Exact analytical solution of a time-reversal-invariant topological superconducting wire
We consider a model proposed before for a time-reversal-invariant topological superconductor which contains a hopping term t, a chemical potential μ, an extended s-wave pairing Δ, and spin-orbit coupling λ. We show that for |Δ|=|λ|, μ=t=0, the model has an exact analytical solution defining new ferm...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/147416 |
| Acceso en línea: | http://hdl.handle.net/11336/147416 |
| Access Level: | acceso abierto |
| Palabra clave: | SUPERCONDUCTOR TOPOLOGICAL EXACT SOLUTION https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
| Sumario: | We consider a model proposed before for a time-reversal-invariant topological superconductor which contains a hopping term t, a chemical potential μ, an extended s-wave pairing Δ, and spin-orbit coupling λ. We show that for |Δ|=|λ|, μ=t=0, the model has an exact analytical solution defining new fermion operators involving nearest-neighbor sites. The many-body ground state is fourfold degenerate due to the existence of two zero-energy modes localized exactly at the first and last sites of the chain. These four states show entanglement in the sense that creating or annihilating a zero-energy mode at the first site is proportional to a similar operation at the last site. By continuity, this property should persist for general parameters. Using these results, we discuss some statements related to the so-called time-reversal anomaly. The addition of a small hopping term t for a chain with an even number of sites breaks the degeneracy, and the ground state becomes unique with an even number of particles. We also consider a small magnetic field B applied to one end of the chain. We compare the many-body excitation energies and spin projection along the spin-orbit direction for both ends of the chains obtained treating t and B as small perturbations with numerical results in a short chain, obtaining good agreement. |
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