arXiv subjects

M. Combescot

Publications and source records attributed to M. Combescot.

At least 19 recordsLinked to original sources

arXiv2014

Effects of fermion exchanges on the polarization of exciton condensates

Exchange processes are responsible for the stability of elementary boson condensates with respect to their possible fragmentation. This remains true for composite bosons when single fermion exchanges are included but spin degrees of freedom are ignored. We here show that their inclusion can produce a "spin-fragmentation" of a condensate of dark excitons, i.e., an unpolarized condensate with equal amount of dark excitons with spins (+2) and (-2). Quite surprisingly, for spatially indirect excitons of semiconductor bilayers, we predict that the condensate polarization can switch from unpolarized to fully polarized, depending on the distance between the layers confining electrons and holes. Remarkably, the threshold distance associated to this switching lies in the regime where experiments are nowadays carried out.

cond-mat.quant-gas↗

arXiv2013

Optical signatures of a fully dark exciton condensate

We propose optical means to reveal the presence of a dark exciton condensate that does not yield any photoluminescence at all. We show that (i) the dark exciton density can be obtained from the blueshift of the excitonic absorption line induced by dark excitons; (ii) the polarization of the dark condensate can be deduced from the blueshift dependence on probe photon polarization and also from Faraday effect, linearly polarized dark excitons leaving unaffected the polarization plane of an unabsorbed photon beam. These effects result from carrier exchanges between dark and bright excitons.

cond-mat.quant-gas↗

arXiv2012

"Gray" BCS condensate of excitons and internal Josephson effect

It has been recently suggested that the Bose-Einstein condensate formed by excitons in the dilute limit must be dark, i.e., not coupled to photons. Here, we show that, under a density increase, the dark exciton condensate must acquire a bright component due to carrier exchange in which dark excitons turn bright. This however requires a density larger than a threshold which seems to fall in the forbidden region of the phase separation between a dilute exciton gas and a dense electron-hole plasma. The BCS-like condensation which is likely to take place on the dense side, must then have a dark and a bright component - which makes it "gray". It should be possible to induce an internal Josephson effect between these two coherent components, with oscillations of the photoluminescence as a strong proof of the existence for this "gray" BCS-like exciton condensate.

cond-mat.quant-gas↗

arXiv2011

BCS ansatz for superconductivity in the canonical ensemble and the Pauli exclusion principle

The usual formulation of the BCS ansatz for superconductivity in the grand canonical ensemble makes the handling of the Pauli exclusion principle between paired electrons straightforward. It however tends to mask that many-body effects between Cooper pairs interacting through the reduced BCS potential are entirely controlled by this exclusion. To show it up, one has to work in the canonical ensemble. Pauli blocking between a fixed number of composite bosons is however known to be difficult to handle. To do it, we here develop a commutator formalism for Cooper pairs, along the line we used for excitons. We then rederive, within the $N$-pair subspace, a few results of BCS superconductivity commonly derived in the grand canonical ensemble, to evidence their Pauli blocking origin. We end by discussing what should be called "Cooper pair wave function".

cond-mat.supr-con↗

arXiv2011

BCS ansatz, Bogoliubov approach to superconductivity and Richardson-Gaudin exact wave function

The Bogoliubov approach to superconductivity provides a strong mathematical support to the wave function ansatz proposed by Bardeen, Cooper and Schrieffer (BCS). Indeed, this ansatz --- with all pairs condensed into the same state --- corresponds to the ground state of the Bogoliubov Hamiltonian. Yet, this Hamiltonian only is part of the BCS Hamiltonian. As a result, the BCS ansatz definitely differs from the BCS Hamiltonian ground state. This can be directly shown either through a perturbative approach starting from the Bogoliubov Hamiltonian, or better by analytically solving the BCS Schr\"{o}dinger equation along Richardson-Gaudin exact procedure. Still, the BCS ansatz leads not only to the correct extensive part of the ground state energy for an arbitrary number of pairs in the energy layer where the potential acts --- as recently obtained by solving Richardson-Gaudin equations analytically --- but also to a few other physical quantities such as the electron distribution, as here shown. The present work also considers arbitrary filling of the potential layer and evidences the existence of a super dilute and a super dense regime of pairs, with a gap \emph{different} from the usual gap. These regimes constitute the lower and upper limits of density-induced BEC-BCS cross-over in Cooper pair systems.

