TY - JOUR

T1 - Equivalence of electric, magnetic, and electromagnetic Chern numbers for topological photonic crystals

AU - De Nittis, Giuseppe

AU - Lein, Max

N1 - Funding Information:
G. D.’s research was supported by FONDECYT, regular No. 1190204. M.L. was supported by JSPS through a WAKATE B grant (Grant No. 16K17761) and a Fusion grant from the WPI-AIMR. The authors would also like to thank the referee for his or her thoughtful suggestions.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - Haldane [S. Raghu and F. D. M. Haldane, Phys. Rev. A 78, 033834 (2008)] predicted an analog of the integer quantum Hall effect in gyrotropic photonic crystals, where the net number of electromagnetic edge modes moving left-to-right is given by a bulk Chern number. His prediction - topological effects are bona fide wave and not quantum phenomena - has been confirmed in a number of experiments [Z. Wang et al., Nature 461, 772-775 (2009)]. However, theoretical physicists have tacitly used three different definitions for the bulk Chern numbers that enter the bulk-edge correspondence - on the basis of electromagnetic Bloch functions, electric Bloch functions, and magnetic Bloch functions. We use vector bundle theoretic arguments to prove that in media such as those considered by Haldane, these three potentially different Chern numbers necessarily agree with one another, and consequently, any one of them can be used in Haldane's photonic bulk-edge correspondence.

AB - Haldane [S. Raghu and F. D. M. Haldane, Phys. Rev. A 78, 033834 (2008)] predicted an analog of the integer quantum Hall effect in gyrotropic photonic crystals, where the net number of electromagnetic edge modes moving left-to-right is given by a bulk Chern number. His prediction - topological effects are bona fide wave and not quantum phenomena - has been confirmed in a number of experiments [Z. Wang et al., Nature 461, 772-775 (2009)]. However, theoretical physicists have tacitly used three different definitions for the bulk Chern numbers that enter the bulk-edge correspondence - on the basis of electromagnetic Bloch functions, electric Bloch functions, and magnetic Bloch functions. We use vector bundle theoretic arguments to prove that in media such as those considered by Haldane, these three potentially different Chern numbers necessarily agree with one another, and consequently, any one of them can be used in Haldane's photonic bulk-edge correspondence.

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U2 - 10.1063/1.5094589

DO - 10.1063/1.5094589

M3 - Article

AN - SCOPUS:85079245788

VL - 61

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 2

M1 - 022901

ER -