Rigorous Results on Topological Superconductivity with Particle Number Conservation

Matthew F. Lapa, Michael Levin

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Most theoretical studies of topological superconductors and Majorana-based quantum computation rely on a mean-field approach to describe superconductivity. A potential problem with this approach is that real superconductors are described by number-conserving Hamiltonians with long-range interactions, so their topological properties may not be correctly captured by mean-field models that violate number conservation and have short-range interactions. To resolve this issue, reliable results on number-conserving models of superconductivity are essential. As a first step in this direction, we use rigorous methods to study a number-conserving toy model of a topological superconducting wire. We prove that this model exhibits many of the desired properties of the mean-field models, including a finite energy gap in a sector of fixed total particle number, the existence of long-range Majorana-like correlations between the ends of an open wire, and a change in the ground state fermion parity for periodic vs antiperiodic boundary conditions. These results show that many of the remarkable properties of mean-field models of topological superconductivity persist in more realistic models with number-conserving dynamics.

Original languageEnglish
Article number257002
JournalPhysical Review Letters
Volume124
Issue number25
DOIs
StatePublished - 26 Jun 2020
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (all)

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