arXiv subjects

Monique Combescot

Publications and source records attributed to Monique Combescot.

At least 19 recordsLinked to original sources

arXiv2023

A fresh view on Frenkel excitons: Electron-hole pair exchange and many-body formalism

We here present a fresh approach to Frenkel excitons in cubic semiconductor crystals, with a special focus on the spin and spatial degeneracies of the electronic states. This approach uses a second quantization formulation of the problem in terms of creation operators for electronic states on all lattice sites -- their creation operators being true fermion operators in the tight-binding limit valid for semiconductors hosting Frenkel excitons. This operator formalism avoids using cumbersome ($6N_s$ x $6N_s$) Slater determinants -- 2 for spin, 3 for spatial degeneracy and $N_s$ for the number of lattice sites -- to represent state wave functions out of which the Frenkel exciton eigenstates are derived. A deep understanding of the tricky Coulomb physics that takes place in the Frenkel exciton problem, is a prerequisite for possibly diagonalizing this very large matrix analytically. This is done in three steps: (i) the first diagonalization, with respect to lattice sites, follows from transforming excitations on the $N_s$ lattice sites $\mathbf{R}_\ell$ into $N_s$ exciton waves $\mathbf{K}_n$, by using appropriate phase prefactors; (ii) the second diagonalization, with respect to spin, follows from the introduction of spin-singlet and spin-triplet electron-hole pair states, through the commonly missed sign change when transforming electron-absence operators into hole operators; (iii) the third diagonalization, with respect to threefold spatial degeneracy, leads to the splitting of the exciton level into one longitudinal and two transverse modes, that result from the singular interlevel Coulomb scattering in the small $\mathbf{K}_n$ limit.

cond-mat.quant-gas↗

arXiv2023

Ab initio quantum approach to electron-hole exchange for semiconductors hosting Wannier excitons

We propose a quantum approach to "electron-hole exchange", better named electron-hole pair exchange, that makes use of the second quantization formalism to describe the problem in terms of Bloch-state electron operators. This approach renders transparent the fact that such singular effect comes from interband Coulomb processes. We first show that, due to the sign change when turning from valence-electron destruction operator to hole creation operator, the interband Coulomb interaction only acts on spin-singlet electron-hole pairs, just like the interband electron-photon interaction, thereby making these spin-singlet pairs optically bright. We then show that when written in terms of reciprocal lattice vectors ${\bf G}_m$, the singularity of the interband Coulomb scattering in the small wave-vector transfer limit entirely comes from the ${\bf G}_m = 0$ term, which renders its singular behavior easy to calculate. Comparison with the usual real-space formulation in which the singularity appears through a sum of "long-range processes" over all ${\bf R}\not= 0$ lattice vectors once more proves that periodic systems are easier to handle in terms of reciprocal vectors ${\bf G}_m$ than in terms of lattice vectors $\bf R$. Well-accepted consequences of the electron-hole exchange on excitons and polaritons are reconsidered and refuted for different major reasons.

cond-mat.mtrl-sci↗

arXiv2023

Symmetry breaking for semiconductor excitons induced by Coulomb coupling between heavy and light holes

Semiconductor excitons are commonly seen as hydrogen atom. This analogy requires a unique hole mass. In reality, this is not so due to the complexity of the semiconductor band structure. The precise consequences on the exciton physics of the Coulomb coupling between heavy and light holes remain a tricky open problem. Through an ``optimized perturbative'' approach that uses excitons with a flexible hole mass as a basis, we show that for zero exciton wave vector, the heavy-light hole mass difference does not split the $(2\times4)$ exciton degeneracy in zinc-blende-like semiconductors, the hole mass for binding energy being close to the average mass inverse. By contrast, for nonzero exciton wave vector, that physically breaks the crystal symmetry, the exciton degeneracy splits into two branches quantized along the exciton wave vector, with nontrivial center-of-mass dependence not only on the heavy and light hole masses, but also on the electron mass.

cond-mat.str-el↗

arXiv2022

From spherical to periodic symmetry: the analog of orbital angular momentum for semiconductor crystals

