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arXiv:2207.03326 · International Conference on Low Temperature Physics (LT)

Possible Condensation of Cooper Triples

Sora Akagami, Hiroyuki Tajima, Kei Iida

Published May 22, 2023• 0 citations
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Abstract

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.

DOI
10.7566/jpscp.38.011010

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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.
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 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 theoretically investigate three-body correlations on the top of a Fermi sea in one-dimensional spinless fermions with antisymmetrized two- and three-body attractive interactions. By investigating the variational problem of three-body states above the Fermi sea, we illuminate the fate of the in-medium three-body cluster states (namely, Cooper triples in the presence of Fermi sea) in the special case with pure attractive three-body interaction as well as in the case with the coexistence of two- and three-body interactions. Our results testify that the fermion-dimer repulsion is canceled by including the three-body interactions, and stable three-body clusters can be formed. We further feature a phase diagram consisting of the ppp-wave Cooper pairing and Cooper tripling phases in a plane of ppp-wave two- and three-body coupling strengths.
Condensation of Cooper pairs and Cooper quartets in fermionic systems with multiple internal degrees of freedom is studied.In this thesis work, I work on two major projects.On the first project I discuss Cooper pair condensation and while on the second I discuss Cooper quartet condensation.Due to the restrictions imposed by Pauli's principle, no two identical fermions can occupy a single quantum state.Therefore for electronic systems with two internal states, the maximum number of electrons that could be bound together is two.However; for a fermionic system having more than two internal states, it is possible that the bound state structure could be quite different.On my thesis I focus on systems that have four internal states.On one hand it is possible that the system will still undergo some types of pairing condensation, but there is also a possibility that the fermions will form a more complex structure where four fermions are bound together which we call a quartet.Physical systems where fermions can have four internal states include a system of spin-3 2 fermionic atoms and a two band electronic system.I look at possible two and four particle bound state structures in such systems.
A two component model of negative U centers coupled with the Fermi sea of itinerant fermions is discussed in connection with high-temperature superconductivity of cuprates, and superfluidity of atomic fermions. We examine the phase transition and the condensed state of this boson-fermion model (BFM) beyond the ordinary mean-field approximation in two and three dimensions. No pairing of fermions and no condensation are found in two-dimensions for any symmetry of the order parameter. The expansion in the strength of the order parameter near the transition yields no linear homogeneous term in the Ginzburg-Landau-Gor'kov equation and a zero upper critical field in any-dimensional BFM, which indicates that previous mean-field discussions of the model are flawed. Normal and anomalous Green's functions are obtained diagrammatically and analytically in the condensed state of a simplest version of 3D BFM. A pairing of bosons analogous to the Cooper pairing of fermions is found. There are three coupled condensates in the model, described by the off-diagonal single-particle boson, pair-fermion and pair-boson fields. These results negate the common wisdom that the boson-fermion model is adequately described by the BCS theory at weak coupling.