The Dirac equation as a model of topological insulators

Journal Article · 21 February 2020 · Philosophical Magazine (2003, Print)

DOI: https://doi.org/10.1080/14786435.2020.1726523 · OSTI ID:1617902

Yuan, Xiao ^[1]; Bowen, Michael ^[2]; Riseborough, Peter ^[1]

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1. Temple Univ., Philadelphia, PA (United States)
2. Drexel Univ., Philadelphia, PA (United States)

The Dirac equation with a spatially dependent mass can be used as a simple, exactly soluble, continuum model of a three-dimensional Topological Insulator. For a bulk system, the sign of the mass determines the parity at the only time-reversal point ( $\underset{\_}{k}=0$) and, thus, leads to the designation of the bulk as being topologically trivial or non-trivial. Since the mass changes sign at the interface between a topologically trivial and non-trivial 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, non-degenerate and, due to the Rashba spin–orbit coupling generated by the loss of inversion symmetry, exhibit spin-momentum 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.

• Research Organization: Temple Univ., Philadelphia, PA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
• Grant/Contract Number: FG02-01ER45872
• OSTI ID: 1617902
• Journal Information: Philosophical Magazine (2003, Print), Vol. 100, Issue 10; ISSN 1478-6435
• Publisher: Taylor & FrancisCopyright Statement
• Country of Publication: United States
• Language: English