Electron-phonon coupling induced topological phase transition in an $α$-$T_{3}$ Haldane-Holstein model
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arXiv
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| Format: | Preprint |
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2024
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| author | Islam, Mijanur Bhattacharyya, Kuntal Basu, Saurabh |
| author_facet | Islam, Mijanur Bhattacharyya, Kuntal Basu, Saurabh |
| contents | We present impelling evidence of topological phase transitions induced by electron-phonon (e-ph) coupling in an $α$-$T_3$ Haldane-Holstein model that presents smooth tunability between graphene ($α=0$) and a dice lattice $(α=1)$. The e-ph coupling has been incorporated via the Lang-Firsov transformation which adequately captures the polaron physics in the high frequency (anti-adiabatic) regime, and yields an effective Hamiltonian of the system through zero phonon averaging at $T=0$. While exploring the signature of the phase transition driven by polaron and its interplay with the parameter $α$, we identify two regions based on the values of $α$, namely, the low to intermediate range $(0 < α\le 0.6)$ and larger values of $α~(0.6 < α< 1)$ where the topological transitions show distinct behaviour. There exists a single critical e-ph coupling strength for the former, below which the system behaves as a topological insulator characterized by edge modes, finite Chern number, and Hall conductivity, with all of them vanishing above this value, and the system undergoes a spectral gap closing transition. Further, the critical coupling strength depends upon $α$. For the latter case $(0.6 < α< 1)$, the scenario is more interesting where there are two critical values of the e-ph coupling at which trivial-topological-trivial and topological-topological-trivial phase transitions occur for $α$ in the range $[0.6:1]$. Our studies on e-ph coupling induced phase transitions show a significant difference with regard to the well-known unique transition occurring at $α= 0.5$ (or at $0.7$) in the absence of the e-ph coupling, and thus underscore the importance of interaction effects on the topological phase transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08467 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Electron-phonon coupling induced topological phase transition in an $α$-$T_{3}$ Haldane-Holstein model Islam, Mijanur Bhattacharyya, Kuntal Basu, Saurabh Mesoscale and Nanoscale Physics We present impelling evidence of topological phase transitions induced by electron-phonon (e-ph) coupling in an $α$-$T_3$ Haldane-Holstein model that presents smooth tunability between graphene ($α=0$) and a dice lattice $(α=1)$. The e-ph coupling has been incorporated via the Lang-Firsov transformation which adequately captures the polaron physics in the high frequency (anti-adiabatic) regime, and yields an effective Hamiltonian of the system through zero phonon averaging at $T=0$. While exploring the signature of the phase transition driven by polaron and its interplay with the parameter $α$, we identify two regions based on the values of $α$, namely, the low to intermediate range $(0 < α\le 0.6)$ and larger values of $α~(0.6 < α< 1)$ where the topological transitions show distinct behaviour. There exists a single critical e-ph coupling strength for the former, below which the system behaves as a topological insulator characterized by edge modes, finite Chern number, and Hall conductivity, with all of them vanishing above this value, and the system undergoes a spectral gap closing transition. Further, the critical coupling strength depends upon $α$. For the latter case $(0.6 < α< 1)$, the scenario is more interesting where there are two critical values of the e-ph coupling at which trivial-topological-trivial and topological-topological-trivial phase transitions occur for $α$ in the range $[0.6:1]$. Our studies on e-ph coupling induced phase transitions show a significant difference with regard to the well-known unique transition occurring at $α= 0.5$ (or at $0.7$) in the absence of the e-ph coupling, and thus underscore the importance of interaction effects on the topological phase transitions. |
| title | Electron-phonon coupling induced topological phase transition in an $α$-$T_{3}$ Haldane-Holstein model |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2404.08467 |