The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal
The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal
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DOI：
10.1016/j.aop.2020.168142
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发表时间：
2020-06-01
影响因子：
3
通讯作者：
Wu, Yi-Ming
中科院分区：
文献类型：
--
作者：
Chubukov, Andrey, V;Abanov, Artem;Wu, Yi-Ming
在量子临界点附近，金属显示出两种相互竞争的趋势：费米子相干性的破坏和一个或多个配对通道中的吸引力。我们分析了Eliashberg理论中一类具有有效动态电子-电子相互作用V（Omega(m)）与1/垂直线成正比的量子临界模型（0 < gamma < 1）的竞争。我们认为这两种倾向在强度上是相当的，但配对倾向更强，并且基态是超导体。然而，我们表明，在配对的起始温度T-p以下存在两种不同的系统行为。在T-cross < T < T-p范围内，费米子保持非相干状态，谱函数A（k, ω）和态密度N（ω）均表现出“空位填充”行为，即N（ω）中最大值的位置由温度决定，而不是由配对间隙决定。在较低的T < T-cross下，费米子获得相干性，A（k, ω）和N(o)表现出常规的“闭合间隙”行为，N（ω）中的峰值位置随着间隙的增大而增大，并随着T的增大而减小。我们认为这两种状态的存在是由于频率为ω = +/-pi T的费米子沿Matsubara轴的特殊行为。具体来说，对于这些费米子来说，与配对竞争的自能成分在正常状态下消失了。我们进一步论证了T点交叉类似于T点交叉的产生，因为Eliashberg方程允许在相同的间隙对称内对的起始温度有无限个拓扑上不同的解。实际上，只有一个具有最高T-p的解会出现，但会生成其他解，并在T处修改间隙函数的形式
Near a quantum-critical point, a metal reveals two competing tendencies: destruction of fermionic coherence and attraction in one or more pairing channels. We analyze the competition within Eliashberg theory for a class of quantum-critical models with an effective dynamical electron-electron interaction V(Omega(m)) proportional to 1/vertical bar Omega(m)vertical bar(gamma) (the gamma-model) for 0 < gamma < 1. We argue that the two tendencies are comparable in strength, yet the one towards pairing is stronger, and the ground state is a superconductor. We show, however, that there exist two distinct regimes of system behavior below the onset temperature of the pairing T-p. In the range T-cross < T < T-p fermions remain incoherent and the spectral function A(k, omega) and the density of states N(omega) both display "gap filling" behavior in which, i.e., the position of the maximum in N(omega) is set by temperature rather than the pairing gap. At lower T < T-cross, fermions acquire coherence, and A(k, omega) and N(o) display conventional "gap closing" behavior, when the peak position in N(omega) scales with the gap and shifts to a smaller value as T increases. We argue that the existence of the two regimes comes about because of special behavior of fermions with frequencies omega = +/-pi T along the Matsubara axis. Specifically, for these fermions, the component of the self-energy, which competes with the pairing, vanishes in the normal state. We further argue that the crossover at T similar to T-cross comes about because Eliashberg equations allow an infinite number of topologically distinct solutions for the onset temperature of the pairing within the same gap symmetry. Only one solution, with the highest T-p, actually emerges, but other solutions are generated and modify the form of the gap function at T