Topological insulators beyond the Brillouin zone via Chern parity
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The topological insulator is an electronic phase stabilized by spin-orbit coupling that supports propagating edge states and is not adiabatically connected to the ordinary insulator. In several ways it is a spin-orbit-induced analog in time-reversal-invariant systems of the integer quantum Hall effect (IQHE). This paper studies the topological insulator phase in disordered two-dimensional systems, using a model graphene Hamiltonian introduced by Kane and Mele [Phys. Rev. Lett. 95, 226801 (2005)] as an example. The nonperturbative definition of a topological insulator given here is distinct from previous efforts in that it involves boundary phase twists that couple only to charge, does not refer to edge states, and can be measured by pumping cycles of ordinary charge. In this definition, the phase of a Slater determinant of electronic states is determined by a Chern parity analogous to Chern number in the IQHE case. Numerically, we find, in agreement with recent network model studies, that the direct transition between ordinary and topological insulators that occurs in band structures is a consequence of the perfect crystalline lattice. Generically, these two phases are separated by a metallic phase, which is allowed in two dimensions when spin-orbit coupling is present. The same approach can be used to study three-dimensional topological insulators.
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The phases φx,y describe twisted boundary conditions that can be used to give a pumping definition of the Z2 invariant in the disordered case.
“The phases φ x,y describe twisted boundary conditions that can be used to give a pumping definition of the Z 2 invariant in the disordered case.”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [61]
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- 30 W.-M. Yao et al., Journal of Physics G 33 (2006), § 32.
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- Authors
- Essin, A. M., & Moore, J. E.
- Affiliations
- University of California, Berkeley (US)
- Lawrence Berkeley National Laboratory (US)
- ORCID
- Moore, J. E.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2007-10-10
- Volume
- 76
- Issue
- 16
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2017901233
- Cited by
- 98
- References
- 35
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 2 · 2023: 2 · 2022: 1 · 2021: 3 · 2020: 3 · 2019: 1 · 2018: 7 · 2017: 7 · 2016: 9 · 2015: 5 · 2014: 3 · 2013: 6 · 2012: 14
- FWCI
- 4.08
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Division of Materials Research
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Keywords
- topological insulators, Chern number, spin-orbit coupling, two-dimensional disordered systems, Kane-Mele model, graphene, charge pumping, metallic phase, topological phase transition, three-dimensional topological insulators
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