cond-mat.supr-con↗

arXiv2011

From one to $N$ Cooper pairs, step by step

We extend the one-pair Cooper configuration towards Bardeen-Cooper-Schrieffer (BCS) model of superconductivity by adding one-by-one electron pairs to an energy layer where a small attraction acts. To do it, we solve Richardson's equations analytically in the dilute limit of pairs on the one-Cooper pair scale. We find, through only keeping the first order term in this expansion, that the $N$ correlated pair energy reads as the energy of $N$ isolated pairs within a $N(N-1)$ correction induced by the Pauli exclusion principle which tends to decrease the average pair binding energy when the pair number increases. Quite remarkably, extension of this first-order result to the dense regime gives the BCS condensation energy exactly. This leads us to suggest a different understanding of the BCS condensation energy with a pair number equal to the number of pairs feeling the potential and an average pair binding energy reduced by Pauli blocking to half the single Cooper pair energy - instead of the more standard but far larger superconducting gap.

cond-mat.supr-con↗

arXiv2010

Two-Cooper-pair problem and the Pauli exclusion principle

While the one-Cooper pair problem is now a textbook exercise, the energy of two pairs of electrons with opposite spins and zero total momentum has not been derived yet, the exact handling of Pauli blocking between bound pairs being not that easy for N=2 already. The two-Cooper pair problem however is quite enlightening to understand the very peculiar role played by the Pauli exclusion principle in superconductivity. Pauli blocking is known to drive the change from 1 to $N$ pairs, but no precise description of this continuous change has been given so far. Using Richardson procedure, we here show that Pauli blocking increases the free part of the two-pair ground state energy, but decreases the binding part when compared to two isolated pairs - the excitation gap to break a pair however increasing from one to two pairs. When extrapolated to the dense BCS regime, the decrease of the pair binding while the gap increases strongly indicates that, at odd with common belief, the average pair binding energy cannot be of the order of the gap.

cond-mat.supr-con↗

arXiv2009

"Moth-eaten effect" driven by Pauli blocking, revealed for Cooper pairs

We extend the well-known Cooper's problem beyond one pair and study how this dilute limit is connected to the many-pair BCS condensate. We find that, all over from the dilute to the dense regime of pairs, Pauli blocking induces the same "moth-eaten effect" as the one existing for composite boson excitons. This effect makes the average pair binding energy decrease linearly with pair number, bringing it, in the standard BCS configuration, to half the single-pair value. This proves that, at odds with popular understanding, the BCS gap is far larger than the broken pair energy. The increase comes from Pauli blocking between broken and unbroken pairs. Possible link between our result and the BEC-BCS crossover is also discussed.

cond-mat.supr-con↗

arXiv2009

Biexciton oscillator strength

Our goal is to provide a physical understanding of the elementary coupling between photon and biexciton and to derive the physical characteristics of the biexciton oscillator strength, following the procedure we used for trion. Instead of the more standard two-photon absorption, this work concentrates on molecular biexciton created by photon absorption in an exciton gas. We first determine the appropriate set of coordinates in real and momentum spaces to describe one biexciton as two interacting excitons. We then turn to second quantization and introduce the "Fourier transform in the exciton sense" of the biexciton wave function which is the relevant quantity for oscillator strength. We find that, like for trion, the oscillator strength for the formation of one biexciton out of one photon plus a \emph{single} exciton is extremely small: it is one biexciton volume divided by one sample volume smaller than the exciton oscillator strength. However, due to their quantum nature, trion and biexciton have absorption lines which behave quite differently. Electrons and trions are fermionic particles impossible to pile up all at the same energy. This would make the weak trion line spread with electron density, the peak structure only coming from singular many-body effects. By contrast, the bosonic nature of exciton and biexciton makes the biexciton peak mainly rise with exciton density, this rise being simply linear if we forget many-body effects between the photocreated exciton and the excitons present in the sample.

