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

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.

arXiv comment12 pages, no figures

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• Hyperbolic Supersymmetric Quantum Hall Effect
• Gravitational instantons and anomalous chiral symmetry breaking
• A curvature bound from gravitational catalysis in thermal backgrounds
• Graphene, Dirac equation and analogue gravity
• Gravitational catalysis of chiral and color symmetry breaking of quark matter in hyperbolic space
• Dirac-Weyl equation on a hyperbolic graphene surface under perpendicular magnetic fields
• Renormalization flow towards gravitational catalysis in the 3d Gross-Neveu model
• The solutions of Dirac equation on the hyperboloid under perpendicular magnetic fields
• Quantum geometric tensors from sub-bundle geometry
• Flux-induced midgap states between strain-engineered flat bands
• Fate of chiral symmetry in Riemann-Cartan geometry