The Dirac equation as a model of topological insulators
Abstract
The Dirac equation with a spatially dependent mass can be used as a simple, exactly soluble, continuum model of a threedimensional Topological Insulator. For a bulk system, the sign of the mass determines the parity at the only timereversal point ( $\underset{\_}{k}=0$) and, thus, leads to the designation of the bulk as being topologically trivial or nontrivial. Since the mass changes sign at the interface between a topologically trivial and nontrivial materials, topological surface states appear on that boundary. We present that electron scattering experiments may provide an alternate probe of the topological character of the surface states. For infinitely thick slabs, the states on the opposite sides of the slab decouple. The spatial decoupling results in the surface states become gapless, nondegenerate and, due to the Rashba spin–orbit coupling generated by the loss of inversion symmetry, exhibit spinmomentum locking. We review several characteristic properties of the topological surface states which are dependent on the topological quantum numbers and show that, using this model, they can be calculated exactly using simple approaches.
 Authors:

 Temple Univ., Philadelphia, PA (United States)
 Drexel Univ., Philadelphia, PA (United States)
 Publication Date:
 Research Org.:
 Temple Univ., Philadelphia, PA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22). Materials Sciences & Engineering Division
 OSTI Identifier:
 1617902
 Grant/Contract Number:
 FG0201ER45872
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Philosophical Magazine (2003, Print)
 Additional Journal Information:
 Journal Name: Philosophical Magazine (2003, Print); Journal Volume: 100; Journal Issue: 10; Journal ID: ISSN 14786435
 Publisher:
 Taylor & Francis
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Topological insulators; Dirac equation; Weyl cone; berry phase; Chern number; experimental manifestations; electron diffraction
Citation Formats
Yuan, Xiao, Bowen, Michael, and Riseborough, Peter. The Dirac equation as a model of topological insulators. United States: N. p., 2020.
Web. doi:10.1080/14786435.2020.1726523.
Yuan, Xiao, Bowen, Michael, & Riseborough, Peter. The Dirac equation as a model of topological insulators. United States. https://doi.org/10.1080/14786435.2020.1726523
Yuan, Xiao, Bowen, Michael, and Riseborough, Peter. Fri .
"The Dirac equation as a model of topological insulators". United States. https://doi.org/10.1080/14786435.2020.1726523. https://www.osti.gov/servlets/purl/1617902.
@article{osti_1617902,
title = {The Dirac equation as a model of topological insulators},
author = {Yuan, Xiao and Bowen, Michael and Riseborough, Peter},
abstractNote = {The Dirac equation with a spatially dependent mass can be used as a simple, exactly soluble, continuum model of a threedimensional Topological Insulator. For a bulk system, the sign of the mass determines the parity at the only timereversal point (k_=0) and, thus, leads to the designation of the bulk as being topologically trivial or nontrivial. Since the mass changes sign at the interface between a topologically trivial and nontrivial materials, topological surface states appear on that boundary. We present that electron scattering experiments may provide an alternate probe of the topological character of the surface states. For infinitely thick slabs, the states on the opposite sides of the slab decouple. The spatial decoupling results in the surface states become gapless, nondegenerate and, due to the Rashba spin–orbit coupling generated by the loss of inversion symmetry, exhibit spinmomentum locking. We review several characteristic properties of the topological surface states which are dependent on the topological quantum numbers and show that, using this model, they can be calculated exactly using simple approaches.},
doi = {10.1080/14786435.2020.1726523},
journal = {Philosophical Magazine (2003, Print)},
number = 10,
volume = 100,
place = {United States},
year = {2020},
month = {2}
}
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