Inhomogeneous magnetic catalysis on graphene's honeycomb lattice

TL;DR

This study numerically examines how magnetic fields influence charge-density-wave order in graphene's honeycomb lattice, revealing that local magnetic fields induce order parameter profiles and scaling behaviors consistent with continuum theories.

Contribution

It provides a numerical analysis of inhomogeneous magnetic catalysis on graphene, demonstrating the local order parameter's dependence on magnetic field strength and profile, including finite size effects.

Findings

Order parameter scales as the square-root of local magnetic field at criticality.

Spatial profile of order parameter mimics magnetic field distribution.

Finite size effects influence critical interaction and universal amplitude ratios.

Abstract

We investigate the ordering instability of interacting (and for simplicity, spinless) fermions on graphene's honeycomb lattice by numerically computing the Hartree self-consistent solution for the charge-density-wave order parameter in presence of both uniform and non-uniform magnetic fields. For a uniform field the overall behavior of the order parameter is found to be in accord with the continuum theory. In the inhomogeneous case, the spatial profile of the order parameter resembles qualitatively the form of the magnetic field itself, at least when the interaction is not overly strong. We find that right at the zero-field critical point of the infinite system the local order parameter scales as the square-root of the local strength of the magnetic field, apparently independently of the assumed field's profile. The finite size effects on various parameters of interest, such as the critical interaction and the universal amplitude ratio of the interaction-induced gap to the Landau level energy at criticality are also addressed.