约化或赝QED中Chern-Simons项对动力学费米子质量的影响
On the influence of a Chern-Simons term in the dynamical fermion masses in Reduced or Pseudo QED
摘要：
混合维理论已经被用来描述凝聚态系统，其中费米子被限制在一个平面上，而与它们相互作用的规范场保持四维。在这里，我们研究动态破缺的手征对称性的混合维理论的框架，已成功地描述石墨烯和其他平面狄拉克材料，并已被称为伪或减少量子电动力学。我们探讨的规范和费米子部门之间的相互作用时，被认为是陈-西蒙斯项，并通过探索费米子自能的张量结构，我们表明，辐射修正可能会引起两个，狄拉克和Halfenstein质量项。进一步，通过在适当的截断下求解相应的Schwinger-Dyson方程，我们非微扰地研究了不同电磁耦合和Chern-Simons系数下费米子质量的动力学产生.我们还表明，对于确定的参数值，从每个手征的贡献抵消和手征对称性可能会恢复。这一结果的物理系统的可能影响，特别是在什么关系的手征磁效应，进行了讨论。
英文摘要：
Mixed dimensional theories have been used to describe condensed matter systems where fermions are constrained to a plane while the gauge fields they interact with remain four-dimensional. Here we investigate dynamical breaking of chiral symmetry in the framework of a mixed-dimensional theory that has been successful in describing graphene and other planar Dirac materials and has been dubbed as Pseudo or Reduced Quantum Electrodynamics. We explore the interplay between the gauge and fermion sector when a Chern-Simons term is considered and, by exploring the tensor structure of the fermion self energy, we show that the radiative corrections may induce both, a Dirac and a Haldane mass term. Furthermore, by solving the corresponding Schwinger-Dyson equation in a suitable truncation, we explore non-perturbatively the dynamical generation of fermion masses for different values of the electromagnetic coupling and the Chern-Simons coefficient. We also show that for definite parameter values, the contributions from each chirality cancel out and the chiral symmetry may be restored. Possible implications of this result for physical systems, in particular on what concerns the chiral magnetic effect, are discussed.
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