Topological superconductors as nonrelativistic limits of Jackiw-Rossi and Jackiw-Rebbi models

TL;DR

This paper demonstrates how nonrelativistic topological superconductors can be derived from relativistic models, revealing the origin of fermion zero modes and unifying their understanding across different regimes.

Contribution

It establishes a connection between relativistic Jackiw-Rossi and Jackiw-Rebbi models and nonrelativistic topological superconductors, explaining fermion zero modes as their remnants.

Findings

Nonrelativistic p_x+ip_y superconductor derived from Jackiw-Rossi model.

Fermion zero modes in superconductors linked to relativistic origins.

3D Jackiw-Rebbi limit leads to a p+is superconductor with zero modes.

Abstract

We argue that the nonrelativistic Hamiltonian of p_x+ip_y superconductor in two dimensions can be derived from the relativistic Jackiw-Rossi model by taking the limit of large Zeeman magnetic field and chemical potential. In particular, the existence of a fermion zero mode bound to a vortex in the p_x+ip_y superconductor can be understood as a remnant of that in the Jackiw-Rossi model. In three dimensions, the nonrelativistic limit of the Jackiw-Rebbi model leads to a "p+is" superconductor in which spin-triplet p-wave and spin-singlet s-wave pairings coexist. The resulting Hamiltonian supports a fermion zero mode when the pairing gaps form a hedgehoglike structure. Our findings provide a unified view of fermion zero modes in relativistic (Dirac-type) and nonrelativistic (Schr\"odinger-type) superconductors.