cond-mat.mes-hall↗

arXiv2009

Analytical approach to semiconductor Bloch equations

Although semiconductor Bloch equations have been widely used for decades to address ultrafast optical phenomena in semiconductors, they have a few important drawbacks: (i) Coulomb terms between free electron-hole pairs require Hartree-Fock treatment which, in its usual form, preserves excitonic poles but loses biexcitonic resonances. (ii) Solving the resulting coupled differential equations imposes heavy numerics which completely hide the physics. This can be completely avoided if, instead of free electron-hole pairs, we use correlated pairs, i.e., excitons. Their interactions are easy to handle through the recently constructed composite-exciton many-body theory, which allows us to \emph{analytically} obtain the time evolution of the polarization induced by a laser pulse. This polarization comes from Coulomb interactions between virtual excitons, but also from Coulomb-free fermion exchanges, which are dominant at large detuning.

cond-mat.mes-hall↗

arXiv2009

Role of Fermion Exchanges in Statistical Signatures of Composite Bosons

We study statistical signatures of composite bosons made of two fermions using a new many-body approach. Extending number-states to composite bosons, two-particle correlations as well as the dispersion of the probability distribution are analyzed. We show that the particle composite nature reduces the anti-bunching effect predicted for elementary bosons. Furthermore, the probability distribution exhibits a dispersion which is greater for composite bosons than for elementary bosons. This dispersion corresponds to the one of sub-Poissonian processes, as for a quantum state, but, unlike its elementary boson counterpart, it is not minimum. In general, our work shows that it is necessary to take into account the Pauli exclusion principle which takes place between fermionic components of composite bosons - along the line here used - to possibly extract statistical properties in a precise way.

quant-ph↗

arXiv2009

Shiva and Kali diagrams for composite quantum particle many-body effects

For half a century, Feynman diagrams have provided an enlightening way of representing many-body effects between elementary fermions and bosons. They however are quite inappropriate to visualize fermion exchanges taking place between a large number of composite quantum particles. We propose to replace them by "Shiva diagrams" for cobosons made of two fermions and by Shiva-like and "Kali diagrams" for cofermions made of three fermions. We also show how these fermion exchanges formally appear in a many-body theory appropriate to composite quantum particles. This theory relies on an operator algebra based on commutators and anticommutators, the usual scalar algebra based on Green functions being valid for elementary bosons or fermions having strict commutation relations, only.

cond-mat.mes-hall↗

arXiv2009

Composite boson many-body theory for Frenkel excitons

We present a many-body theory for Frenkel excitons which takes into account their composite nature exactly. Our approach is based on four commutators similar to the ones we previously proposed for Wannier excitons. They allow us to calculate any physical quantity dealing with $N$ excitons in terms of "Pauli scatterings" for carrier exchange in the absence of carrier interaction and "interaction scatterings" for carrier interaction in the absence of carrier exchange. We show that Frenkel excitons have a novel "transfer assisted exchange scattering", specific to these excitons. It comes from indirect Coulomb processes between localized atomic states. These indirect processes, commonly called "electron-hole exchange" in the case of Wannier excitons and most often neglected, are crucial for Frenkel excitons, as they are the only ones responsible for the excitation transfer. We also show that in spite of the fact that Frenkel excitons are made of electrons and holes on the same atomic site, so that we could naively see them as elementary particles, they definitely are composite objects, their composite nature appearing through various properties, not always easy to guess. The present many-body theory for Frenkel excitons is thus going to appear as highly valuable to securely tackle their many-body physics, as in the case of nonlinear optical effects in organic semiconductors.

