2020/01/31 by Frank Schindler, Barry Bradlyn, Mark H. Fischer +1 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Cooper pair #Graphene research and applications #MAJORANA #Mathematics #Pairing #Physics #Position (finance) #Quantum #Quantum many-body systems #Quantum mechanics #Superconductivity #Symmetry protected topological order #Theoretical physics #Topological Materials and Phenomena #Topological entropy in physics #Topological insulator #Topological order #Topological quantum number #Topology (electrical circuits) #cond-mat.mes-hall #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevlett.124.247001
published as Phys. Rev. Lett. 124, 247001 (2020) · 6 pages, 3 figures, accepted manuscript, supplement included
openalex publication_date 2020/06/15 · arxiv created 2020/07/01 · arxiv updated 2020/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The modern understanding of topological insulators is based on Wannier obstructions in position space. Motivated by this insight, we study topological superconductors from a position-space perspective. For a one-dimensional superconductor, we show that the wave function of an individual Cooper pair decays exponentially with separation in the trivial phase and polynomially in the topological phase. For the position-space Majorana representation, we show that the topological phase is characterized by a nonzero Majorana polarization, which captures an irremovable and quantized separation of Majorana Wannier centers from the atomic positions. We apply our results to diagnose second-order topological superconducting phases in two dimensions. Our work establishes a vantage point for the generalization of topological quantum chemistry to superconductivity.