2018/06/20 by Giuseppe De Nittis, De Nittis, Giuseppe, Max Lein +1
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Photonic Crystals and Applications #Photorefractive and Nonlinear Optics #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.1806.07783
openalex publication_date 2018/06/20 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
Haldane predicted an analog of the Integer Quantum Hall Effect in gyrotropic\nphotonic crystals, where the net number of electromagnetic edge modes moving\nleft-to-right is given by a bulk Chern number. His prediction --- topological\neffects are bona fide wave and not quantum phenomena --- has been confirmed in\na number of experiments. However, theoretical physicists have tacitly used\nthree different definitions for the bulk Chern numbers that enter the bulk-edge\ncorrespondence --- on the basis of electromagnetic Bloch functions, electric\nBloch functions and magnetic Bloch functions. We use vector bundle theoretic\narguments to prove that in media such as those considered by Haldane these\nthree potentially different Chern numbers necessarily agree with one another,\nand consequently, any one of them can be used in Haldane's photonic bulk-edge\ncorrespondence.\n