对称(几何)
理论物理学
物理
拓扑(电路)
光子晶体
数学
纯数学
量子力学
几何学
组合数学
作者
Giuseppe De Nittis,Max Lein
出处
期刊:Advances in Theoretical and Mathematical Physics
[International Press of Boston, Inc.]
日期:2019-01-01
卷期号:23 (6): 1467-1531
被引量:4
标识
DOI:10.4310/atmp.2019.v23.n6.a2
摘要
In a seminal paper Haldane conjectured that topological phenomena are not particular to quantum systems, and indeed experiments realized unidirectional, backscattering-free edge modes with electromagnetic waves. This raises two immediate questions: (1) Are there other topological effects in electromagnetic media? And (2) is Haldane's Quantum Hall Effect for light really analogous to the Quantum Hall Effect?
We conclusively answer both of these questions by classifying topological photonic crystals according to material (as opposed to crystallographic) symmetries. It turns out there are four topologically distinct types of media, of which only one, gyrotropic media, is topologically non-trivial in $d = 2 , 3$. That means there are no as-of-yet undiscovered topological effects; in particular, there is no analog of the Quantum Spin Hall Effect in classical electromagnetism. Moreover, at least qualitatively, Haldane's Quantum Hall Effect for light is analogous to the Quantum Hall Effect from condensed matter physics as both systems as in the same topological class, class A. Our ideas are directly applicable to other classical waves.
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