Correlated pairs and a mass action law in two‐component Fermi systems excitons in an electron‐hole plasma

Stolz, H.; Zimmermann, R.

doi:10.1002/pssb.2220940114

Cited by 80 publications

(32 citation statements)

References 16 publications

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“…In contrast to [8] we do not apply an eigenfunction expansion of the T-matrix which is complicated by the non-Hermiticity of the problem which originates from the Pauli blocking, 1 -fa -f b in (2.15). Extensive use will be made of the well-known optical theorem [la] which is derived in the Appendix together with a further relation.…”

Section: Bound and Scattering Contributionsmentioning

confidence: 95%

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The Mass Action Law in Two‐Component Fermi Systems Revisited Excitons and Electron‐Hole Pairs

Zimmermann

Stolz

1985

Physica Status Solidi (b)

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101

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Taking up the quantum-statistical derivation of a mass action law for two-component Fermi systems with Coulomb interaction given previously an improved density formula for either species is presented. It expresses the densities as a sum of a free quasi-particle part and a correlated contribution resulting from bound and scattering states. Avoiding the resolvent-technique for the solution of the T-matrix equation the correlated density is directly expressed in terms of on-shell quantities, eventually the scattering phase shifts. The ionisation equilibrium of excitons, electrons, and holes is quantitatively analyzed by model calculations for a cut-off Coulomb potential. The possibility of Bose-Einstein condensation of scattering states is inspected.Auf der Grundlage einer fruher angegebenen quantenstatistischen Ableitung eines Massenwirkungsgesetzes fur Zweikomponenten-Fermisysteme mit Coulomb-Wechselwirkung wird ein verbesserter Ausdruck fur die Dichten der Teilchensorten angegeben. Die Dichten ergeben sich als Summe einer Dichte freier Quasiteilchen und eines Korrelationsbeitrages, der von den Bindungs-und Streuzustinden herruhrt. Bei der Behandlung der T-Matrix-Gleichung wird auf die Anwendung der Resolvententechnik verzichtet, und die korrelierte Dichte wird direkt durch aus der T-Matrix abgeleitete ,,on-shell"-GroOen, letzten Endes durch die Streuphasen, ausgedruckt. Das Ionisationsgleichgewicht von Exzitonen, Elektronen und Lochern wird anhand von Modellrechnungen fur ein ,,cut-off"-Coulomb-Potential untersucht. Die Moglichkeit der Bose-Einstein-Kondensation von Streuzustlnden wird betrachtet.

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Section: Bound and Scattering Contributionsmentioning

confidence: 95%

“…Thus in an earlier paper [8] we were led to start right from the beginning with a quasiparticle approach to the spectral function of single particles. Bound states are brought into play by the T-matrix approximation to the self-energy.…”

Section: Introductionmentioning

confidence: 98%

The Mass Action Law in Two‐Component Fermi Systems Revisited Excitons and Electron‐Hole Pairs

Zimmermann

Stolz

1985

Physica Status Solidi (b)

Self Cite

101

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“…There is a long-standing argument whether EMT is a crossover or a first-order phase transition accompanied by a bistability at sufficiently low temperatures. [16][17][18][19][20][21][22] In general, bistability appears in diverse systems such as electronic circuits, optoelectronic systems, magnetic systems, molecular and biological systems, etc. Figure 1(a) depicts the schematic view of bistability in the parameter space, where the function y(x) exhibits a bistable region as a function of the control parameter x.…”

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confidence: 99%

“…Such a positive feedback can induce a hysteresis of the ionization ratio of excitons as defined by  = nf/ntotal (ntotal = nf + nex, with nf and nex the densities of free e-h pairs and excitons, respectively) with respect to the total pair e-h density, invoking the possibility that EMT becomes a first-order phase transition. [16][17][18][19][20][21][22] Experimentally, the problem of EMT has long been studied using e.g. photoluminescence spectroscopy.…”

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confidence: 99%

Rate Equation Analysis of the Dynamics of First-order Exciton Mott Transition

Sekiguchi

Shimano

2017

J. Phys. Soc. Jpn.

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We performed a rate equation analysis on the dynamics of exciton Mott transition (EMT) with assuming a detailed balance between excitons and unbound electron-hole (e-h) pairs. Based on the Saha equation with taking into account the empirical expression for the band-gap renormalization effect caused by the unbound e-h pairs, we show that the ionization ratio of excitons exhibits a bistability as a function of total e-h pair density at low temperatures. We demonstrate that an incubation time emerges in the dynamics of EMT from oversaturated exciton gas phase on the verge of the bistable region. The incubation time shows a slowing down behavior when the pair density approaches toward the saddle-node bifurcation of the hysteresis curve of the exciton ionization ratio.Photocontrol of condensed matter systems has gained continuing interests over decades, [1][2][3] e.g. in semiconductors, 4,5) Mott insulators, 3,6-9) spin crossover complexes, [10][11][12] and superconductors. 13,14) Among diverse material systems, photoexcited electron-hole (e-h) systems in semiconductors offer a unique arena to study the rich variety of phases emergent in many particle systems, and their non-equilibrium dynamics. 4,15) One of the intriguing aspects of e-h systems is that the strength of inter-particle Coulomb interaction can be effectively controlled by changing the density of photoexcited carriers through the screening effect, by simply changing the excitation light intensity. The change of the Coulomb interaction causes a phase transition, or crossover, from the insulating exciton gas phase in the low density regime to the metallic e-h plasma in the high density regime, referred to as exciton Mott transition (EMT). There is a long-standing argument whether EMT is a crossover or a first-order phase transition accompanied by a bistability at sufficiently low temperatures. [16][17][18][19][20][21][22] In general, bistability appears in diverse systems such as electronic circuits, optoelectronic systems, magnetic systems, molecular and biological systems, etc. Figure

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“…For equilibrium nonideal plasmas the correlated density has been employed in refs. [15,29] and under the name of the generalized Beth-Uhlenbeck approach it has been used in ref. [30] for nuclear matter studies.…”

Section: Extended Quasiparticle Picturementioning

confidence: 99%

Correlations in many-body systems with two-time Green’s functions

Köhler

Morawetz

2001

Phys. Rev. C

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The Kadanoff-Baym (KB) equations are solved numerically for infinite nuclear matter. In particular we calculate correlation energies and correlation times. Approximating the Green's functions in the KB collision kernel by the free Green's functions the Levinson equation is obtained. This approximation is valid for weak interactions and/or low densities. It relates to the extended quasi-classical approximation for the spectral function. Comparing the Levinson, Born and KB calculations allows for an estimate of higher order spectral corrections to the correlations. A decrease in binding energy is reported due to spectral correlations and off-shell parts in the reduced density matrix.

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Correlated pairs and a mass action law in two‐component Fermi systems excitons in an electron‐hole plasma

Cited by 80 publications

References 16 publications

The Mass Action Law in Two‐Component Fermi Systems Revisited Excitons and Electron‐Hole Pairs

The Mass Action Law in Two‐Component Fermi Systems Revisited Excitons and Electron‐Hole Pairs

Rate Equation Analysis of the Dynamics of First-order Exciton Mott Transition

Correlations in many-body systems with two-time Green’s functions

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