论文标题
在金属中的量子关键点处的超导性与非Fermi液体之间的相互作用。 I：$γ$ - 模型及其相图为$ t = 0 $。 $ 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 $0 < γ<1$
论文作者
论文摘要
我们分析了一类量子 - 关键模型，在这种模型中，可以明确地进行动量整合和特定配对对称性的选择，并且可以在有效的模型中使用动力学电子交互$ v（ω_m）\ sim 1/| | |^$ |^umg（$ sodel）在有效的模型中分析非fermi液体与配对之间的竞争。在本文中，我们考虑了$ t = 0 $和$ 0 <γ<1 $的情况。我们认为配对的趋势更强，基态是超导体。但是，我们认为，由于存在一个离散的拓扑差距$Δ_n（ω_m）$（$ n = 0，1，2 ...，\ infty $），超导状态是高度不平凡的。所有解决方案都具有相同的空间配对对称性，但时间域不同：$δ_n（ω_m）$更改标志$ n $ timper $ n $ timper timper timper timper timper timper y Matsubara频率$ω_m$。 $ n = 0 $ solution $δ_0（ω_m）$是签名的，并且趋向于$ω_m= 0 $的有限值，例如BCS理论。 $ n = \ infty $解决方案对应于无穷小的$δ（ω_m）$。作为证明，我们在整个$ 0 <γ<1 $的整个频率轴上获得了线性化间隙方程的精确解决方案，以及非线性间隙方程的近似解决方案。我们认为，无限的解决方案的存在会打开差距波动的新通道。我们将分析扩展到相互作用的配对组件具有附加因子$ 1/n $的情况下，并表明存在关键的$ n_ {cr}> 1 $，在此上面超过1 $，超导率消失了，基态将成为非fermi液体。我们显示所有解决方案一旦$ n $都会同时发生$ n $，$ n $都会变得小于$ n_ $ n_ {cr} $ {cr} $。
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 $N_{cr}$.
