标题： 超导性开始时量子临界金属中配对敏感度的非BCS行为 显示英文标题

标题： Non-BCS behavior of the pairing susceptibility near the onset of superconductivity in a quantum-critical metal

摘要： 我们分析量子临界金属中动力配对敏感度$\chi_{pp} (\omega_m)$在$T=0$的情况，其中超导性在配对相互作用超过一定阈值后从非费米液体基态出现。 我们得到$\chi_{pp} (\omega_m)$作为完全修饰的动力配对顶点$\Phi (\omega_m)$与裸露的$\Phi_0 (\omega_m)$的比值（两者都极小）。 对于从费米液体出发的超导性，配对敏感度在$T_c$以上为正，在$T_c$处发散，并在其以下变为负。 对于非费米液体之外的超导性，$\chi_{pp} (\omega_m)$的行为在两个方面有所不同：(i) 它仅在某些原始$\Phi_0 (\omega_m)$的子类中在成对开始时在$T=0$处发散，并且在其他$\Phi_0 (\omega_m)$中保持非奇异，(ii) 在不稳定性之下，它成为连续参数$\phi$的非唯一函数，对于任意的$\Phi_0 (\omega_m)$都如此。 在某些范围内的$\phi$中，磁化率是负的，并在该范围的边界处发散。 我们认为，磁化率的这种行为反映了量子临界金属中超导转变的多重临界性质，当不稳定性之下，无限多个超导态同时出现，具有不同幅度的序参量，直到极小的一个。 显示英文摘要

摘要： We analyze the dynamical pairing susceptibility $\chi_{pp} (\omega_m)$ at $T=0$ in a quantum-critical metal, where superconductivity emerges out of a non-Fermi liquid ground state once the pairing interaction exceeds a certain threshold. We obtain $\chi_{pp} (\omega_m)$ as the ratio of the fully dressed dynamical pairing vertex $\Phi (\omega_m)$ and the bare $\Phi_0 (\omega_m)$ (both infinitesimally small). For superconductivity out of a Fermi liquid, the pairing susceptibility is positive above $T_c$, diverges at $T_c$, and becomes negative below it. For superconductivity out of a non-Fermi liquid, the behavior of $\chi_{pp} (\omega_m)$ is different in two aspects: (i) it diverges at the onset of pairing at $T=0$ only for a certain subclass of bare $\Phi_0 (\omega_m)$ and remains non-singular for other $\Phi_0 (\omega_m)$, and (ii) below the instability, it becomes a non-unique function of a continuous parameter $\phi$ for an arbitrary $\Phi_0 (\omega_m)$. The susceptibility is negative in some range of $\phi$ and diverges at the boundary of this range. We argue that this behavior of the susceptibility reflects a multi-critical nature of a superconducting transition in a quantum-critical metal when immediately below the instability an infinite number of superconducting states emerges simultaneously with different amplitudes of the order parameter down to an infinitesimally small one.