Stability of the quantum spin Hall effect: Effects of interactions, disorder, andZ2topology
Open accessAbstract
The stability to interactions and disorder of the quantum spin Hall effect (QSHE) proposed for time-reversal-invariant two-dimensional systems is discussed. The QSHE requires an energy gap in the bulk and gapless edge modes that conduct spin-up and spin-down excitations in opposite directions. When the number of Kramers pairs of edge modes is odd, certain one-particle scattering processes are forbidden due to a topological ${\mathbb{Z}}_{2}$ index. We show that in a many-body description, there are other scattering processes that can localize the edge modes and destroy the QSHE: the region of stability for both classes of models (even or odd number of Kramers pairs) is obtained explicitly in the chiral boson theory. For a single Kramers pair, the QSHE is stable to weak interactions and disorder, while for two Kramers pairs it is not; however, the two-pair case can be stabilized by either finite attractive or repulsive interactions. For the simplest case of a single pair of edge modes, it is shown that changing the screening length in an edge with screened Coulomb interactions can be used to drive a phase transition between the QSHE state and the ordinary insulator.
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If there are two Kramers pairs of edge modes, a right-mover can back-scatter to the left-mover that is not its time-reversal conjugate, and this process will in general eliminate these two Kramers pairs from the low-energy theory.
“However, if we have two Kramers pairs of edge modes, then a right-mover can back-scatter to the left-mover that is not its time-reversal conjugate (62,63). This process will, in general, eliminate these two Kramers pairs from the low-energy theory.”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [62]
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- Authors
- Xu, C., & Moore, J. E.
- Affiliations
- University of California, Berkeley (US)
- Lawrence Berkeley National Laboratory (US)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2006-01-23
- Volume
- 73
- Issue
- 4
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1969057621
- Cited by
- 571
- References
- 26
- Citations by year
- 2026: 7 · 2025: 21 · 2024: 26 · 2023: 17 · 2022: 21 · 2021: 28 · 2020: 25 · 2019: 31 · 2018: 25 · 2017: 32 · 2016: 27 · 2015: 39 · 2014: 39 · 2013: 58 · 2012: 46
- FWCI
- 11.83
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- quantum spin Hall effect, topological phase stability, disorder, interaction, Z2 topological index, Kramers pairs, edge states, screened Coulomb interaction, phase transitions, time-reversal invariant systems, two-dimensional systems
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