三维时间反演对称拓扑绝缘体的量子反常抵消和玻色化
Cancellation of quantum anomalies and bosonization of three-dimensional time-reversal symmetric topological insulators
摘要：
三维空间中的强时间反演对称（TRS）拓扑绝缘体（TI）具有无质量狄拉克费米子形式的无隙表面态。我们用玻色化方法研究了这些表面态，发现由于表面狄拉克费米子的宇称反常，所得到的玻色理论具有拓扑贡献。我们认为，量子异常的存在，事实上，表面状态存在的主要原因，由表面和散装异常必须取消的原则。考察其他类别的拓扑绝缘体，我们认为，这一原则一般成立。超越纯粹的拓扑考虑，我们将动态的表面电子态的玻色子理论。此外，我们还讨论了玻色子理论的热力学，并提出了表面狄拉克费米子的玻色子场表示。
英文摘要：
The strong time-reversal symmetric (TRS) topological insulator (TI) in three space dimensions features gapless surface states in the form of massless Dirac fermions. We study these surface states with the method of bosonization, and find that the resulting bosonic theory has a topological contribution due to the parity anomaly of the surface Dirac fermions. We argue that the presence of a quantum anomaly is, in fact, the main reason for the existence of a surface state, by the principle that anomalies of a surface and bulk must cancel. Inspecting other classes of topological insulators, we argue that this principle holds in general. Moving beyond purely topological considerations, we incorporate the dynamics of the surface electron states into the bosonic theory. Additionally, we discuss the thermodynamics of the bosonic theory and propose a representation of the surface Dirac fermions in terms of the bosonic fields.
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