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arXiv:cond-mat/9803325 · Physical Review Letters

Four-Particle Condensate in Strongly Coupled Fermion Systems

GERD RÖPKE, Alexander Schnell, Peter Schuck, Ph. Nozières

Published Apr 13, 1998• 270 citations
arXivHTMLPDF

Abstract

Four-particle correlations in fermion systems at finite temperatures are investigated with special attention to the formation of a condensate. Instead of the instability of the normal state with respect to the onset of pairing described by the Gorkov equation, a new equation is obtained which describes the onset of ``quartetting.'' Applying to symmetric nuclear matter, below a critical density, the four-particle condensation ( $\ensuremath{\alpha}$-like quartetting) is found to be favored over deuteron condensation (triplet pairing). This pairing-quartetting competition is expected to be a general feature of interacting fermion systems, such as the exciton-biexciton system in excited semiconductors. Possible experimental consequences are pointed out.

DOI
10.1103/physrevlett.80.3177

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The European Physical Journal Special Topics•May 1, 2017•1 citation
Four-particle correlations in fermion systems at finite temperatures are investigated with special attention to the formation of a condensate. Instead of the instability of the normal state with respect to the onset of pairing described by the Gorkov equation, a new equation is obtained which describes the onset of ``quartetting.'' Applying to symmetric nuclear matter, below a critical density, the four-particle condensation ( \ensuremathα\ensuremath{\alpha}\ensuremathα-like quartetting) is found to be favored over deuteron condensation (triplet pairing). This pairing-quartetting competition is expected to be a general feature of interacting fermion systems, such as the exciton-biexciton system in excited semiconductors. Possible experimental consequences are pointed out.
We investigate the quartet correlations in four-component fermionic systems at the thermodynamic limit within a variational many-body theory. The Bardeen-Cooper-Schrieffer (BCS)--type variational wave function is extended to the systems with the coexistence of pair and quartet correlations at zero temperature. Special attention is paid to the application of the present framework to an $\ensuremath{\alpha}$-particle condensation in symmetric nuclear matter, where the coexistence of deuteron and $\ensuremath{\alpha}$ condensations is anticipated. We also discuss how physical properties, such as quasiparticle dispersion, can be modified by the pair and quartet correlations and show a hierarchical structure of in-medium cluster formations in infinite nuclear matter. The present results may also contribute to the interdisciplinary understanding of fermionic condensations beyond the BCS paradigm in many-body systems.
Nonrelativistic nuclear matter is considered as a special example of a many-particle system. Quantum statistical methods are applied to treat the formation and dissolution of bound states in dense matter. The formation of quantum condensates is investigated. Special aspects are the transition from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) pairing as well as the occurrence of quartetting. Consequences for the structure of nuclei are compared with experimental data. Exercises to illustrate the main features of in-medium effects in nuclear matter are given.
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.
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.
Low-density nuclear matter at finite temperature is considered representing the strong coupling situation of a highly correlated fermion system. One-particle self-energies and the density of states in the vicinity of the pairing transition point are presented. Within the Green function approach, model calculations are performed using the thermodynamic TTT matrix in ladder approximation. As a main result the formation of a pseudogap in the level density near the critical temperature of the pairing phase transition has been found. It is shown that compared to mean-field approaches the scenario of the onset of the pairing transition is essentially changed if correlations are taken into account.
The possibility that a four component Fermi gas with attractive interaction can form a quartet condensate at low density is pointed out. It is discussed that for quartets only the Bose-Einstein Condensatio (BEC) phase exists and that the analogue to the weak coupling long coherence BCS phase of pairing is absent. Precurser phenomena in finite nuclei are presented. For instance, the present understanding of the structure of the Hoyle state in 12C being the gateway for Carbon production in the universe is reviewed. It is pointed out that a crucial test of any theory is the good reproduction of the experimental results for the inelastic form factor from ground to the Hoyle state. The performances of the so-called THSR wavwe function are outlined confirming the α particle condensation hypothesis proposed 15 years back in [1].