Finitesize effects in the dynamic conductivity and Faraday effect of quantum anomalous Hall insulators
Abstract
Here, we theoretically study the finitesize effects in the dynamical response of a quantum anomalous Hall insulator in the disk geometry. Semianalytic and numerical results are obtained for the wave functions and energies of the disk within a continuum Dirac Hamiltonian description subject to a topological infinite mass boundary condition. Using the Kubo formula, we obtain the frequencydependent longitudinal and Hall conductivities and find that optical transitions between edge states contribute dominantly to the real part of the dynamic Hall conductivity for frequency values both within and beyond the bulk band gap. We also find that the topological infinite mass boundary condition changes the lowfrequency Hall conductivity to ${e}^{2}/h$ in a finitesize system from the wellknown value ${e}^{2}/2h$ in an extended system. The magnetooptical Faraday rotation is then studied as a function of frequency for the setup of a quantum anomalous Hall insulator mounted on a dielectric substrate, showing both finitesize effects of the disk and FabryPérot resonances due to the substrate. Our work shows the vital role played by the boundary condition in the topological properties of finitesize systems through its effects on the electronic wave functions.
 Authors:

 Univ. of Science and Technology of China, Hefei (China). Hefei National Lab. for Physical Sciences at the Microscale
 Univ. of Alabama, Tuscaloosa, AL (United States). Dept. of Physics and Astronomy
 Publication Date:
 Research Org.:
 Univ. of Alabama, Tuscaloosa, AL (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES); National Natural Science Foundation of China (NSFC)
 OSTI Identifier:
 1598559
 Grant/Contract Number:
 SC0019326; 2017YFB0405703; 2016YFA0301700
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review B
 Additional Journal Information:
 Journal Volume: 100; Journal Issue: 20; Journal ID: ISSN 24699950
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Zeng, Junjie, Hou, Tao, Qiao, Zhenhua, and Tse, WangKong. Finitesize effects in the dynamic conductivity and Faraday effect of quantum anomalous Hall insulators. United States: N. p., 2019.
Web. doi:10.1103/PhysRevB.100.205408.
Zeng, Junjie, Hou, Tao, Qiao, Zhenhua, & Tse, WangKong. Finitesize effects in the dynamic conductivity and Faraday effect of quantum anomalous Hall insulators. United States. https://doi.org/10.1103/PhysRevB.100.205408
Zeng, Junjie, Hou, Tao, Qiao, Zhenhua, and Tse, WangKong. Wed .
"Finitesize effects in the dynamic conductivity and Faraday effect of quantum anomalous Hall insulators". United States. https://doi.org/10.1103/PhysRevB.100.205408. https://www.osti.gov/servlets/purl/1598559.
@article{osti_1598559,
title = {Finitesize effects in the dynamic conductivity and Faraday effect of quantum anomalous Hall insulators},
author = {Zeng, Junjie and Hou, Tao and Qiao, Zhenhua and Tse, WangKong},
abstractNote = {Here, we theoretically study the finitesize effects in the dynamical response of a quantum anomalous Hall insulator in the disk geometry. Semianalytic and numerical results are obtained for the wave functions and energies of the disk within a continuum Dirac Hamiltonian description subject to a topological infinite mass boundary condition. Using the Kubo formula, we obtain the frequencydependent longitudinal and Hall conductivities and find that optical transitions between edge states contribute dominantly to the real part of the dynamic Hall conductivity for frequency values both within and beyond the bulk band gap. We also find that the topological infinite mass boundary condition changes the lowfrequency Hall conductivity to e2/h in a finitesize system from the wellknown value e2/2h in an extended system. The magnetooptical Faraday rotation is then studied as a function of frequency for the setup of a quantum anomalous Hall insulator mounted on a dielectric substrate, showing both finitesize effects of the disk and FabryPérot resonances due to the substrate. Our work shows the vital role played by the boundary condition in the topological properties of finitesize systems through its effects on the electronic wave functions.},
doi = {10.1103/PhysRevB.100.205408},
journal = {Physical Review B},
number = 20,
volume = 100,
place = {United States},
year = {2019},
month = {11}
}
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