Majorana edge states in Kitaev chains of the BDI symmetry class
Majorana edge states in Kitaev chains possessing an effective time reversal symmetry with one fermionic site per unit cell are studied. For a semi-infinite chain the equations for the wave functions of Majorana zero modes can be reduced to a single Wiener-Hopf equation, which has an exact analytical...
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| Format: | Article |
| Language: | English |
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SciPost
2023-11-01
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| Series: | SciPost Physics Core |
| Online Access: | https://scipost.org/SciPostPhysCore.6.4.080 |
| _version_ | 1797625405528604672 |
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| author | Anton Bespalov |
| author_facet | Anton Bespalov |
| author_sort | Anton Bespalov |
| collection | DOAJ |
| description | Majorana edge states in Kitaev chains possessing an effective time reversal symmetry with one fermionic site per unit cell are studied. For a semi-infinite chain the equations for the wave functions of Majorana zero modes can be reduced to a single Wiener-Hopf equation, which has an exact analytical solution. We use this solution to determine the asymptotic behaviors of the Majorana wave functions at large distances from the edge of the chain for several infinite-range models described in the literature with focus on a model with slow power-law falloff of pairing and hopping amplitudes. For these models we also determine the asymptotic behavior of the energy of the fermionic state composed of two Majorana modes in the limit of long (finite) Kitaev chains. |
| first_indexed | 2024-03-11T09:56:06Z |
| format | Article |
| id | doaj.art-884ea2a47c6e4fe7b37566d081bbda06 |
| institution | Directory Open Access Journal |
| issn | 2666-9366 |
| language | English |
| last_indexed | 2024-03-11T09:56:06Z |
| publishDate | 2023-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Core |
| spelling | doaj.art-884ea2a47c6e4fe7b37566d081bbda062023-11-16T15:45:56ZengSciPostSciPost Physics Core2666-93662023-11-016408010.21468/SciPostPhysCore.6.4.080Majorana edge states in Kitaev chains of the BDI symmetry classAnton BespalovMajorana edge states in Kitaev chains possessing an effective time reversal symmetry with one fermionic site per unit cell are studied. For a semi-infinite chain the equations for the wave functions of Majorana zero modes can be reduced to a single Wiener-Hopf equation, which has an exact analytical solution. We use this solution to determine the asymptotic behaviors of the Majorana wave functions at large distances from the edge of the chain for several infinite-range models described in the literature with focus on a model with slow power-law falloff of pairing and hopping amplitudes. For these models we also determine the asymptotic behavior of the energy of the fermionic state composed of two Majorana modes in the limit of long (finite) Kitaev chains.https://scipost.org/SciPostPhysCore.6.4.080 |
| spellingShingle | Anton Bespalov Majorana edge states in Kitaev chains of the BDI symmetry class SciPost Physics Core |
| title | Majorana edge states in Kitaev chains of the BDI symmetry class |
| title_full | Majorana edge states in Kitaev chains of the BDI symmetry class |
| title_fullStr | Majorana edge states in Kitaev chains of the BDI symmetry class |
| title_full_unstemmed | Majorana edge states in Kitaev chains of the BDI symmetry class |
| title_short | Majorana edge states in Kitaev chains of the BDI symmetry class |
| title_sort | majorana edge states in kitaev chains of the bdi symmetry class |
| url | https://scipost.org/SciPostPhysCore.6.4.080 |
| work_keys_str_mv | AT antonbespalov majoranaedgestatesinkitaevchainsofthebdisymmetryclass |