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Title: Finite-size effects in the dynamic conductivity and Faraday effect of quantum anomalous Hall insulators

Abstract

Here, we theoretically study the finite-size 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 frequency-dependent 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 low-frequency Hall conductivity to e 2 / h in a finite-size system from the well-known value e 2 / 2 h in an extended system. The magneto-optical 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 finite-size effects of the disk and Fabry-Pérot resonances due to the substrate. Our work shows the vital role played by the boundary condition in the topological properties of finite-size systems through its effects on the electronic wave functions.

Authors:
 [1];  [1]; ORCiD logo [1]; ORCiD logo [2]
  1. Univ. of Science and Technology of China, Hefei (China). Hefei National Lab. for Physical Sciences at the Microscale
  2. 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 (NNSFC)
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 2469-9950
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, Wang-Kong. Finite-size 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, Wang-Kong. Finite-size effects in the dynamic conductivity and Faraday effect of quantum anomalous Hall insulators. United States. doi:https://doi.org/10.1103/PhysRevB.100.205408
Zeng, Junjie, Hou, Tao, Qiao, Zhenhua, and Tse, Wang-Kong. Wed . "Finite-size effects in the dynamic conductivity and Faraday effect of quantum anomalous Hall insulators". United States. doi:https://doi.org/10.1103/PhysRevB.100.205408. https://www.osti.gov/servlets/purl/1598559.
@article{osti_1598559,
title = {Finite-size effects in the dynamic conductivity and Faraday effect of quantum anomalous Hall insulators},
author = {Zeng, Junjie and Hou, Tao and Qiao, Zhenhua and Tse, Wang-Kong},
abstractNote = {Here, we theoretically study the finite-size 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 frequency-dependent 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 low-frequency Hall conductivity to e2/h in a finite-size system from the well-known value e2/2h in an extended system. The magneto-optical 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 finite-size effects of the disk and Fabry-Pérot resonances due to the substrate. Our work shows the vital role played by the boundary condition in the topological properties of finite-size 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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