Spontaneous symmetry breakings in graphene subjected to in-plane magnetic field

TL;DR

This paper investigates how in-plane magnetic fields induce spontaneous symmetry breaking in graphene, leading to excitonic condensates with complex order parameters, and explores the effects of interactions and temperature on phase transitions.

Contribution

It introduces a theoretical framework for excitonic condensate formation in graphene under in-plane magnetic fields, including the role of Coulomb interactions and renormalization effects.

Findings

Excitonic condensates form even at weak magnetic fields and interactions.

The order parameter is a U(2) matrix allowing spin and valley rotations.

Various phase transitions, including BKT and Ising types, are possible due to freezing of degrees of freedom.

Abstract

Application of the magnetic field parallel to the plane of the graphene sheet leads to the formation of electron- and hole-like Fermi surfaces. Such situation is shown to be unstable with respect to the formation of an excitonic condensate even for an arbitrary weak magnetic field and interaction strength. At temperatures lower than the mean-field temperature the order parameter amplitude is formed. The order parameter itself is a U(2) matrix allowing for the combined rotations in the spin and valley spaces. These rotations smoothly interpolate between site and bond centered spin density waves and spin flux states. The trigonal warping, short range interactions, and the three particle Umklapp processes freeze some degrees of freedom at temperatures much smaller than the mean-field transition temperature and make either Berezinskii-Kosterlitz-Thouless (driven either by vortices or half-vortices) or Ising type transitions possible. Strong logarithmic renormalization for the coupling constants of these terms by the Coulomb interaction are calculated within one-loop renormalization group. It is found that in the presence of the Coulomb interaction some short range interaction terms become much greater than one might expect from the naive dimensionality counting.