Probing topological degeneracy on a torus using superconducting altermagnets
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915036492988416 |
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| author | Heung, Tsz Fung Franz, Marcel |
| author_facet | Heung, Tsz Fung Franz, Marcel |
| contents | The notion of topological order (TO) can be defined through the characteristic ground state degeneracy of a system placed on a manifold with non-zero genus $g$, such as a torus. This ground state degeneracy has served as a key tool for identifying TOs in theoretical calculations but it has never been possible to probe experimentally because fabricating a device in the requisite toroidal geometry is generally not feasible. Here we discuss a practical method that can be used to overcome this difficulty in a class of topologically ordered systems that consist of a TO and its time reversal conjugate $\overline{\rm TO}$. The key insight is that a system possessing such ${\rm TO}\otimes\overline{\rm TO}$ order fabricated on an annulus behaves effectively as TO on a torus, provided that one supplies a symmetry-breaking perturbation that gaps out the edge modes. We illustrate this general principle using a specific example of a spin-polarized $p_x\pm ip_y$ chiral superconductor which is closely related to the Moore-Read Pfaffian fractional quantum Hall state. Specifically, we introduce a simple model with altermagnetic normal state which, in the presence of an attractive interaction, hosts a helical $(p_x-ip_y)^\uparrow\otimes(p_x+ip_y)^\downarrow$ superconducting ground state. We demonstrate that when placed on an annulus with the appropriate symmetry-breaking edge perturbation this planar two-dimensional system, remarkably, exhibits the same pattern of ground state degeneracy as a $p_x+ ip_y$ superconductor on a torus. We discuss broader implications of this behavior and ways it can be tested experimentally. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probing topological degeneracy on a torus using superconducting altermagnets Heung, Tsz Fung Franz, Marcel Superconductivity Mesoscale and Nanoscale Physics Strongly Correlated Electrons The notion of topological order (TO) can be defined through the characteristic ground state degeneracy of a system placed on a manifold with non-zero genus $g$, such as a torus. This ground state degeneracy has served as a key tool for identifying TOs in theoretical calculations but it has never been possible to probe experimentally because fabricating a device in the requisite toroidal geometry is generally not feasible. Here we discuss a practical method that can be used to overcome this difficulty in a class of topologically ordered systems that consist of a TO and its time reversal conjugate $\overline{\rm TO}$. The key insight is that a system possessing such ${\rm TO}\otimes\overline{\rm TO}$ order fabricated on an annulus behaves effectively as TO on a torus, provided that one supplies a symmetry-breaking perturbation that gaps out the edge modes. We illustrate this general principle using a specific example of a spin-polarized $p_x\pm ip_y$ chiral superconductor which is closely related to the Moore-Read Pfaffian fractional quantum Hall state. Specifically, we introduce a simple model with altermagnetic normal state which, in the presence of an attractive interaction, hosts a helical $(p_x-ip_y)^\uparrow\otimes(p_x+ip_y)^\downarrow$ superconducting ground state. We demonstrate that when placed on an annulus with the appropriate symmetry-breaking edge perturbation this planar two-dimensional system, remarkably, exhibits the same pattern of ground state degeneracy as a $p_x+ ip_y$ superconductor on a torus. We discuss broader implications of this behavior and ways it can be tested experimentally. |
| title | Probing topological degeneracy on a torus using superconducting altermagnets |
| topic | Superconductivity Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2411.17964 |