The many-body physics of composite bosons

Combescot, Monique; Betbeder‐Matibet, O.; Dubin, F.

doi:10.1016/j.physrep.2007.11.003

Cited by 156 publications

(168 citation statements)

References 45 publications

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“…To take advantage of this physical fact, one has to represent the four fermions as two cobosons while properly handling fermion exchange between them. This precisely is what the coboson many-body formalism [15,29,30] allows us to do. Here, we use this formalism to reveal, through Shiva diagrams, the fermion-exchange physics that occurs between bright and dark excitons and to grasp the topological equivalence of scattering processes that produces equal brightness-conserving scatterings.…”

mentioning

confidence: 84%

Scattering amplitudes for dark and bright excitons

Shiau¹,

Combescot²,

Combescot³

et al. 2017

EPL

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Using the composite boson many-body formalism that takes single-exciton states rather than free carrier states as a basis, we derive the integral equation fulfilled by the exciton-exciton effective scattering from which the role of fermion exchanges can be unraveled. For excitons made of (±1/2)-spin electrons and (±3/2)-spin holes, as in GaAs heterostructures, one major result is that most spin configurations lead to brightness-conserving scatterings with equal amplitude ∆, in spite of the fact that they involve different carrier exchanges. A brightness-changing channel also exists when two opposite-spin excitons scatter: dark excitons (2, −2) can end either in the same dark states with an amplitude ∆e, or in opposite-spin bright states (1, −1), with a different amplitude ∆o, the number of carrier exchanges being even or odd respectively. Another major result is that these amplitudes are linked by a striking relation, ∆e + ∆o = ∆, which has decisive consequence for exciton Bose-Einstein condensation. Indeed, this relation leads to the conclusion that the exciton condensate can be optically observed through a bright part only when excitons have a large dipole, that is, when the electrons and holes are well separated in two adjacent layers. In contrast to the structureless 4 He, a number of bosonic condensates have more than one component inherited from the internal spin and orbital degrees of freedom of their constituents, the superfluid then being multi-component. Dipolar Bose gases [1] and superfluid phases of 3 He [2] are prime examples. This also occurs to excitons, which are composite bosons (cobosons for short) made of one conduction electron and one valence hole. Since electrons and holes carry spins, so do excitons, their condensate depending on these internal degrees of freedom. Recently, it has been shown that signatures of exciton condensates were long held back by the missed fact that the lowest-energy states are dark [3, 4], that is, not coupled to light. This fact precludes a direct photoluminescence observation of exciton condensate in a very dilute regime. Unambiguous optical evidences for Bose-Einstein condensation are bound to the density regime where dark and bright components coexist coherently [5]. The expected darkening[6-10] of the exciton gas upon cooling has been recently seen. Macroscopic spatial coherence of the bright component has also been revealed [7,10], in this way providing the most unambiguous evidence for the coexistence of dark and bright exciton condensates.As a rule, the energy of a condensate depends weakly on its internal degrees of freedom, all possible "spin" phases being essentially degenerate. These degeneracies are lifted once interactions are taken into account. One then has to determine which combination of the competing phases produces the lowest energy that rules the macroscopic properties of the condensate. In this Letter, we show that the relation between brightness-conserving and brightness-changing scattering amplitudes constitutes a crucial element to charact...

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confidence: 84%

Scattering amplitudes for dark and bright excitons

Shiau¹,

Combescot²,

Combescot³

et al. 2017

EPL

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“…In this work, we approach the four-body scattering problem through the coboson many-body formalism [19,20] that was developed in the 2000's to address semiconductor excitons with Coulomb attraction between electrons and holes and equally strong Coulomb repulsion between electrons and between holes. We recently showed [21] that this formalism takes a much simpler form when the interaction is restricted to attraction between different fermion species, as commonly used for fermionic-atom dimers, because the potential then reads as a one-body operator in the pair subspace (see Eq.…”

Section: Introductionmentioning

confidence: 99%

“…Equations (13,19) are the main results of this section. The scattering length in the Born approximation follows from ζ( 0 0 0 0 ), while its value at all orders in interaction is obtained by solving Eq.…”

mentioning

confidence: 99%

Correlated-pair approach to composite-boson scattering lengths

2016

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We derive the scattering length of composite bosons (cobosons) within the framework of the composite boson many-body formalism that uses correlated-pair states as a basis, instead of free fermion states. The integral equation constructed from this physically relevant basis makes transparent the role of fermion exchange in the coboson-coboson effective scattering. Three potentials used for Cooper pairs, fermionic-atom dimers, and semiconductor excitons are considered. While the s-wave scattering length for the BCS-like potential is just equal to its Born value, the other two are substantially smaller. For fermionic-atom dimers and semiconductor excitons, our results, calculated within a restricted correlated-pair basis, are in good agreement with those obtained from procedures numerically more demanding. We also propose model coboson-coboson scatterings that are separable and thus easily workable, and that produce scattering lengths which match quantitatively well with the numerically-obtained values for all fermion mass ratios. These separable model scatterings can facilitate future works on many-body effects in coboson gases.

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“…A decade ago, one of us has developed a new framework [12] for many-body effects between composite bosons. Most of its applications dealt with semiconductor excitons.…”

Section: Introductionmentioning

confidence: 99%

Competition between BCS-pairing and “moth-eaten effect” in BEC–BCS crossover

Zhu

Combescot

2012

Solid State Communications

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We study the change in condensation energy from a single pair of fermionic atoms to a large number of pairs interacting via the reduced BCS potential. We find that the energy-saving due to correlations decreases when the pair number increases because the number of empty states available for pairing gets smaller ("moth-eaten effect"). However, this decrease dominates the 3D kinetic energy increase of the same amount of noninteracting atoms only when the pair number is a sizeable fraction of the number of states available for pairing. As a result, in BEC-BCS crossover of 3D systems, the condensation energy per pair first increases and then decreases with pair number while in 2D, it always is controlled by the "moth-eaten effect" and thus simply decreases.

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The many-body physics of composite bosons

Cited by 156 publications

References 45 publications

Scattering amplitudes for dark and bright excitons

Scattering amplitudes for dark and bright excitons

Correlated-pair approach to composite-boson scattering lengths

Competition between BCS-pairing and “moth-eaten effect” in BEC–BCS crossover

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