Effect of the boundary on thermodynamic quantities such as magnetization
Name
Chen-2012-Effect of the boundary.pdf
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435.49 KB
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Author(s)
Chen, Kuang-Ting
Lee, Patrick A.
Date Issued
November 2012
Journal
Physical Review B
Publisher
American Physical Society
Citation
Chen, Kuang-Ting, and Patrick A. Lee. “Effect of the Boundary on Thermodynamic Quantities Such as Magnetization.” Phys. Rev. B 86, no. 19 (November 2012). © 2012 American Physical Society
Version
Final published version
Abstract
In this paper, we investigate in general how thermodynamic quantities such as the polarization, magnetization, and the magnetoelectric tensor are affected by the boundaries. We show that when the calculation with periodic boundary conditions does not involve a Berry's phase, the quantity in question is determined unambiguously by the bulk, even in the presence of gapless surface states. When the calculation involves a Berry's phase, the bulk can only determine the quantity up to some quantized value, given that (i) there are no gapless surface states, (ii) the surfaces do not break the symmetries preserved by the bulk, and (iii) the system is kept at charge neutrality. If any of the above conditions is violated, the quantity is then determined entirely by the details at the boundary. Due to the strong dependence on the boundary, this kind of thermodynamic quantity, such as the isotropic magnetoelectric coefficient, cannot be measured in the bulk without careful control at the boundary. One thus cannot distinguish between a topological insulator and a trivial insulator in three dimensions by any local measurement in the bulk.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.86.195111
