标题： 强耦合电子-玻色子超导体中$T_c$的上界 显示英文标题

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

摘要： 米格达-伊利亚舍夫（Migdal-Eliashberg）理论（METh）描述由玻色子介导的超导性，在临界温度 $\sqrt{\lambda}$ 处存在 $T_c$ 发散现象，当电子-玻色子耦合较强时表现为 $\lambda$。 在常规的METh中，只有在 $\lambda_E = \lambda \, \omega_D/\varepsilon_F\ll1$ 的极限情况下才能进入强耦合区域，其中 $\omega_D$ 是德拜频率，$\varepsilon_F$ 是费米能级。 在这里，我们突破了这一限制，讨论二维约化杨-SYK（Y-SYK）模型，在此模型中，对于任意值的 $\lambda_E$ 都是可解的。 我们发现，对于较大的 $\lambda$，$T_c\approx 0.18 \,\omega_D \sqrt{\lambda}$ 在 $\lambda_E$ 保持较小的情况下成立，并在 $\lambda_E$ 较大时交叉到一个普遍的 $T_c \approx 0.04\, \varepsilon_F$ 值。 $T_c$ 的饱和是由于对大 $\lambda_E$ 下玻色子动力学的自洽处理，且在理论上被认为在 Y-SYK 框架之外也具有定性有效性。 特别是，根据$\lambda$的值，这种自洽方法导致描述多重量子临界电子系统类别的配对。 这些结果展示了在 METh 中$T_c$的$\sqrt{\lambda}$增长如何饱和到一个与$\lambda$和$\omega_D$无关的普适值，从而为强电子-玻色子耦合下的临界温度提供了上限。 显示英文摘要

摘要： Migdal-Eliashberg theory (METh) of boson-mediated superconductivity contains a $\sqrt{\lambda}$ divergence in the critical temperature $T_c$ at strong electron-boson coupling $\lambda$. In conventional METh, the strong-coupling regime can be accessed only in the limit that $\lambda_E = \lambda \, \omega_D/\varepsilon_F\ll1$, where $\omega_D$ 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 $\lambda_E$. We find that $T_c\approx 0.18 \,\omega_D \sqrt{\lambda}$ for large $\lambda$, provided $\lambda_E$ remains small, and crosses over to a universal value of $T_c \approx 0.04\, \varepsilon_F$ for large $\lambda_E$. The saturation of $T_c$ is due to a self-consistent account of the boson dynamics for large $\lambda_E$ and is arguably qualitatively valid beyond the Y-SYK framework. In particular, depending on the value of $\lambda$, this self-consistent approach leads to pairing that describes multiple classes of quantum critical electronic systems. These results demonstrate how the $\sqrt{\lambda}$ growth of $T_c$ in METh saturates to a universal value independent of $\lambda$ and $\omega_D$, providing an upper bound on the critical temperature at strong electron-boson coupling.