Superconducting Analogue of the Parafermion Fractional Quantum Hall States
Read-Rezayi Z_{k} parafermion wave functions describe ν=2+(k/kM+2) fractional quantum Hall (FQH) states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this paper, we...
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| Format: | Article |
| Language: | English |
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American Physical Society
2014-07-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.4.031009 |
| _version_ | 1818825454139736064 |
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| author | Abolhassan Vaezi |
| author_facet | Abolhassan Vaezi |
| author_sort | Abolhassan Vaezi |
| collection | DOAJ |
| description | Read-Rezayi Z_{k} parafermion wave functions describe ν=2+(k/kM+2) fractional quantum Hall (FQH) states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this paper, we study the ν=2/k FQH-superconductor heterostructure and find the superconducting analogue of the Z_{k} parafermion FQH state. Our main tool is the mapping of the FQH into coupled one-dimensional chains, each with a pair of counterpropagating modes. We show that by inducing intrachain pairing and charge preserving backscattering with identical couplings, the one-dimensional chains flow into gapless Z_{k} parafermions when k<4. By studying the effect of interchain coupling, we show that every parafermion mode becomes massive except for the two outermost ones. Thus, we achieve a fractional topological superconductor whose chiral edge state is described by a Z_{k} parafermion conformal field theory. For instance, we find that a ν=2/3 FQH in proximity to a superconductor produces a Z_{3} parafermion superconducting state. This state is topologically indistinguishable from the non-Abelian part of the ν=12/5 Read-Rezayi state. Both of these systems can host Fibonacci anyons capable of performing universal quantum computation through braiding operations. |
| first_indexed | 2024-12-19T00:12:01Z |
| format | Article |
| id | doaj.art-0807e83b5a2f4a7f9840b941c2876edb |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-19T00:12:01Z |
| publishDate | 2014-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-0807e83b5a2f4a7f9840b941c2876edb2022-12-21T20:45:59ZengAmerican Physical SocietyPhysical Review X2160-33082014-07-014303100910.1103/PhysRevX.4.031009Superconducting Analogue of the Parafermion Fractional Quantum Hall StatesAbolhassan VaeziRead-Rezayi Z_{k} parafermion wave functions describe ν=2+(k/kM+2) fractional quantum Hall (FQH) states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this paper, we study the ν=2/k FQH-superconductor heterostructure and find the superconducting analogue of the Z_{k} parafermion FQH state. Our main tool is the mapping of the FQH into coupled one-dimensional chains, each with a pair of counterpropagating modes. We show that by inducing intrachain pairing and charge preserving backscattering with identical couplings, the one-dimensional chains flow into gapless Z_{k} parafermions when k<4. By studying the effect of interchain coupling, we show that every parafermion mode becomes massive except for the two outermost ones. Thus, we achieve a fractional topological superconductor whose chiral edge state is described by a Z_{k} parafermion conformal field theory. For instance, we find that a ν=2/3 FQH in proximity to a superconductor produces a Z_{3} parafermion superconducting state. This state is topologically indistinguishable from the non-Abelian part of the ν=12/5 Read-Rezayi state. Both of these systems can host Fibonacci anyons capable of performing universal quantum computation through braiding operations.http://doi.org/10.1103/PhysRevX.4.031009 |
| spellingShingle | Abolhassan Vaezi Superconducting Analogue of the Parafermion Fractional Quantum Hall States Physical Review X |
| title | Superconducting Analogue of the Parafermion Fractional Quantum Hall States |
| title_full | Superconducting Analogue of the Parafermion Fractional Quantum Hall States |
| title_fullStr | Superconducting Analogue of the Parafermion Fractional Quantum Hall States |
| title_full_unstemmed | Superconducting Analogue of the Parafermion Fractional Quantum Hall States |
| title_short | Superconducting Analogue of the Parafermion Fractional Quantum Hall States |
| title_sort | superconducting analogue of the parafermion fractional quantum hall states |
| url | http://doi.org/10.1103/PhysRevX.4.031009 |
| work_keys_str_mv | AT abolhassanvaezi superconductinganalogueoftheparafermionfractionalquantumhallstates |