Dynamical current-current correlation of the hexagonal lattice and graphene

TL;DR

This paper investigates the dynamical current-current correlation function in hexagonal lattices, revealing anisotropic behavior and comparing analytical and numerical results, with implications for understanding electronic properties in graphene.

Contribution

It introduces a novel analysis of current correlations in hexagonal lattices, highlighting differences from Dirac approximation predictions and providing detailed comparisons.

Findings

Correlation function is anisotropic in the hexagonal lattice.

Analytical isotropic solutions do not match numerical results.

Differences persist even in the Dirac regime.

Abstract

We discuss the dynamical current-current correlation function of the hexagonal lattice using a local current operator defined on a continuum-replica model of the original lattice model. In the Dirac approximation, the correlation function can be decomposed into a parallel and perpendicular contribution. We show that this is not possible for the hexagonal lattice even in the Dirac regime. A comparison between the analytical isotropic solution and the numerical results for the honeycomb lattice is given.