Dynamical correlation functions and the related physical effects in three-dimensional Weyl/Dirac semimetals

TL;DR

This paper derives exact dynamical correlation functions for 3D Weyl/Dirac semimetals, revealing their electromagnetic responses and effects of electron interactions, which are crucial for understanding their transport and optical properties.

Contribution

It provides a unified derivation of correlation functions using Passarino-Veltman reduction and establishes generalized Kramers-Kronig relations for these materials.

Findings

Exact chiral magnetic conductivity obtained.

Recovery of previous results in certain limits.

Discussion of electron interaction effects within RPA.

Abstract

We present a unified derivation of the dynamical correlation functions including density-density, density-current and current-current, of three-dimensional Weyl/Dirac semimetals by use of the Passarino-Veltman reduction scheme at zero temperature. The generalized Kramers-Kronig relations with arbitrary order of subtraction are established to verify these correlation functions. Our results lead to the exact chiral magnetic conductivity and directly recover the previous ones in several limits. We also investigate the magnetic susceptibilities, the orbital magnetization and briefly discuss the impact of electron interactions on these physical quantities within the random phase approximation. Our work could provide a starting point for the investigation of the nonlocal transport and optical properties due to the higher-order spatial dispersion in three-dimensional Weyl/Dirac semimetals.