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Time-reversal-invariant topological superconductivity in one and two dimensions

Haim, Arbel and Oreg, Yuval (2019) Time-reversal-invariant topological superconductivity in one and two dimensions. Physics Reports, 825 . pp. 1-48. ISSN 0370-1573. doi:10.1016/j.physrep.2019.08.002.

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A topological superconductor is characterized by having a pairing gap in the bulk and gapless self-hermitian Majorana modes at its boundary. In one dimension, these are zero-energy modes bound to the ends, while in two dimensions these are chiral gapless modes traveling along the edge. Majorana modes have attracted a lot of interest due to their exotic properties, which include non-abelian exchange statistics. Progress in realizing topological superconductivity has been made by combining spin–orbit coupling, conventional superconductivity, and magnetism. The existence of protected Majorana modes, however, does not inherently require the breaking of time-reversal symmetry by magnetic fields. Indeed, pairs of Majorana modes can reside at the boundary of a time-reversal-invariant topological superconductor (TRITOPS). It is the time-reversal symmetry which then protects this so-called Majorana Kramers’ pair from gapping out. This is analogous to the case of the two-dimensional topological insulator, with its pair of helical gapless boundary modes, protected by time-reversal symmetry. Realizing the TRITOPS phase will be a major step in the study of topological phases of matter. In this paper we describe the physical properties of the TRITOPS phase, and review recent proposals for engineering and detecting them in condensed matter systems, in one and two spatial dimensions. We mostly focus on extrinsic superconductors, where superconductivity is introduced through the proximity effect. We emphasize the role of interplay between attractive and repulsive electron–electron interaction as an underlying mechanism. When discussing the detection of the TRITOPS phase, we focus on the physical imprint of Majorana Kramers’ pairs, and review proposals of transport measurement which can reveal their existence.

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Additional Information:© 2019 Published by Elsevier B.V. Received 8 August 2019, Accepted 12 August 2019, Available online 14 August 2019.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Israel Science FoundationUNSPECIFIED
Binational Science Foundation (USA-Israel)UNSPECIFIED
European Research Council (ERC)340210
Subject Keywords:Topological superconductivity; Topological states of matter; Time-reversal symmetry; Majorana zero modes; Proximity effect
Record Number:CaltechAUTHORS:20190814-101137520
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Official Citation:Arbel Haim, Yuval Oreg, Time-reversal-invariant topological superconductivity in one and two dimensions, Physics Reports, Volume 825, 2019, Pages 1-48, ISSN 0370-1573, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97885
Deposited By: Tony Diaz
Deposited On:14 Aug 2019 20:41
Last Modified:16 Nov 2021 17:35

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