arXiv subjects

O. Betbeder-Matibet

Publications and source records attributed to O. Betbeder-Matibet.

30 records · Page 2Linked to original sources

arXiv2004

Scattering rates and lifetime of exact and boson excitons

Although excitons are not exact bosons, they are commonly treated as such provided that their composite nature is included in effective scatterings dressed by exchange. We here \emph{prove} that, \emph{whatever these scatterings are}, they cannot give both the scattering rates $T_{ij}^{-1}$ and the exciton lifetime $τ_0$, correctly: A striking factor 1/2 exists between $τ_0^{-1}$ and the sum of $T_{ij}^{-1}$'s, which originates from the composite nature of excitons, irretrievably lost when they are bosonized. This result, which appears as very disturbing at first, casts major doubts on bosonization for problems dealing with \emph{interacting} excitons.

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arXiv2004

Theory of spin precession monitored by laser pulse

We first predict the splitting of a spin degenerate impurity level when this impurity is irradiated by a circularly polarized laser beam tuned in the transparency region of a semiconductor. This splitting, which comes from different exchange processes between the impurity electron and the virtual pairs coupled to the pump beam, induces a spin precession around the laser beam axis, which lasts as long as the pump pulse. It can thus be used for ultrafast spin manipulation. This effect, which has similarities with the exciton optical Stark effect we studied long ago, is here derived using the concepts we developed very recently to treat many-body interactions between composite excitons and which make the physics of this type of effects quite transparent. They, in particular, allow to easily extend this work to other experimental situations in which a spin rotates under laser irradiation.

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arXiv2004

Excitons dressed by a sea of excitons

We here consider an exciton $i$ embedded in a sea of $N$ identical excitons 0. If the excitons are bosonized, a bosonic enhancement factor, proportional to $N$, is found for $i=0$. If the exciton composite nature is kept, this enhancement not only exists for $i=0$, but also for any exciton having a center of mass momentum equal to the sea exciton momentum. This physically comes from the fact that an exciton with such a momentum can be transformed into a sea exciton by ``Pauli scattering'', \emph{i}. \emph{e}., carrier exchange with the sea, making this $i$ exciton not so much different from a 0 exciton. This possible scattering, directly linked to the composite nature of the excitons, is irretrievably lost when the excitons are bosonized. This work in fact deals with the quite tricky scalar products of $N$-exciton states. It actually constitutes a crucial piece of our new many-body theory for interacting composite bosons, because all physical effects involving these composite bosons ultimately end by calculating such scalar products. The ``Pauli diagrams'' we here introduce to represent them, allow to visualize many-body effects linked to carrier exchange in an easy way. They are conceptually different from Feynman diagrams, because of the special feature of the ``Pauli scatterings'': These scatterings, which originate from the departure from boson statistics, do not have their equivalent in Feynman diagrams, the commutation rules for exact bosons (or fermions) being included in the first line of the usual many-body theories.

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arXiv2004

The trion: two electrons plus one hole versus one electron plus one exciton

We first show that, for problems dealing with trions, it is totally hopeless to use the standard many-body description in terms of electrons and holes and its associated Feynman diagrams. We then show how, by using the description of a trion as an electron interacting with an exciton, we can obtain the trion absorption through far simpler diagrams, written with electrons and \emph{excitons}. These diagrams are quite novel because, for excitons being not exact bosons, we cannot use standard procedures designed to deal with interacting true fermions or true bosons. A new many-body formalism is necessary to establish the validity of these electron-exciton diagrams and to derive their specific rules. It relies on the ``commutation technique'' we recently developed to treat interacting close-to-bosons. This technique generates a scattering associated to direct Coulomb processes between electrons and excitons and a dimensionless ``scattering'' associated to electron exchange inside the electron-exciton pairs -- this ``scattering'' being the original part of our many-body theory. It turns out that, although exchange is crucial to differentiate singlet from triplet trions, this ``scattering'' enters the absorption explicitly when the photocreated electron and the initial electron have the same spin -- \emph{i}. \emph{e}., when triplet trions are the only ones created -- \emph{but not} when the two spins are different, although triplet trions are also created in this case. The physical reason for this rather surprising result will be given.

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arXiv2003

Novel approach to nonlinear susceptibility

The calculation of the third order susceptibility still is a long standing fundamental problem of particular importance in nonlinear nanooptics: Indeed, cancellation of size-dependent terms coming from uncorrelated excitations is expected, but up to now shown for very simple Hamiltonians only. Using a many-body theory recently developed to handle interacting close-to-bosons, we prove it here for \emph{arbitrary} H. This new formalism actually provides the first clean way to calculate nonlinear susceptibilities, with results different from previous ones.

