Abstract

Fundamentals of fermion-condensation physics are outlined. Fermion condensation is a phase transition occurring in a strongly correlated Fermi system upon a topological reconstruction of the Landau ground state and leading to the formation of a fermion condensate that possesses the dispersionless single-particle spectrum \(\epsilon({\mathbf{p}})=0\) in the momentum-space region adjacent to the Fermi surface and, accordingly, an anomalously enhanced density of single-particle states. A original method is developed for solving the set of nonlinear integral equations of fermion-condensation theory. This method makes it possible to analyze the problem of quantum chaos in strongly interacting multifermion systems. The computational technique used is demonstrated by applying it to superdense quark–gluon plasma, where the structure of exchange quark–quark interaction is well known. In electron systems featuring a fermion condensate, the magnitude of the gap appearing in the single-particle spectrum owing to Cooper pairing is shown to be much larger than that in Bardeen–Cooper–Schrieffer (BCS) theory. This explains both a high superconducting-transition temperature \(T_{c}\) and, with allowance for \(C_{4}\) crystal-lattice symmetry, the \(D\)-wave pairing-gap structure observed in cuprates. It is found that, in addition to the BCS gap \(\Delta\), the spectrum of single-particle excitations of superconducting systems where a fermion condensate is present develops a nonsuperconducting gap \(\Upsilon\) that owes its existence to the interaction of condensate particles with normal quasiparticles residing outside the condensate region in momentum space. The question of whether these results are pertinent to the two-gap structure recently unearthed in the excitation spectrum of cuprates upon analyzing ARPES data is addressed.

中文翻译：

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费米子凝聚：理论与实验

摘要

概述了费米子凝聚物理的基本原理。Fermion冷凝是在Landau基态的拓扑重建时发生在强相关Fermi系统中的相变，并导致形成具有无分散单粒子光谱\（\ epsilon（{\ mathbf {p} }）= 0 \）在费米表面附近的动量空间区域中，因此，单粒子态的密度异常增加。提出了一种求解费米凝聚理论的非线性积分方程组的原始方法。这种方法可以分析强相互作用的多费米子系统中的量子混沌问题。通过将其应用于超稠密夸克-胶子等离子体中，证明了所用的计算技术，在该夸克-胶子等离子体中，交换夸克-夸克相互作用的结构是众所周知的。在具有费米子冷凝物的电子系统中，由于库珀配对而在单粒子光谱中出现的间隙的大小显示出比Bardeen-Cooper-Schrieffer（BCS）理论中的大得多。这解释了高的超导转变温度\（T_ {c} \）并且考虑到（C_ {4} \）晶格对称性，在铜酸盐中观察到了\（D \）-波配对间隙结构。发现，除了BCS间隙\（\ Delta \）以外，存在费米子冷凝物的超导系统的单粒子激发光谱还产生了一个非超导间隙\（\ Upsilon \），这归因于它的存在。凝结颗粒与位于动量空间中凝结区域之外的普通准颗粒之间的相互作用。这些问题是否与最近分析ARPES数据时在铜酸盐激发光谱中发现的两间隙结构有关。