磁场中罗巴切夫斯基平面上狄拉克费米子的能隙产生
Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field
摘要：
本文研究了四费米子模型中，外协变恒定磁场作用下，二维常负曲率空间（罗巴切夫斯基平面）中费米子的对称性破缺和能隙产生。结果表明，由于磁催化和负曲率催化现象，在自由理论中，临界耦合常数为零，在手征极限下也存在对称性破缺凝聚。我们分析了零，弱，强磁场的情况下的间隙方程的解决方案。作为一个副产品，我们计算的态密度和霍尔电导率的非相互作用的费米子，可能是相关的石墨烯的研究。
英文摘要：
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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