1. One-dimensional $\mathbb{Z}_4$ topological superconductor
- Author
-
Tymczyszyn, Max and McCann, Edward
- Subjects
Condensed Matter - Mesoscale and Nanoscale Physics ,Condensed Matter - Superconductivity - Abstract
We describe the mean-field model of a one-dimensional topological superconductor with two orbitals per unit cell. Time-reversal symmetry is absent, but a nonsymmorphic symmetry, involving a translation by a fraction of the unit cell, mimics the role of time-reversal symmetry. As a result, the topological superconductor has $\mathbb{Z}_4$ topological phases, two which support Majorana bound states and two which do not, in agreement with a prediction based on K-theory classification [K. Shiozaki et al., Phys. Rev. B 93, 195413 (2016)]. As with the Kitaev chain, the presence of Majorana bound states gives rise to the $4\pi$-periodic Josephson effect. A random matrix with nonsymmorphic time-reversal symmetry may be block diagonalized, and every individual block has time-reversal symmetry described by one of the Gaussian orthogonal, unitary or symplectic ensembles. We show how this is manifested in the energy level statistics of a random system in the $\mathbb{Z}_4$ class as the spatial period of the nonsymmorphic symmetry is varied from much less than to of the order of the system size., Comment: 8 pages, 4 figures, plus supplementary 11 pages
- Published
- 2024
- Full Text
- View/download PDF