# Orbital Magnetism of Bloch Electrons III. Application to Graphene

## TL;DR

This paper provides an exact calculation of graphene's orbital susceptibility, revealing additional contributions beyond traditional models and emphasizing the role of interband effects and atomic orbital phases.

## Contribution

It applies a rigorous theory to a two-band graphene model, identifying new susceptibility contributions and clarifying the limitations of previous Peierls phase approaches.

## Key findings

- Additional susceptibility contributions from interband and Fermi surface effects.
- The phase between atomic orbitals affects orbital susceptibility.
- Corrections to the Peierls phase are necessary for accurate modeling.

## Abstract

The orbital susceptibility for graphene is calculated exactly up to the first order with respect to the overlap integrals between neighboring atomic orbitals. The general and rigorous theory of orbital susceptibility developed in the preceding paper is applied to a model for graphene as a typical two-band model. It is found that there are contributions from interband, Fermi surface, and occupied states in addition to the Landau--Peierls orbital susceptibility. The relative phase between the atomic orbitals on the two sublattices related to the chirality of Dirac cones plays an important role. It is shown that there are some additional contributions to the orbital susceptibility that are not included in the previous calculations using the Peierls phase in the tight-binding model for graphene. The physical origin of this difference is clarified in terms of the corrections to the Peierls phase.