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.
@article{arxiv.2001.02682,
title = {Pairing Obstructions in Topological Superconductors},
author = {Frank Schindler and Barry Bradlyn and Mark H. Fischer and Titus Neupert},
journal= {arXiv preprint arXiv:2001.02682},
year = {2020}
}
Comments
6 pages, 3 figures, accepted manuscript, supplement included