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arXiv:2102.03701 · Physical Review A

Condensation of Cooper triples

Sora Akagami, Hiroyuki Tajima, Kei Iida

Published Oct 11, 2021• 16 citations
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Abstract

The condensation of Cooper pairs, originating from the Fermi-surface instability due to a weakly attractive interaction between two fermions, opened a new frontier for exploring many-body physics in interdisciplinary contexts. In this work, we discuss the possible condensation of Cooper triples, which are three-body counterparts of Cooper pairs for three-component fermions with a three-body attraction. Although each composite trimer-like state obeys the Fermi-Dirac statistics, its aggregate can form a condensate at zero center-of-mass momentum in the presence of the internal degrees of freedom associated with the relative momenta of constituent particles of momenta close to the Fermi surface. Such condensation can be regarded as bosonization in infinite-component fermions. We propose a variational wave function for the condensate of Cooper triples in analogy with the Bardeen-Cooper-Schrieffer ground state, and we obtain the ground-state energy.

DOI
10.1103/physreva.104.l041302

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The condensation of Cooper pairs, originating from the Fermi-surface instability due to a weakly attractive interaction between two fermions, opened a new frontier for exploring many-body physics in interdisciplinary contexts. In this work, we discuss the possible condensation of Cooper triples, which are three-body counterparts of Cooper pairs for three-component fermions with a three-body attraction. Although each composite trimer-like state obeys the Fermi-Dirac statistics, its aggregate can form a condensate at zero center-of-mass momentum in the presence of the internal degrees of freedom associated with the relative momenta of constituent particles of momenta close to the Fermi surface. Such condensation can be regarded as bosonization in infinite-component fermions. We propose a variational wave function for the condensate of Cooper triples in analogy with the Bardeen-Cooper-Schrieffer ground state, and we obtain the ground-state energy.
We theoretically discuss the possible condensation of Cooper triples, which correspond to a threebody version of Cooper pairs, in three-component Fermi systems with three-body attractive interactions.A macroscopic number of Cooper triples can occupy a zero center-of-mass momentum state in the presence of a Fermi surface of constituent particles, even though the three-body operator exhibits anti-commutation relation associated with the Fermi-Dirac statistics.Such a condensation with internal degrees of freedom is similar to bosonization in a system of infinite-component fermions.We propose a variational wave function for condensed Cooper triples and show that in the ground state, the condensed state is energetically favored compared to the normal state.Also, we discuss effects of the Fermi-surface distortion in a lattice system described by a three-component Hubbard model.
We investigate many-body properties of equally populated three-component fermions with attractive three-body contact interaction. A diagrammatic approach suggests the possible occurrence of Cooper triples at low temperature, which are a three-body counterpart of Cooper pairs with a two-body attraction. In one-dimension, the presence of Cooper triples is accompanied by conformal symmetry breaking, which is in turn related to an asymptotic freedom of the low-dimensional, multi-component system. While trimer states present at sufficiently low density have the binding energy reduced by the Pauli blocking and the thermal agitation, Cooper triples are predicted to take over for the even larger Fermi surface. We develop a minimal framework that bridges such a crossover from tightly-bound trimers to Cooper triples with increasing particle number density.
We investigate many-body properties of equally populated three-component fermions with attractive threebody contact interaction in one dimension.A diagrammatic approach suggests the possible occurrence of Cooper triples at low temperature, which are three-body counterparts of Cooper pairs with a two-body attraction.We develop a minimal framework that bridges the crossover from tightly bound trimers to Cooper triples with increasing chemical potential and show how the formation of Cooper triples occurs in the grand-canonical phase diagram.Moreover, we argue that this nontrivial crossover is similar to the hadron-quark crossover proposed in dense matter.A coexistence of medium-induced triples and the underlying Fermi sea at positive chemical potential is analogous to quarkyonic matter consisting of baryonic excitations and the underlying quark Fermi sea.The comparison with the existing quantum Monte Carlo results implies that the emergence of these kinds of three-body states can be a microscopic origin of the peak of the sound velocity along the crossover.
We investigate the formation of Bose-Einstein condensation and a population imbalance in a three-component Fermi superfluid by increasing the U(3) invariant attractive interaction. We consider the system at zero temperature in three dimensions as well as in two dimensions. Within mean-field theory, we derive explicit formulas for the number densities, the gap order parameter, the condensate density, and the condensate fraction of the uniform system and analyze them in the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of Cooper pairs to the Bose-Einstein condensate (BEC) of strongly bound molecular dimers. In addition we study this Fermi mixture trapped by a harmonic potential: We calculate the density profiles of the three components and the condensate density profile of Cooper pairs in the BCS-BEC crossover.
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 ϵ(p)=0\epsilon({\mathbf{p}})=0ϵ(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 TcT_{c}Tc​ and, with allowance for C4C_{4}C4​ crystal-lattice symmetry, the DDD -wave pairing-gap structure observed in cuprates. It is found that, in addition to the BCS gap Δ\DeltaΔ , the spectrum of single-particle excitations of superconducting systems where a fermion condensate is present develops a nonsuperconducting gap Υ\UpsilonΥ 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.
We theoretically investigate ground-state properties of a three-component Fermi gas with pairwise contact interactions between different components near a triatomic resonance where bound trimers are about to appear. Using variational equations for in-medium two- and three-body cluster states in three dimensions, we elucidate the competition of pair and triple formations due to the Fermi surface effects. We present the ground-state phase diagram that exhibits transition from a Cooper pair to Cooper triple state and crossover from a Cooper triple to tightly bound trimer state at negative scattering lengths. This three-body crossover is analogous to the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover observed in a two-component Fermi gas. We predict that the threshold scattering length ${a}_{\ensuremath{-}}$ for three-body states can be shifted towards the weak-coupling side due to the emergence of Cooper triples.