Pairing Obstructions in Topological Superconductors

Frank Schindler, Barry Bradlyn, Mark H. Fischer, Titus Neupert

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number247001
JournalPhysical review letters
Issue number24
StatePublished - Jun 19 2020
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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