Rigorous results on topological superconductivity with particle number conservation

Dr. Matthew Lapa (Hosted by Nussinov), University of Chicago

Most theoretical studies of topological superconductors and their unpaired Majorana fermions rely on a mean-field (or Bogoliubov-de Gennes) approach to describe superconductivity, which violates particle number conservation (PNC). Recently, A.J. Leggett has suggested that this violation of PNC could pose a serious conceptual problem for the program of Majorana-based quantum computation. In this talk I will present recent work designed to address this concern. I will first introduce a fully number-conserving toy model of a topological superconducting wire in which superconductivity is induced by proximity to a nearby bulk superconductor. I will then present rigorous proofs that this model possesses many of the desired properties of the well-known mean-field models, including a finite energy gap in a sector of fixed total particle number, and the existence of long range “Majorana-like” correlations between the ends of the wire. 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.