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arXiv 2004.13220cond-mat.str-elcond-mat.supr-con
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在金属量子临界点超导性和非费米液体之间的相互作用。I:$γ$ -模型及其在$T=0$的phase diagram。案例$0 < γ<1$

Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. I: The $γ$-model and its phase diagram at $T=0$. The case $0 < γ<1$

Artem Abanov, Andrey V. Chubukov

摘要:

我们分析了一类量子临界模型,其中动量积分和选择一个特定的配对对称性可以明确地完成,和非费米液体和配对之间的竞争可以分析在一个有效的模型与动态电子-电子相互作用$V(Ω_m)\sim 1/|Ω_m|^γ$($γ$ -模型)。在本文中,在该系列的第一,我们考虑的情况下$T=0$和$0<γ<1$。我们认为,配对的倾向更强,基态是超导体。然而,我们认为,超导态是高度非平凡的,因为存在一组离散的拓扑不同的解决方案的配对间隙$Δ_n (ω_m)$($n = 0, 1, 2..., \infty$)。所有的解决方案具有相同的空间配对对称性,但在时域不同:$Δ_n (ω_m)$改变符号$n$时间作为松原频率$ω_m$的函数。$n =0$解$Δ_0 (ω_m)$是符号保持的,并且在$ω_m =0$处趋向于有限值,就像BCS理论中一样。$n = \infty$解对应于无穷小的$Δ(ω_m)$。作为证明,我们得到了在$T=0$上线性化能隙方程在整个频率轴上的精确解,以及非线性能隙方程的近似解,我们认为,无限多解的存在开辟了一个新的能隙涨落通道。我们将分析扩展到相互作用的配对分量具有附加因子$1/N$的情况,并表明存在一个临界$N_{cr} >1$,超过该临界,超导性消失,基态变为非费米液体.

英文摘要:

We analyze a class of quantum-critical models, in which momentum integration and the selection of a particular pairing symmetry can be done explicitly, and the competition between non-Fermi liquid and pairing can be analyzed within an effective model with dynamical electron-electron interaction $V(Ω_m)\sim 1/|Ω_m|^γ$ (the $γ$-model). In this paper, the first in the series, we consider the case $T=0$ and $0<γ<1$. We argue that tendency to pairing is stronger, and the ground state is a superconductor. We argue, however, that superconducting state is highly non-trivial as there exists a discrete set of topologically distinct solutions for the pairing gap $Δ_n (ω_m)$ ($n = 0, 1, 2..., \infty$). All solutions have the same spatial pairing symmetry, but differ in the time domain: $Δ_n (ω_m)$ changes sign $n$ times as a function of Matsubara frequency $ω_m$. The $n =0$ solution $Δ_0 (ω_m)$ is sign-preserving and tends to a finite value at $ω_m =0$, like in BCS theory. The $n = \infty$ solution corresponds to an infinitesimally small $Δ(ω_m)$. As a proof, we obtain the exact solution of the linearized gap equation at $T=0$ on the entire frequency axis for all $0<γ<1$, and an approximate solution of the non-linear gap equation.We argue that the presence of an infinite set of solutions opens up a new channel of gap fluctuations. We extend the analysis to the case where the pairing component of the interaction has additional factor $1/N$ and show that there exists a critical $N_{cr} >1$, above which superconductivity disappears, and the ground state becomes a non-Fermi liquid.We show that all solutions develop simultaneously once $N$ gets smaller than $N_{cr}$.

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