# Dielectric function and plasmons of doped three-dimensional Luttinger semimetals

## TL;DR

This paper develops an analytical theory for dielectric screening and plasmon behavior in doped three-dimensional Luttinger semimetals, providing insights into their collective excitations and damping mechanisms.

## Contribution

It introduces an analytical approach to calculate dielectric functions and plasmon dispersion in Luttinger semimetals with arbitrary doping and mass asymmetry.

## Key findings

- Derived an analytical dielectric screening function in RPA
- Calculated plasmon dispersion relations
- Analyzed Landau damping of collective modes

## Abstract

Luttinger semimetals are three-dimensional electron systems with a parabolic band touching and an effective total spin $J=3/2$. In this paper, we present an analytical theory of dielectric screening of inversion-symmetric Luttinger semimetals with an arbitrary carrier density and conduction-valence effective mass asymmetry. Assuming a spherical approximation for the single-particle Luttinger Hamiltonian, we determine analytically the dielectric screening function in the random phase approximation for arbitrary values of the wave vector and frequency, the latter in the complex plane. We use this analytical expression to calculate the dispersion relation and Landau damping of the collective modes in the charge sector (i.e., plasmons).