The angular momentum formalism provides a powerful way to classify atomic states. Yet, requiring a spherical symmetry from the very first line, this formalism cannot be used for periodic systems, even though cubic semiconductor states are commonly classified according to atomic notations. Although never noted, it is possible to define the analog of the orbital angular momentum, by only using the potential felt by the electrons. The spin-orbit interaction for crystals then takes the $\mathbfcal{\hat{L}}\cdot \hat{\vS}$ form, with $\mathbfcal{\hat{L}}$ reducing to $\hat{\vL}=\vr\times\hat{\vp}$ for spherical symmetry. This provides the long-missed support for using the eigenvalues of $\mathbfcal{\hat{L}}$ and $\mathbfcal{\hat{J}}=\mathbfcal{\hat{L}}+\hat{\vS}$, as quantum indices to label cubic semiconductor states. Importantly, these quantum indices also control the phase factor that relates valence electron to hole operators, in the same way as particle to antiparticle, in spite of the fact that the hole is definitely not the valence-electron antiparticle. Being associated with a broader definition, the ($\mathbfcal{\hat{L}},\mathbfcal{\hat{J}}$) analogs of the $(\hat{\vL},\hat{\vJ})$ angular momenta, must be distinguished by names: we suggest "spatial momentum" for $\mathbfcal{\hat{L}}$ that acts in the real space, and "hybrid momentum" for $\mathbfcal{\hat{J}}$ that also acts on spin, the potential symmetry being specified as "cubic spatial momentum". This would cast $\hat{\vJ}$ as a "spherical hybrid momentum", a bit awkward for the concept is novel.

cond-mat.mtrl-sci↗

arXiv2022

Signature of electromagnetic quantum fluctuations in exciton physics

Quantum fluctuations of the electromagnetic field are known to produce the atomic Lamb shift. We here reveal their iconic signature in semiconductor physics, through the blue-shift they produce to optically bright excitons, thus lifting the energy of these excitons above their dark counterparts. The electromagnetic field here acts in its full complexity: in addition to the longitudinal part via interband \textit{virtual Coulomb} processes, the transverse part -- which has been missed up to now -- also acts via resonant and nonresonant \textit{virtual photons}. These two parts beautifully combine to produce a bright exciton blue-shift independent of the exciton wave-vector direction. Our work readily leads to a striking prediction: long-lived excitons must have a small bright-dark splitting. Although the analogy between exciton and hydrogen atom could lead us to see the bright exciton shift as a Lamb shift, this is not fully so: the atom shift entirely comes from virtual photons, whereas the Coulomb interaction also contributes to the exciton shift through the so-called "electron-hole exchange".

cond-mat.mtrl-sci↗

arXiv2021

From hybrid polariton to dipolariton using non-hermitian Hamiltonians to handle particle lifetimes

We consider photons strongly coupled to the excitonic excitations of a coupled quantum well, in the presence of an electric field. We show how under a field increase, the hybrid polariton made of photon coupled to hybrid carriers lying in the two wells, transforms into a dipolariton made of photon coupled to direct and indirect excitons. We also show how the cavity photon lifetime and the coherence time of the carrier wave vectors, that we analytically handle through non-hermitian Hamiltonians, affect these polaritonic states. While the hybrid polaritons display a spectral singularity, where the eigenvalues coalesce and known as exceptional point, that depends on detuning and lifetimes, we find that the three dipolaritonic states display an anti-crossing without exceptional point, due to interaction between photons, direct and indirect excitons.

cond-mat.mes-hall↗

arXiv2021

Exploring the change of semiconductor hole mass under Coulomb scattering

Semiconductor valence holes are known to have heavy and light effective masses; but the consequence of this mass difference on Coulomb scatterings has been considered intractable and thus ignored up to now. The reason is that the heavy/light index is quantized along the hole momentum that changes in a Coulomb scattering; so, a heavy hole can turn light, depending on the scattering angle. This mass change has never been taken into account in many-body problems, and a single ``average'' hole mass has been used instead. In order to study the missed consequences of this crude approximation, the first necessary step is to determine the Coulomb scatterings with valence holes in a precise way. We here derive these scatterings from scratch, starting from the threefold valence-electron spatial level, all the way through the spin-orbit splitting, the Kohn-Luttinger effective Hamiltonian, its spherical approximation, and the phase factors that appear when turning from valence electron to hole operators, that is, all the points of semiconductor physics that render valence holes so different from a naïve positive charge.

cond-mat.str-el↗

arXiv2021

Missing understanding of the phase factor between valence-electron and hole operators

