论文标题
零能量模式，分数费米数和涡流定理涡流式费物系统中的定理
Zero-energy modes, fractional fermion numbers and the index theorem in a vortex-Dirac fermion system
论文作者
论文摘要
拓扑材料的物理学最近引起了物理学家和数学家的广泛关注。 Dirac Fermions的索引和费米数在拓扑绝缘子和拓扑超导体中起着重要作用。当Dirac Fermions夫妇与具有孤子状结构（例如扭结，涡旋，单孔，字符串和麸皮）等对象时，存在零能量模式。我们讨论了与涡流和扭结相互作用的Dirac Fermions系统。这种系统将在存在Dirac Fermions的拓扑绝缘子的表面上实现。费米数是分数化的，这与费米昂零能激发模式的存在有关。当化学势消失时，零能量模式可以被视为主要的费物模式。我们的讨论包括与双层超导体中磁场中的扭结相关的半流量量子涡流的情况。 Fermion零能量模式的可正常波函数在半流量量子涡流的核心中不存在。当孤子标量字段具有奇异性时，狄拉克运算符和费米昂的索引具有额外的贡献。
Physics of topological materials have attracted much attention from both physicists and mathematicians recently. The index and the fermion number of Dirac fermions play an important role in topological insulators and topological superconductors. A zero-energy mode exists when Dirac fermions couple to objects with soliton-like structure such as kinks, vortices, monopoles, strings and branes. We discuss a system of Dirac fermions interacting with a vortex and a kink. This kind of systems will be realized on the surface of topological insulators where Dirac fermions exist. The fermion number is fractionalized and this is related to the presence of fermion zero-energy excitation modes. A zero-energy mode can be regarded as a Majorana fermion mode when the chemical potential vanishes. Our discussion includes the case where there is a half-flux quantum vortex associated with a kink in a magnetic field in a bilayer superconductor. A normalizable wave function of fermion zero-energy mode does not exist in the core of the half-flux quantum vortex. The index of Dirac operator and the fermion number have additional contributions when a soliton scalar field has a singularity.
