Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field

TL;DR

This paper investigates how magnetic fields and negative curvature induce symmetry breaking and gap generation in Dirac fermions on the Lobachevsky plane, with implications for graphene physics.

Contribution

It demonstrates that magnetic and curvature effects lead to symmetry breaking at zero coupling, providing new insights into fermion behavior in curved spaces with magnetic fields.

Findings

Critical coupling constant is zero due to catalysis effects.

Symmetry breaking occurs even in free theory in the chiral limit.

Calculated density of states and Hall conductivity relevant for graphene.

Abstract

We study symmetry breaking and gap generation for fermions in the 2D space of constant negative curvature (the Lobachevsky plane) in an external covariantly constant magnetic field in a four-fermion model. It is shown that due to the magnetic and negative curvature catalysis phenomena the critical coupling constant is zero and there is a symmetry breaking condensate in the chiral limit even in free theory. We analyze solutions of the gap equation in the cases of zero, weak, and strong magnetic fields. As a byproduct we calculate the density of states and the Hall conductivity for noninteracting fermions that may be relevant for studies of graphene.