A theorem for the existence of Majorana fermion modes in spin-orbit-coupled semiconductors

Journal Article · Fri Jan 15 04:00:00 EST 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2009.11.003· OSTI ID:21336086

Tewari, Sumanta ^[1]; Sau, Jay D; Das Sarma, S ^[2]

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1. Department of Physics and Astronomy, Clemson University, Clemson, SC 29634 (United States)
2. 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), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 325; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
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