with quadratic band touching, revealing how strong spin-orbit coupling influences screening, self-energy, and quasiparticle behavior, with implications for materials like alpha-Sn and HgTe.

## Contribution

It provides a detailed analysis of dielectric screening and quasiparticle properties in Luttinger semimetals, incorporating interband effects and comparing with experimental data.

## Key findings

- Reduced plasma frequency due to interband coupling
- Enhanced spectral weight at small wavevectors
- Significant deviation of quasiparticle properties at low carrier density

## Abstract

Due to strong spin-orbit coupling, charge carriers in three-dimensional quadratic band touching Luttinger semimetals have non-trivial wavefunctions characterized by a pseudospin of 3/2. We compute the dielectric permittivity of such semimetals at finite doping, within the random phase approximation. Because of interband coupling, the dielectric screening shows a reduced plasma frequency and an increased spectral weight at small wavevectors, compared to a regular quadratic band. This weakens the effective Coulomb potential, modifying the single-particle self-energy for which we present both analytical and numerical results. At a low carrier density, the quasiparticle properties of this model strongly deviate from that of a single quadratic band. We compare our findings with experimental results for alpha-Sn, HgSe, HgTe, YPtBi and Pr2Ir2O7.