One-dimensional $\mathbb{Z}_4$ topological superconductor
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909283688382464 |
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| author | Tymczyszyn, Max McCann, Edward |
| author_facet | Tymczyszyn, Max McCann, Edward |
| contents | 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 $4π$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07633 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One-dimensional $\mathbb{Z}_4$ topological superconductor Tymczyszyn, Max McCann, Edward Mesoscale and Nanoscale Physics Superconductivity 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 $4π$-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. |
| title | One-dimensional $\mathbb{Z}_4$ topological superconductor |
| topic | Mesoscale and Nanoscale Physics Superconductivity |
| url | https://arxiv.org/abs/2404.07633 |