Topological phases of noncentrosymmetric superconductors: Edge states, Majorana fermions, and non-Abelian statistics
Open accessAbstract
The existence of edge states and zero-energy modes in vortex cores is a hallmark of topologically nontrivial phases realized in various condensed-matter systems such as the fractional quantum Hall states, $p+ip$ superconductors, and ${\mathbit{Z}}_{2}$ insulators (quantum spin Hall state). We examine this scenario for two-dimensional noncentrosymmetric superconductors which allow the parity mixing of Cooper pairs. It is found that even when the $s$-wave pairing gap is nonzero, provided that the superconducting gap of spin-triplet pairs is larger than that of spin-singlet pairs, gapless edge states and zero-energy Majorana modes in vortex cores emerge, characterizing topological order. Furthermore, it is shown that for Rashba superconductors, the quantum spin Hall effect produced by gapless edge states exists even under an applied magnetic field which breaks time-reversal symmetry provided that the field direction is perpendicular to the propagating direction of the edge modes. This result making a sharp contrast to the ${\mathbit{Z}}_{2}$ insulator is due to an accidental symmetry inherent in the Rashba model. It is also demonstrated that in the case with magnetic fields, the non-Abelian statistics of vortices is possible under a particular but realistic condition.
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There are analogous ways to create a Majorana fermion using strong spin-orbit quantum wells rather than topological insulators.
“There are analogous ways to create a Majorana fermion using strong spin-orbit quantum wells rather than topological insulators (96, 97, 98).”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [96]
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- Authors
- Sato, M., & Fujimoto, S.
- Affiliations
- The Institute for Solid State Physics, The University of Tokyo (JP)
- Kyoto University (JP)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2009-03-04
- Volume
- 79
- Issue
- 9
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1970663662
- Cited by
- 597
- References
- 52
- Citations by year
- 2026: 16 · 2025: 16 · 2024: 31 · 2023: 22 · 2022: 32 · 2021: 38 · 2020: 34 · 2019: 26 · 2018: 40 · 2017: 32 · 2016: 53 · 2015: 41 · 2014: 45 · 2013: 57 · 2012: 50
- FWCI
- 21.15
- 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 › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- noncentrosymmetric superconductors, topological superconductivity, edge states, Majorana fermions, zero modes, vortex core, spin-triplet pairing, quantum spin Hall effect, non-Abelian statistics, time-reversal symmetry breaking, topological order
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