This paper provides the long-missing foundation to connect semiconductor and atomic notations and to support results incorrectly obtained by doing as if semiconductor electrons possessed an orbital angular momentum. We here show that the phase factor between valence-electron destruction operator and hole creation operator is the same as the one between particle and antiparticle in quantum relativity, namely $\hat{a}_{m}=(-1)^{j-m} \hat{b}^†_{-m}$ provided that $m=(j,j-1\cdots,-j)$ labels the degenerate states of the $(2j+1)$-fold electron level at hand. This result is remarkable because $(i)$ the hole is definitely not a naive antiparticle due to the remaining valence electrons; $(ii)$ unlike atomic electrons in a central potential, semiconductor electrons in a periodic crystal do not have orbital angular momentum $\textbf{L}=\textbf{r}\wedge\textbf{p}$ nor angular momentum $\textbf{J}=\textbf{L}+\textbf{S}$. Consequently, $(j,m)$ for semiconductor electrons merely are convenient notations to label the states of a degenerate level. To illustrate the physical implications, we discuss the interband couplings between photons and semiconductor, in terms of valence electrons and of holes: the phase factor is crucial to establish that bright excitons are in a spin-singlet state.

cond-mat.quant-gas↗

arXiv2020

Understanding Semiconductor Valence Mass

The Bloch theorem mathematically proves that in a periodic crystal, electrons can acquire a negative mass. The present work aims to provide a physical understanding for why this is so. We successively analyze the consequences of the 3-fold orbital valence state coupling to (i) a non-degenerate orbital level in the conduction band, (ii) a 3-fold orbital level in the conduction band, and (iii) spin states through spin-orbit interaction. We show that it is not at all trivial for valence electrons to acquire a negative mass for whatever their momentum with respect to the crystal axes: it is necessary to not only have a coupling to a degenerate orbital conduction level, but also a symmetry breaking of the 3-fold valence subspace by the spin quantization axis, as induced by spin-orbit interaction. Due to the relativistic origin of this interaction, the existence of negative valence masses thus constitutes an unexpected signature of quantum relativity.

cond-mat.mtrl-sci↗

arXiv2020

Photocreation of a dark electron-hole pair in a quantum dot

Photon absorption in a semiconductor produces bright excitons that recombine very fast into photons. We here show that in a quantum dot set close to a p-doped reservoir, this absorption can produce a dark duo, i.e., an electron-hole pair that does not emit light. This unexpected effect relies on the fact that the wave function for a hole leaks out of a finite-barrier dot less than for electron. This difference can render the positively charged trio unstable in the dot by tuning the applied bias voltage in a field-effect device. The unstable trio that would result from photon absorption in a positively charged dot, has to eject one of its two holes. The remaining duo can be made dark with a probability close to 100% after a few pumping cycles with linearly polarized photons, in this way engineering long-lived initial states for quantum information processing.

cond-mat.mes-hall↗

arXiv2020

Fundamental differences between exciton and quantum dot duo

We present five major reasons why semiconductor exciton, that is, a correlated electron-hole pair in a bulk, quantum well, or quantum wire, is conceptually different from a pair in a quantum dot: (1) the origin of pair binding, (2) the interaction with additional carriers, (3) the quantum nature of the pair, (4) the coupling to photon, and (5) the photon-absorption mechanism. Due to these differences, we should refrain from calling an electron-hole pair in a quantum dot an exciton, as commonly done; we propose to call it a duo. Within the same frame of chamber musics, we likewise propose to call three and four carriers in a dot, a trio and a quatuor, instead of a trion and a biexciton.

cond-mat.mtrl-sci↗

arXiv2019

Optical signature of quantum coherence in fully dark exciton condensates

We predict that the collision of two fully dark exciton condensates produces interference fringes which are not only dark but also bright. So, quite surprisingly, the collision of coherent states made of dark excitons produces light. This remarkable effect, which is many-body in essence, comes from the composite boson nature of excitons, through the fermion exchanges they can have which transform dark states into bright states. The possibility of optically detecting quantum coherence in a regime where the system is hidden by its total darkness, was up to now considered as hopeless.

cond-mat.quant-gas↗

arXiv2019

Spin-orbit coupling: atom versus semiconductor crystal

We reconsider a key point in semiconductor physics, the splitting of the valence band states induced by the spin-orbit interaction, through a novel approach which uses neither the group theory formalism, nor the usual $\textbf{L}\cdot\textbf{S}$ formulation valid for atoms but conceptually incorrect for periodic lattices, the angular momenta $\textbf{L}$ and $\textbf{J}$ having no meaning due to the absence of spherical symmetry. We show that for zinc-blende structures, the valence band eigenstates resulting from spin-orbit coupling are uniquely determined by: (i) the equivalence of the ($x,y,z$) crystal axes, (ii) the three-fold degeneracy of the valence band. The fact that these two conditions are also fulfilled by atomic $p$ states allows us to understand why the spin-orbit eigenstates for three-fold atomic and valence electrons have exactly the same structure, albeit the drastic differences in the potential and electronic symmetries. We also come back to the commonly accepted understanding of the exciton-photon interaction in terms of bright and dark excitons having total angular momenta $J=(1,2)$ respectively and present a simple derivation of this interaction which only relies on spin conservation.

