### Abstract

We study an extended Aubry-André-Harper model with simultaneous modulation of hopping on-site potential and p-wave superconducting pairing. For the case of commensurate modulation of β=1/2 it is shown that the model hosts four different types of topological states: Adiabatic cycles can be defined which pump particles two types of Majorana fermions or Cooper pairs. In the incommensurate case we calculate the phase diagram of the model in several regions. We characterize the phases by calculating the mean inverse participation ratio and perform multifractal analysis. In addition we characterize whether the phases found are topologically trivial or not. We find an interesting critical extended phase when incommensurate hopping modulation is present. The rise between the inverse participation ratio in regions separating localized and extended states is gradual rather than sharp. When in addition the on-site potential modulation is incommensurate we find several sharp rises and falls in the inverse participation ratio. In these two cases all different phases exhibit topological edge states. For the commensurate case we calculate the evolution of the Hofstadter butterfly and the band Chern numbers upon variation of the pairing parameter for zero and finite on-site potential. For zero on-site potential the butterflies are triangularlike near zero pairing when gap closure occurs they are squarelike and hexagonal-like for larger pairing but with the Chern numbers switched compared to the triangular case. For the finite case gaps at quarter and three-quarters filling close and lead to a switch in Chern numbers.

Original language | English |
---|---|

Article number | 064202 |

Journal | Physical Review B |

Volume | 100 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2019 Aug 12 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B*,

*100*(6), [064202]. https://doi.org/10.1103/PhysRevB.100.064202

}

*Physical Review B*, vol. 100, no. 6, 064202. https://doi.org/10.1103/PhysRevB.100.064202

**Generalized Aubry-André-Harper model with modulated hopping and p -wave pairing.** / Yahyavi, M.; Hetényi, B.; Tanatar, B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Generalized Aubry-André-Harper model with modulated hopping and p -wave pairing

AU - Yahyavi, M.

AU - Hetényi, B.

AU - Tanatar, B.

PY - 2019/8/12

Y1 - 2019/8/12

N2 - We study an extended Aubry-André-Harper model with simultaneous modulation of hopping on-site potential and p-wave superconducting pairing. For the case of commensurate modulation of β=1/2 it is shown that the model hosts four different types of topological states: Adiabatic cycles can be defined which pump particles two types of Majorana fermions or Cooper pairs. In the incommensurate case we calculate the phase diagram of the model in several regions. We characterize the phases by calculating the mean inverse participation ratio and perform multifractal analysis. In addition we characterize whether the phases found are topologically trivial or not. We find an interesting critical extended phase when incommensurate hopping modulation is present. The rise between the inverse participation ratio in regions separating localized and extended states is gradual rather than sharp. When in addition the on-site potential modulation is incommensurate we find several sharp rises and falls in the inverse participation ratio. In these two cases all different phases exhibit topological edge states. For the commensurate case we calculate the evolution of the Hofstadter butterfly and the band Chern numbers upon variation of the pairing parameter for zero and finite on-site potential. For zero on-site potential the butterflies are triangularlike near zero pairing when gap closure occurs they are squarelike and hexagonal-like for larger pairing but with the Chern numbers switched compared to the triangular case. For the finite case gaps at quarter and three-quarters filling close and lead to a switch in Chern numbers.

AB - We study an extended Aubry-André-Harper model with simultaneous modulation of hopping on-site potential and p-wave superconducting pairing. For the case of commensurate modulation of β=1/2 it is shown that the model hosts four different types of topological states: Adiabatic cycles can be defined which pump particles two types of Majorana fermions or Cooper pairs. In the incommensurate case we calculate the phase diagram of the model in several regions. We characterize the phases by calculating the mean inverse participation ratio and perform multifractal analysis. In addition we characterize whether the phases found are topologically trivial or not. We find an interesting critical extended phase when incommensurate hopping modulation is present. The rise between the inverse participation ratio in regions separating localized and extended states is gradual rather than sharp. When in addition the on-site potential modulation is incommensurate we find several sharp rises and falls in the inverse participation ratio. In these two cases all different phases exhibit topological edge states. For the commensurate case we calculate the evolution of the Hofstadter butterfly and the band Chern numbers upon variation of the pairing parameter for zero and finite on-site potential. For zero on-site potential the butterflies are triangularlike near zero pairing when gap closure occurs they are squarelike and hexagonal-like for larger pairing but with the Chern numbers switched compared to the triangular case. For the finite case gaps at quarter and three-quarters filling close and lead to a switch in Chern numbers.

UR - http://www.scopus.com/inward/record.url?scp=85070617870&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070617870&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.100.064202

DO - 10.1103/PhysRevB.100.064202

M3 - Article

AN - SCOPUS:85070617870

VL - 100

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 6

M1 - 064202

ER -