Dynamical current-current correlation in the two-dimensional parabolic Dirac system

TL;DR

This paper provides a theoretical analysis of current-current correlations in a 2D parabolic Dirac system, deriving analytical expressions for susceptibility, RKKY interaction, and orbital susceptibility, highlighting their dependence on dispersion anisotropy.

Contribution

It introduces analytical formulas for key response functions in a 2D parabolic Dirac system, including RPA susceptibility and RKKY interaction, considering both isotropic and anisotropic dispersions.

Findings

Derived analytical expressions for RPA susceptibility and RKKY interaction.

Linked dynamical polarization and spin susceptibility to current-current response.

Analyzed effects of dispersion anisotropy on response functions.

Abstract

We theoretically investigate the current-current correlation of the two-dimensional (2D) parabolic Dirac system in hexogonal lattice. The analytical expressions of the random phase approximation (RPA) susceptibility, Ruderman-Kittel-Kasuya-Yosida (RKKY) Hamiltonian, and the diamagnetic orbital susceptibility in noninteracting case base on the density-density or current-current correlation function are derived and quantitatively analyzed. In noninteracting case, the dynamical polarization with- in RPA and spin transverse susceptibility as well as the RKKY interaction (when close to the half-filling) are related to the the current-current response in the 2D parabolic Dirac system. Both the case of anisotropic dispersion and isotropic dispersion are discussed.