标题： 超导体中的通用间隙到临界温度比：统计力学视角 显示英文标题

标题： The Universal Gap-to-Critical Temperature Ratio in Superconductors: a Statistical Mechanical Perspective

摘要： 我们提出了一种统计力学框架来统一超导能隙$\Delta$、伪能隙$\Delta^\ast$和临界温度$T_\mathrm{c}$之间的观测关系。在这个模型中，费米子作为复合玻色子耦合，并且随着温度下降而凝聚以占据单一束缚态。 我们推导了一个简洁的公式，用$\Delta$和$\Delta^\ast$表示$T_\mathrm{c}$，即：$$\frac{\Delta}{k_\mathrm{B} T_\mathrm{c}} = 1.4+4\log(\Delta^\ast/\Delta).$$。该表达式在没有伪能隙的情况下重现了标准BCS能隙与$T_\mathrm{c}$的比率，同时自然地解释了非常规超导体中这一比率的增强。 该模型通过与几种铜氧化物和铁基超导体的实验数据比较得到支持，突显了其普适性。 这一表述还为观测到的伪能隙相持续进入过掺杂区域提供了理论解释。 显示英文摘要

摘要： We propose a statistical mechanical framework to unify the observed relationship between the superconducting energy gap $\Delta$, the pseudogap $\Delta^\ast$, and the critical temperature $T_\mathrm{c}$. In this model, fermions couple as a composite boson and condense to occupy a single bound state as the temperature drops. We derive a concise formula for $T_\mathrm{c}$ in terms of $\Delta$ and $\Delta^\ast$, namely: $$\frac{\Delta}{k_\mathrm{B} T_\mathrm{c}} = 1.4+4\log(\Delta^\ast/\Delta).$$ This expression reproduces the standard BCS gap-to-$T_\mathrm{c}$ ratio in the absence of a pseudogap, while naturally explaining its enhancement in unconventional superconductors. The model is supported by comparisons with experimental data from several cuprates and iron-based superconductors, which highlight its generality. This formulation also offers a theoretical explanation for the observed persistence of the pseudogap phase into the overdoped regime.