Role of Topology and Symmetry for the Edge Currents of a 2D Superconductor
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866909478788530176 |
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| author | Holst, Maximilian F. Sigrist, Manfred Fischer, Mark H. |
| author_facet | Holst, Maximilian F. Sigrist, Manfred Fischer, Mark H. |
| contents | The bulk-boundary correspondence guarantees topologically protected edge states in a two-dimensional topological superconductor. Unlike in topological insulators, these edge states are, however, not connected to a quantized (spin) current as the electron number is not conserved in a Bogolyubov-de Gennes Hamiltonian. Still, edge currents are in general present. Here, we use the two-dimensional Rashba system as an example to systematically analyze the effect symmetry reductions have on the order-parameter mixing and the edge properties in a superconductor of Altland-Zirnbauer class DIII (time-reversal-symmetry preserving) and D (time-reversal-symmetry breaking). In particular, we employ both Ginzburg-Landau and microscopic modeling to analyze the bulk superconducting properties and edge currents appearing in a strip geometry. We find edge (spin) currents independent of bulk topology and associated topological edge states which evolve continuously even when going through a phase transition into a topological state. Our findings emphasize the importance of symmetry over topology for the understanding of the non-quantized edge currents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_12337 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Role of Topology and Symmetry for the Edge Currents of a 2D Superconductor Holst, Maximilian F. Sigrist, Manfred Fischer, Mark H. Superconductivity The bulk-boundary correspondence guarantees topologically protected edge states in a two-dimensional topological superconductor. Unlike in topological insulators, these edge states are, however, not connected to a quantized (spin) current as the electron number is not conserved in a Bogolyubov-de Gennes Hamiltonian. Still, edge currents are in general present. Here, we use the two-dimensional Rashba system as an example to systematically analyze the effect symmetry reductions have on the order-parameter mixing and the edge properties in a superconductor of Altland-Zirnbauer class DIII (time-reversal-symmetry preserving) and D (time-reversal-symmetry breaking). In particular, we employ both Ginzburg-Landau and microscopic modeling to analyze the bulk superconducting properties and edge currents appearing in a strip geometry. We find edge (spin) currents independent of bulk topology and associated topological edge states which evolve continuously even when going through a phase transition into a topological state. Our findings emphasize the importance of symmetry over topology for the understanding of the non-quantized edge currents. |
| title | Role of Topology and Symmetry for the Edge Currents of a 2D Superconductor |
| topic | Superconductivity |
| url | https://arxiv.org/abs/2108.12337 |