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。 IV：$γ$型号及其相图为$ 1 <γ<2 $
Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. IV: The $γ$ model and its phase diagram at $1<γ<2$
论文作者
论文摘要
在本文中，我们继续分析一组具有有效的动力学电子 - 电子相互作用$ V（ω_m）\ Propto 1/|ω_m|^γ$的量子 - 临界（QC）系统的配对与非FERMI液体行为之间的相互作用。在以前的论文中，我们研究了$ 0 <γ<1 $和$γ\ \ 1 $的情况。我们认为，无间隙玻色子的配对与大型玻色子的BCS/EliAshberg配对根本不同，而对于前者来说，存在无限数量的GAP函数$Δ_N（ω_m）$ at $ t = 0 $ t = 0 $ n = 0,1,2 $ n = 0,1,2 $ e} $ e $ e $ e e $ e e $ e e $ t $Δ_n（ω_m）$。在这里，我们将分析扩展到更大的$ 1 <γ<2 $。我们认为，随着$γ$接近$ 2 $，$ e_ {c，n} $的频谱逐渐变得越来越浓密，最终以$γ\至2 $连续变得连续。这增加了“纵向”间隙波动的强度，这倾向于减少实际的超导$ t_c $，并引起预成立对的伪gap区域。我们还以$γ> 1 $的价格检测到真实轴上的两个功能，它们在$γ\至2 $时变得至关重要。首先，状态的密度朝着一组离散的$δ-$函数发展。其次，在上半平面上出现了一系列动力涡流。 These two features come about because on a real axis, the real part of the interaction, $V' (Ω) \propto \cos(πγ/2)/|Ω|^γ$, becomes repulsive for $γ>1$, and the imaginary $V^{''} (Ω) \propto \sin(πγ/2)/|Ω|^γ$, gets progressively smaller at $γ\to 2$.真实轴上的功能与使用Matsubara轴上使用$δ_n（ω_m）$获得的$ e_ {c，n} $的连续频谱的开发一致。我们在下一篇论文中分别考虑$γ= 2 $。
In this paper we continue our analysis of the interplay between the pairing and the non-Fermi liquid behavior in a metal for a set of quantum-critical (QC) systems with an effective dynamical electron-electron interaction $V(Ω_m) \propto 1/|Ω_m|^γ$ (the $γ$-model). In previous papers we studied the cases $0<γ<1$ and $γ\approx 1$. We argued that the pairing by a gapless boson is fundamentally different from BCS/Eliashberg pairing by a massive boson as for the former there exists an infinite number of topologically distinct solutions for the gap function $Δ_n (ω_m)$ at $T=0$ ($n=0,1,2...$), each with its own condensation energy $E_{c,n}$. Here we extend the analysis to larger $1< γ<2$. We argue that the discrete set of solutions survives, and the spectrum of $E_{c,n}$ gets progressively denser as $γ$ approaches $2$ and eventually becomes continuous at $γ\to 2$. This increases the strength of "longitudinal" gap fluctuations, which tend to reduce the actual superconducting $T_c$ and give rise to a pseudogap region of preformed pairs. We also detect two features on the real axis for $γ>1$ which become critical at $γ\to 2$. First, the density of states evolves towards a set of discrete $δ-$functions. Second, an array of dynamical vortices emerges in the upper frequency half-plane. These two features come about because on a real axis, the real part of the interaction, $V' (Ω) \propto \cos(πγ/2)/|Ω|^γ$, becomes repulsive for $γ>1$, and the imaginary $V^{''} (Ω) \propto \sin(πγ/2)/|Ω|^γ$, gets progressively smaller at $γ\to 2$. The features on the real axis are consistent with the development of a continuum spectrum of $E_{c,n}$ obtained using $Δ_n (ω_m)$ on the Matsubara axis. We consider the case $γ=2$ separately in the next paper.
