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Physics of Atomic Nuclei

Fermion Condensation: Theory and Experiment

VICTOR A. KHODEL, J. W. Clark, MIKHAIL V. ZVEREV

Published Mar 1, 2020• 0 citations
Publisher

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.

DOI
10.1134/s1063778820020167

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A model of a Fermi liquid with the fermion condensate (FC) is applied to the consideration of quasiparticle excitations in high-temperature superconductors, in their superconducting and normal states. Within our model the appearance of the fermion condensate presents a quantum phase transition that separates the regions of normal and strongly correlated electron liquids. Beyond the phase transition point the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other---fermion condensate localized at the Fermi surface and characterized by almost dispersionless single-particle excitations. In the superconducting state the quasiparticle dispersion in systems with FC can be presented by two straight lines, characterized by effective masses MFC∗{M}_{\mathrm{FC}}^{*}MFC∗​ and ML∗,{M}_{L}^{*},ML∗​, respectively, and intersecting near the binding energy, which is of the order of the superconducting gap. This same quasiparticle picture persists in the normal state, thus manifesting itself over a wide range of temperatures as new energy scales. Arguments are presented that fermion systems with FC have features of a ``quantum protectorate'' [R. B. Laughlin and D. Pines, Proc. Natl. Acad. Sci. U.S.A. 97, 28 (2000); P. W. Anderson, cond-mat/0007185 (unpublished); cond-mat/0007287 (unpublished)].
A original microscopic theory of superfluidity and superconductivity driven by the single particle (SPC) and pair condensation (PC) of attracting bosons both in Fermi and in Bose systems is developed. This theory (as distinct from the existing theories) for Fermi systems contains two order parameters Δ F and Δ B characterizing the attracting fermion pairs and boson pairs, respectively. In such systems superconducting (SC) phase transition is accompanied, as a rule, by the formation of k-space composite bosons (e.g. Cooper pairs and bipolarons) with their subsequent transition to the superfluid (SF) state by attractive SPC and PC. A novel Fermi-liquid and SF Bose-liquid theories are elaborated for description this two-stage Fermi–Bose-liquid (FBL) scenario of SC (or SF) transition. The crossover from k- to real (r)-space pairing regime for BCS-like coupling constants γ F ≃ 0.7-0.9 and the irrelevance of r-space pairs to the superconductivity are shown. The developed SF Bose-liquid theory predicts the first-order phase transition SPC ↔ PC of attracting 3d-bosons with the kink-like behaviors of all SC (SF) parameters near [Formula: see text] in accordance with the observations in 4 He , 3 He and superconductors. It is argued that the coexistence of the order parameters Δ F and Δ B leads to the superconductivity by two FBL scenarios. One of these scenarios is realized in the so-called fermion (type I, II and III) superconductors (FSC) (where formation of k-space composite bosons and their condensation occur at the same temperature) and the other in the boson (type II and III) superconductors (BSC) (where BCS-like pairing take place in the normal state with manifesting of the second-order phase transition and opening of the pseudogap at T=T F > T c ). There the gapless superfluidity (superconductivity) is caused by the gapless excitation spectrum of bosons at [Formula: see text] and not by the presence of point or line nodes of the BCS-like gap Δ F assumed in some s-, p- and d-pairing models. The 3D- and 2D-insulator–metal–superconductor phase diagrams are presented. The necessary and sufficient microscopic criterions for superfluidity is formulated. The theory proposed are in close agreement with the observations in 4 He , 3 He , superconductors, nuclear and neutron star matter, cosmology, etc.
This article gives a detailed review of our current theoretical understanding of the crossover from cooperative Cooper pairing to independent bound-state formation and Bose–Einstein condensation in Fermi systems with increasing attractive interactions. Introduction There are two well-known paradigms for understanding the phenomena of superconductivity and superfluidity: (I) BCS theory [1], in which the normal state is a degenerate Fermi liquid that undergoes a pairing instability at a temperature T c ≪ ε f , the degeneracy scale. The formation of Cooper pairs and their condensation (macroscopic occupation of a single quantum state) both occur simultaneously at the transition temperature T c . (II) Bose–Einstein condensation (BEC) of bosons at a T c of the order of their degeneracy temperature. At a fundamental level these bosons (for example, 4 He or excitons) are invariably composite objects made up of an even number of fermions. The composite particles form at some very high temperature scale of the order of their dissociation temperature T dissoc , and these “pre-formed” bosons then condense at the BEC T c ≪ T dissoc . In most cases of experimental interest the system under consideration clearly falls into one category or the other. For instance, 3 He is a Fermi superfluid described by (I) whereas 4 He is a Bose superfluid (II). Essentially all cases of superconductivity in metals that we understand reasonably well are much closer to (I) than to (II), as evidenced by the existence of fermionic quasiparticles above T c .
