Collective mode across the BCS-BEC crossover in Holstein model
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arXiv
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| Format: | Preprint |
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2024
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| author | Park, Tae-Ho Choi, Han-Yong |
| author_facet | Park, Tae-Ho Choi, Han-Yong |
| contents | We investigate the emergence of the collective mode in the phonon spectra of the superconducting state within the Holstein model by varying the electron-phonon coupling. Using dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG) technique, we calculate the phonon spectra. In the superconducting state with a pairing gap ($Δ_P$), the peak position of the collective mode ($ω_{col}$) evolves from the Bardeen-Cooper-Schrieffer (BCS) regime, manifesting near $2Δ_P$ and increasing with coupling, to the Bose-Einstein condensation (BEC) regime, where $ω_{col}$ decreases with increasing coupling. The decrease of $ω_{col}$ matches well with the reduction of superfluid stiffness, which originates from the increasing phase fluctuations of local pairs with coupling strength. In the crossover regime with intermediate coupling, $ω_{col}$ aligns with the soft phonon mode ($ω_s$) of the normal state and decreases with increasing coupling when $ω_s < 2Δ_P$. Additionally, comparing the collective mode weight to $Δ_P$ suggests that the collective mode predominantly stems from U(1) gauge symmetry breaking across all coupling strengths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14782 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Collective mode across the BCS-BEC crossover in Holstein model Park, Tae-Ho Choi, Han-Yong Superconductivity Strongly Correlated Electrons We investigate the emergence of the collective mode in the phonon spectra of the superconducting state within the Holstein model by varying the electron-phonon coupling. Using dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG) technique, we calculate the phonon spectra. In the superconducting state with a pairing gap ($Δ_P$), the peak position of the collective mode ($ω_{col}$) evolves from the Bardeen-Cooper-Schrieffer (BCS) regime, manifesting near $2Δ_P$ and increasing with coupling, to the Bose-Einstein condensation (BEC) regime, where $ω_{col}$ decreases with increasing coupling. The decrease of $ω_{col}$ matches well with the reduction of superfluid stiffness, which originates from the increasing phase fluctuations of local pairs with coupling strength. In the crossover regime with intermediate coupling, $ω_{col}$ aligns with the soft phonon mode ($ω_s$) of the normal state and decreases with increasing coupling when $ω_s < 2Δ_P$. Additionally, comparing the collective mode weight to $Δ_P$ suggests that the collective mode predominantly stems from U(1) gauge symmetry breaking across all coupling strengths. |
| title | Collective mode across the BCS-BEC crossover in Holstein model |
| topic | Superconductivity Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2411.14782 |