Probing topological degeneracy on a torus using superconducting altermagnets

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Heung, Tsz Fung, Franz, Marcel
Natura: Preprint
Pubblicazione: 2024
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866915036492988416
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