cond-mat.mes-hall↗

arXiv2019

Composite boson signature in the interference pattern of atomic dimer condensates

We predict the existence of high frequency modes in the interference pattern of two condensates made of fermionic-atom dimers. These modes, which result from fermion exchanges between condensates, constitute a striking signature of the dimer composite nature. From the 2-coboson spatial correlation function, that we derive analytically, and the Shiva diagrams that visualize many-body effects specific to composite bosons, we identify the physical origin of these high frequency modes and determine the conditions to see them experimentally by using bound fermionic-atom pairs trapped on optical lattice sites. The dimer granularity which appears in these modes comes from Pauli blocking that prevents two dimers to be located at the same lattice site.

cond-mat.quant-gas↗

arXiv2019

Two-level System coupled to Phonons: Full Analytical Solution

We propose an analytical procedure to fully solve a two-level system coupled to phonons. Instead of using the common formulation in terms of linear and quadratic system-phonon couplings, we introduce different phonons depending on the system electronic level. We use this approach to recover known results for the linear-coupling limit in a simple way. More importantly, we derive results for the quadratic coupling induced by a phonon frequency change, a problem considered up to now as not analytically solvable.

quant-ph↗

arXiv2018

Coboson many-body formalism for atom-dimer scattering length

We use the composite boson (coboson) many-body formalism to tackle scattering lengths for cold fermionic atoms. We show that bound dimers can be taken as elementary entities provided that fermion exchanges between them are treated exactly, as can be done through the coboson formalism. This alternative tool extended to cold atom physics not only makes transparent many-body processes through Shiva diagrams specific to cobosons, but also simplifies calculations. Indeed, the integral equation we derive for the atom-dimer scattering length and solve by restricting the dimer relative motion to the ground state, gives values in remarkable agreement with the exact scattering length values for all fermion mass ratios. This remarkable agreement also holds true for the dimer-dimer scattering length, except for equal fermion masses where our restricted procedure gives a value slightly larger than the accepted one ($0.64a_d$ instead of $0.60a_d$). All this proves that the scattering of a cold-atom dimer with an atom or another dimer is essentially controlled by the dimer relative-motion ground state, a physical result not obvious at first.

cond-mat.quant-gas↗

arXiv2018

Cross-over from trion-hole to exciton-polaron in n-doped semiconductor quantum wells

We present a theoretical study of photo-absorption in n-doped two-dimensional (2D) and quasi-2D semiconductors that takes into account the interaction of the photocreated exciton with Fermi-sea (FS) electrons through (i) Pauli blocking, (ii) Coulomb screening, and (iii) excitation of FS electron-hole pairs---that we here restrict to one. The system we tackle is thus made of one exciton plus zero or one FS electron-hole pair. At low doping, the system ground state is predominantly made of a "trion-hole"---a trion (two opposite-spin electrons plus a valence hole) weakly bound to a FS hole---with a small exciton component. As the trion is poorly coupled to photon, the intensity of the lowest absorption peak is weak; it increases with doping, thanks to the growing exciton component, due to a larger coupling between 2-particle and 4-particle states. Under a further doping increase, the trion-hole complex is less bound because of Pauli blocking by FS electrons, and its energy increases. The lower peak then becomes predominantly due to an exciton dressed by FS electron-hole pairs, that is, an exciton-polaron. As a result, the absorption spectra of $n$-doped semiconductor quantum wells show two prominent peaks, the nature of the lowest peak turning from trion-hole to exciton-polaron under a doping increase. Our work also nails down the physical mechanism behind the increase with doping of the energy separation between the trion-hole peak and the exciton-polaron peak, even before the anti-crossing, as experimentally observed.

cond-mat.mes-hall↗

arXiv2017

Many-body formalism for thermally excited wave-packets: A way to connect the quantum regime to the classical regime

Free classical particles have well-defined momentum and position, while free quantum particles have well-defined momentum but a position fully delocalized over the sample volume. We develop a many-body formalism based on wave-packet operators that connects these two limits, the thermal energy being distributed between the state spatial extension and its thermal excitation. The corresponding `mixed quantum-classical' states, which render the Boltzmann operator diagonal, are the physically relevant states when the temperature is finite. The formulation of many-body Hamiltonians in terms of these thermally excited wave-packets and the resulting effective scatterings is provided.

quant-ph↗