Upper bound on $T_c$ in a strongly coupled electron-boson superconductor

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Main Authors: Gnezdilov, Nikolay V., Boyack, Rufus
Format: Preprint
Published: 2025
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author Gnezdilov, Nikolay V.
Boyack, Rufus
author_facet Gnezdilov, Nikolay V.
Boyack, Rufus
contents Migdal-Eliashberg theory of boson-mediated superconductivity contains a $\sqrtλ$ divergence in the critical temperature $T_c$ for strong electron-boson coupling $λ$. In the conventional Migdal-Eliashberg theory, the strong-coupling regime can be accessed only in the limit that $λ_E = λ\, ω_D/\varepsilon_F\ll1$, where $ω_D$ is the Debye frequency and $\varepsilon_F$ is the Fermi energy. Here we go beyond this restriction in the context of the two-dimensional Yukawa-SYK (Y-SYK) model, which is solvable for arbitrary values of $λ_E$. We find that $T_c\approx 0.18 \,ω_D \sqrtλ$ for large $λ$, provided $λ_E$ remains small, and crosses over to a universal value of $T_c \approx 0.04\, \varepsilon_F$ for large $λ_E$. The saturation of $T_c$ is due to a self-consistent account of the boson dynamics for large $λ_E$ and remains valid provided the vertex corrections are negligible. Depending on the value of $λ$, this self-consistent approach leads to pairing that describes multiple classes of quantum critical electronic systems. These results demonstrate how the $\sqrtλ$ growth of $T_c$ in Migdal-Eliashberg theory saturates to a universal value independent of $λ$ and $ω_D$, providing an upper bound on the critical temperature at strong electron-boson coupling.
format Preprint
id arxiv_https___arxiv_org_abs_2505_02894
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Upper bound on $T_c$ in a strongly coupled electron-boson superconductor
Gnezdilov, Nikolay V.
Boyack, Rufus
Strongly Correlated Electrons
Superconductivity
Migdal-Eliashberg theory of boson-mediated superconductivity contains a $\sqrtλ$ divergence in the critical temperature $T_c$ for strong electron-boson coupling $λ$. In the conventional Migdal-Eliashberg theory, the strong-coupling regime can be accessed only in the limit that $λ_E = λ\, ω_D/\varepsilon_F\ll1$, where $ω_D$ is the Debye frequency and $\varepsilon_F$ is the Fermi energy. Here we go beyond this restriction in the context of the two-dimensional Yukawa-SYK (Y-SYK) model, which is solvable for arbitrary values of $λ_E$. We find that $T_c\approx 0.18 \,ω_D \sqrtλ$ for large $λ$, provided $λ_E$ remains small, and crosses over to a universal value of $T_c \approx 0.04\, \varepsilon_F$ for large $λ_E$. The saturation of $T_c$ is due to a self-consistent account of the boson dynamics for large $λ_E$ and remains valid provided the vertex corrections are negligible. Depending on the value of $λ$, this self-consistent approach leads to pairing that describes multiple classes of quantum critical electronic systems. These results demonstrate how the $\sqrtλ$ growth of $T_c$ in Migdal-Eliashberg theory saturates to a universal value independent of $λ$ and $ω_D$, providing an upper bound on the critical temperature at strong electron-boson coupling.
title Upper bound on $T_c$ in a strongly coupled electron-boson superconductor
topic Strongly Correlated Electrons
Superconductivity
url https://arxiv.org/abs/2505.02894