论文标题
在金属中的量子临界点处的超导性与非Fermi液体之间的相互作用。 ii。 $γ$ - 模型在有限$ t $的$ 0 <γ<1 $的
Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal. II. The $γ$-model at a finite $T$ for $0<γ<1$
论文作者
论文摘要
在本文中，我们继续分析量子 - 关键系统的非Fermi液体与超导性之间的相互作用，其低能物理学的描述是由具有动态电子电子相互作用的有效模型来描述的。在纸上我[A。 Abanov和A. V. Chubukov，Phys Rev B. 102，024524（2020）]我们两个人分析了$ t = 0 $的$γ$模型，$ t = 0 $，$ 0 <γ<1 $，并认为存在一个离散的，无限的，无限的拓扑在超跟踪间隙的拓扑差异，所有这些都具有相同的spatialsmetlemermetermemermemermetery。 $ n $ th解决方案的间隙函数$δ_n（ω_m）$会随着Matsubara频率的功能而更改标志$ n $ timpers。在本文中，我们分析了有限$ t $的线性差距方程。我们表明，存在一组无限的配对不稳定性温度，$ t_ {p，n} $和eigenFunction $Δ_n（ω__{m}）$变化符号$ n $ timess $ n $ timper timper timper timess的功能。我们认为$δ_n（ω_{m}）$在$ t_ {p，n} $下保留其功能表格，并且在$ t = 0 $下与非线性间隙方程的$ n $ th解决方案相吻合。像纸上I一样，我们将模型扩展到与粒子孔通道中的相比，配对通道中的相互作用具有额外的因子$ 1/n $的情况。我们表明$ t_ {p，0} $在大$ n $上保持有限，这是由于带有matsubara频率的费米子的特殊属性$ \pmπt$，但所有其他$ t_ {p，n} $终止于$ n_ {cr} = o（1）$。对于$ n> n_ {cr} $，差距函数在$ t \ to 0 $中消失，并且对于$ n <n_ {cr} $仍然有限。这与$ t = 0 $分析一致。
In this paper we continue the analysis of the interplay between non-Fermi liquid and superconductivity for quantum-critical systems, the low-energy physics of which is described by an effective model with dynamical electron-electron interaction $V(Ω_m) \propto 1/|Ω_m|^γ$ (the $γ$ model). In paper I [A. Abanov and A. V. Chubukov, Phys Rev B. 102, 024524 (2020)] two of us analyzed the $γ$ model at $T=0$ for $0<γ<1$ and argued that there exist a discrete, infinite set of topologically distinct solutions for the superconducting gap, all with the same spatial symmetry. The gap function $Δ_n (ω_m)$ for the $n$th solution changes sign $n$ times as the function of Matsubara frequency. In this paper we analyze the linearized gap equation at a finite $T$. We show that there exist an infinite set of pairing instability temperatures, $T_{p,n}$, and the eigenfunction $Δ_n (ω_{m})$ changes sign $n$ times as a function of a Matsubara number $m$. We argue that $Δ_n (ω_{m})$ retains its functional form below $T_{p,n}$ and at $T=0$ coincides with the $n$th solution of the nonlinear gap equation. Like in paper I, we extend the model to the case when the interaction in the pairing channel has an additional factor $1/N$ compared to that in the particle-hole channel. We show that $T_{p,0}$ remains finite at large $N$ due to special properties of fermions with Matsubara frequencies $\pm πT$, but all other $T_{p,n}$ terminate at $N_{cr} = O(1)$. The gap function vanishes at $T \to 0$ for $N > N_{cr}$ and remains finite for $N < N_{cr}$. This is consistent with the $T =0$ analysis.
