A theorem for the existence of Majorana fermion modes in spin-orbit-coupled semiconductors
- Department of Physics and Astronomy, Clemson University, Clemson, SC 29634 (United States)
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD 20742-4111 (United States)
We prove an index theorem for the existence of Majorana zero modes in a semiconducting thin film with a sizable spin-orbit coupling when it is adjacent to an s-wave superconductor. The theorem, which is analogous to the Jackiw-Rebbi index theorem for the zero modes in mass domain walls in one-dimensional Dirac theory, applies to vortices with odd flux-quantum in a semiconducting film in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect. The momentum space construction of the zero-mode solution presented here is complementary to the approximate real space solution of the Bogoliubov-de Gennes equations at a vortex core (Sau et al., arXiv:0907.2239), proving the existence of non-degenerate zero-energy Majorana excitations and the resultant non-Abelian topological order in the semiconductor heterostructure. With increasing magnitude of the proximity-induced pairing potential, the non-Abelian superconducting state makes a topological quantum phase transition to an ordinary s-wave superconducting state which no topological order.
- OSTI ID:
- 21336086
- Journal Information:
- Annals of Physics (New York), Vol. 325, Issue 1; Other Information: DOI: 10.1016/j.aop.2009.11.003; PII: S0003-4916(09)00221-8; Copyright (c) 2009 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
APPROXIMATIONS
EXCITATION
FERMIONS
L-S COUPLING
MAJORANA THEORY
MATHEMATICAL SOLUTIONS
ORBITS
PHASE TRANSFORMATIONS
PROXIMITY EFFECT
QUANTUM COMPUTERS
QUANTUM MECHANICS
S WAVES
SEMICONDUCTOR MATERIALS
SPIN
SUPERCONDUCTIVITY
SUPERCONDUCTORS
THIN FILMS
TOPOLOGY
ZEEMAN EFFECT