The two-particle spectrum in a dense Fermion system is treated using a thermodynamic Green function approach. A self-consistent description of possible bound states and a superfluid condensate in a correlated medium is given. A detailed understanding of superfluidity and superconductivity in correlated Fermion systems, especially the transition from the Cooper-paired state (weak-coupling limit) to the Bose condensed state of tightly bound pairs of Fermions (strong coupling limit) [1], is of great interest for very different physical systems. The problem of a unified treatment of Bose–Einstein condensation (BEC) and the Bardeen–Cooper–Schrieffer (BCS) phase arises not only in describing the electron structure of strongly correlated electron superfluids such as superconductors [2], the electronhole system in semiconductors [3], spin-polarized hydrogen and liquid He [4], but also in the theory of nuclear matter [5] and quark–gluon systems [6]. Recently, there have been several new approaches to this stimulating problem. A Monte-Carlo simulation of a finite He system at zero temperature has been performed in Ref. [7]. The microscopic theory of strongly coupled quantum fluids has been treated within the Jastrow approximation (cf. Ref. [8]) to obtain the ground state and low-lying excited states of strongly correlated boson quantum fluids. The crossover from weak to strong coupling superconductivity has been considered using a functional integral representation [2] (see also Ref. [7]).
The appearance of the fermion condensation, which can be compared to the Bose-Einstein condensation, in different Fermi liquids is considered; its properties are discussed; and a large amount of experimental evidence in favor of the existence of the fermion condensate (FC) is presented. We show that the appearance of FC is a signature of the fermion condensation quantum phase transition (FCQPT), which separates the regions of normal and strongly correlated liquids. Beyond the FCQPT point, the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other, FC, localized at the Fermi level. In the superconducting state, the quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by effective masses M FC * and M L * and intersecting near the binding energy E 0, which is of the order of the superconducting gap. The same quasiparticle picture and the energy scale E 0 persist in the normal state. We demonstrate that fermion systems with FC have features of a “quantum protectorate” and show that strongly correlated systems with FC, which exhibit large deviations from the Landau Fermi liquid behavior, can be driven into the Landau Fermi liquid by applying a small magnetic field B at low temperatures. Thus, the essence of strongly correlated electron liquids can be controlled by weak magnetic fields. A reentrance into the strongly correlated regime is observed if the magnetic field B decreases to zero, while the effective mass M* diverges as $$M^ * \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}$$ . The regime is restored at some temperature T∗∝BT^ * \propto \sqrt B T∗∝B​ . The behavior of Fermi systems that approach FCQPT from the disordered phase is considered. This behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. We expect that FCQPT takes place in trapped Fermi gases and in low-density neutron matter, leading to stabilization of the matter by lowering its ground-state energy. When the system recedes from FCQPT, the effective mass becomes density independent and the system is suited perfectly to be conventional Landau Fermi liquid.
Superfluidity is one of the most striking manifestations of quantum mechanics at macroscopic scales, characterized by frictionless flow and the emergence of collective quantum phenomena. The theoretical foundation of superfluidity in fermionic systems was revolutionized by the Bardeen-Cooper-Schrieffer (BCS) theory, developed in 1957 to explain superconductivity in metals. This groundbreaking work provided a microscopic description of how attractive interactions between electrons near the Fermi surface can lead to the formation of Cooper pairs-correlated pairs of fermions that condense into a coherent quantum state. The BCS theory not only explained superconductivity but also laid the groundwork for understanding superfluidity in systems like liquid helium-3 and ultracold fermionic gases, becoming a cornerstone of condensed matter physics.