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arXiv · 0710.2292

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

E. V. Gorbar·V. P. Gusynin
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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.

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E. V. Gorbar, V. P. Gusynin. 2007-10-11. Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field. https://doi.org/10.1016/j.aop.2007.11.005

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