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arXiv2003

The trion as an exciton interacting with a carrier

The X$^-$ trion is essentially an electron bound to an exciton. However, due to the composite nature of the exciton, there is no way to write an exciton-electron interaction potential. We can overcome this difficulty by using a commutation technique similar to the one we introduced for excitons interacting with excitons, which allows to take exactly into account the close-to-boson character of the excitons. From it, we can obtain the X$^-$ trion creation operator in terms of exciton and electron. We can also derive the X$^-$ trion ladder diagram between an exciton and an electron. These are the basic tools for future works on many-body effects involving trions.

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arXiv2002

Trion ladder diagrams

We first derive a new ``commutation technique'' for an exciton interacting with electrons, inspired from the one we recently developed for excitons interacting with excitons. These techniques allow to take \emph{exactly} into account the possible exchanges between carriers. We use it to get the $\mathrm{X}^-$ trion creation operator in terms of exciton and free-electron creation operators. In a last part we generate the ladder diagrams associated to these trions. Although similar to the exciton ladder diagrams, with the hole replaced by an exciton, they are actually much more tricky : (i) Due to the composite nature of the exciton, one cannot identify an exciton-electron potential similar to the Coulomb potential between electron and hole ; (ii) the spins are unimportant for excitons while they are crucial for trions, singlet and triplet states having different energies.

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arXiv2002

Commutation technique for an exciton photocreated close to a metal

Recently, we have derived the changes in the absorption spectrum of an exciton when this exciton is photocreated close to a metal. The resolution of this problem -- which has similarities with Fermi edge singularities -- has been made possible by the introduction of ``exciton diagrams''. The validity of this procedure relied on a dreadful calculation based on standard free electron and free hole diagrams, with the semiconductor-metal interaction included at second order only, and its intuitive extention to higher orders. Using the commutation technique we recently introduced to deal with interacting excitons, we are now able to \emph{prove} that this exciton diagram procedure is indeed valid at any order in the interaction. =

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arXiv2002

Commutation technique for interacting close-to-boson excitons

The correct treatment of the close-to-boson character of excitons is known to be a major problem. In a previous work, we have proposed a ``commutation technique'' to include this close-to-boson character in their interactions. We here extend this technique to excitons with spin degrees of freedom as they are of crucial importance for many physical effects. Although the exciton total angular momentum may appear rather appealing at first, we show that the electron and hole angular momenta are much more appropriate when dealing with scattering processes. As an application of this commutation technique to a specific problem, we reconsider a previous calculation of the exciton-exciton scattering rate and show that the proposed quantity is intrinsically incorrect for fundamental reasons linked to the fermionic nature of the excitons.

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arXiv2002

Density expansion of the energy of N close-to-boson excitons

Pauli exclusion between the carriers of $N$ excitons induces novel many-body effects, quite different from the ones generated by Coulomb interaction. Using our commutation technique for interacting close-to-boson particles, we here calculate the hamiltonian expectation value in the $N$-ground-state-exciton state.Coulomb interaction enters this quantity at first order only by construction ; nevertheless, due to Pauli exclusion, subtle many-body effects take place, which give rise to terms in $(Na_x^3/\mathcal{V})^n$ with $n\geq2$ >. An \emph{exact} procedure to get these density dependent terms is given.

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arXiv2002

Effective bosonic hamiltonian for excitons : a too naive concept

Excitons, being made of two fermions, may appear from far as bosons. Their close-to-boson character is however quite tricky to handle properly. Using our commutation technique especially designed to deal with interacting close-to-boson particles, we here calculate the exact expansion in Coulomb interaction of theexciton-exciton correlations, and show that a naive effective bosonic hamiltonian for excitons cannot produce these X-X correlations correctly.

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arXiv2001

The Effective Bosonic Hamiltonian for Excitons Reconsidered

The effective bosonic hamiltonian for excitons, extensively quoted up to now, cannot be correct because it is (surprisingly) non-hermitian. The oversight physically originates from the intrinsic difficulty of properly defining electron-hole interactions between excitons when dealing with exchange terms. By using our commutation technique, we show that the fermionic character of the excitons cannot be forced into a dressed Coulomb interaction only : The effective bosonic hamiltonian must contain purely fermionic terms of the same order as the Coulomb terms. They are necessary to ensure hermiticity, and they do not reduce to a two-body interaction, Pauli exclusion being N-body by essence.

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