cond-mat.mes-hall↗

arXiv2008

Ground state energy of N Frenkel excitons

By using the composite many-body theory for Frenkel excitons we have recently developed, we here derive the ground state energy of $N$ Frenkel excitons in the Born approximation through the Hamiltonian mean value in a state made of $N$ identical $\mathbf{Q=0}$ excitons. While this quantity reads as a density expansion in the case of Wannier excitons, due to many-body effects induced by fermion exchanges between $N$ composite particles, we show that the Hamiltonian mean value for $N$ Frenkel excitons only contains a first order term in density, just as for elementary bosons. Such a simple result comes from a subtle balance, difficult to guess a priori, between fermion exchanges for two or more Frenkel excitons appearing in Coulomb term and the ones appearing in the $N$ exciton normalization factor - the cancellation being exact within terms in $1/N_{s}$ where $N_{s}$ is the number of atomic sites in the sample. This result could make us naively believe that, due to the tight binding approximation on which Frenkel excitons are based, these excitons are just bare elementary bosons while their composite nature definitely appears at various stages in the precise calculation of the Hamiltonian mean value.

cond-mat.mes-hall↗

arXiv2008

Third order susceptibility: general formalism for photoinduced current density in semiconductors

This paper contains a detailed derivation of the photoinduced current density at third order in the coupling between a semiconductor and a multifrequency photon field, starting from its standard textbook expression as a third order time integral of a triple commutator. Due to a major intrinsic problem linked to this triple commutator, such a derivation has been made possible quite recently only, thanks to the tools developed in the composite-boson many-body theory we have just constructed. The photoinduced current density is shown to ultimately read in a compact form, in terms of the Pauli and Coulomb scatterings for exciton-exciton interactions introduced in this theory. Representation in Shiva diagrams is also given to better grasp the physics of the various contributions.

cond-mat.mes-hall↗

arXiv2008

Closure relations for composite bosons: difference between polaritons and Wannier or Frenkel excitons

We derive the closure relation for $N$ polaritons made of three different types of excitons: bosonized excitons, Frenkel or Wannier excitons. In the case of polaritons made of Wannier excitons, we show how this closure relation, which appears as non-diagonal, may reduce to the one of $N$ elementary bosons, the photons, with its $1/N!$ prefactor, or to the one of $N$ Wannier excitons, with its $(1/N!)^2$ prefactor. Widely different forms of closure relations are thus found depending on the composite bosons at hand. Comparison with closure relations of excitons, either bosonized or kept composite as Frenkel or Wannier excitons, allows us to discuss the influence of a reduction of the number of internal degrees of freedom, as well as the importance of the composite nature of the particles and the existence of fermionic components.

cond-mat.mes-hall↗

arXiv2008

Stability of a Bose-Einstein condensate revisited for composite bosons

It is known that elementary bosons condense in a unique state, not so much because this state has the lowest free particle energy but because it costs a macroscopic amount of energy to put the particles into different states which can then interact through quantum particle exchanges. Since individual exchanges between the two fermions of a composite boson are ignored when composite particles are replaced by elementary bosons, it is of importance to reconsider the exchange energy argument for the stability of the Bose-Einstein condensate in the case of composite bosons. We do this here in the light of the new many-body theory which allows us to take exactly into account all possible exchanges between the fermionic components of the composite bosons. We confirm that the condensate of composite bosons is made of a unique state, this state being moreover pure: a coherent superposition of states close in energy is shown to be less favorable for both elementary and composite bosons.

cond-mat.other↗

arXiv2008

Exciton many-body effects through infinite series of composite-exciton operators

We revisit the approach proposed by Mukamel and coworkers to describe interacting excitons through infinite series of composite-boson operators for both, the system Hamiltonian and the exciton commutator -- which, in this approach, is properly kept different from its elementary boson value. Instead of free electron-hole operators, as used by Mukamel's group, we here work with composite-exciton operators which are physically relevant operators for excited semiconductors. This allows us to get \emph{all} terms of these infinite series explicitly, the first terms of each series agreeing with the ones obtained by Mukamel's group when written with electron-hole pairs. All these terms nicely read in terms of Pauli and interaction scatterings of the composite-exciton many-body theory we have recently proposed. However, even if knowledge of these infinite series now allows to tackle $N$-body problems, not just 2-body problems like third order nonlinear susceptibility $χ^{(3)}$, the necessary handling of these two infinite series makes this approach far more complicated than the one we have developed and which barely relies on just four commutators.

cond-mat.mes-hall↗