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Available under license: CC BY: Creative Commons Attribution 4.0 International License
Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - One-dimensional Z4 topological superconductor
AU - Tymczyszyn, Max
AU - McCann, Edward
PY - 2024/8/9
Y1 - 2024/8/9
N2 - 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 Z4 topological phases, two that support Majorana bound states and two that do not, in agreement with a prediction based on K-theory classification [K. Shiozaki, M. Sato, and K. Gomi, 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 Z4 class as the spatial period of the nonsymmorphic symmetry is varied from much less than to of the order of the system size.
AB - 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 Z4 topological phases, two that support Majorana bound states and two that do not, in agreement with a prediction based on K-theory classification [K. Shiozaki, M. Sato, and K. Gomi, 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 Z4 class as the spatial period of the nonsymmorphic symmetry is varied from much less than to of the order of the system size.
U2 - 10.1103/PhysRevB.110.085416
DO - 10.1103/PhysRevB.110.085416
M3 - Journal article
VL - 110
JO - Physical Review B: Condensed Matter and Materials Physics
JF - Physical Review B: Condensed Matter and Materials Physics
SN - 1098-0121
IS - 8
M1 - 085416
ER -