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.
Distinct Magneto-Optical Response of Frenkel and Wannier Excitons in CrSBr
Wroclaw University of Science and Technology（弗罗茨瓦夫科技大学）；Laboratoire National des Champs Magnétiques Intenses, EMFL, CNRS UPR 3228, Université Grenoble Alpes, Université Toulouse, Université Toulouse 3, INSA-T（强磁场国家实验室）；King’s College London（伦敦国王学院）；University of Chemistry and Technology Prague（布拉格化工大学）
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 resul…
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 composit…
Optical measurements and first-principles calculations of the band structure and exciton states in direct-gap bulk and few-layer PbI2 indicate that the n = 1 exciton is Frenkel-like in nature in that its energy exhibits a weak dependence on thickness down to atomic-length scales. Results reveal large increases of the gap and exciton binding energy with decreasing number of layers, and a transition of the fundamental gap, which becomes indirect for 1-2 monolayers. Calculated values are in reasonable agreement with a particle-in-a-box model relying on the Wannier-Mott theory of exciton formation…
Topological Frenkel excitons in 2D molecular crystals
Université de Strasbourg（斯特拉斯堡大学）；CNRS（法国国家科学研究中心）；Institute of Physics, Czech Academy of Sciences（捷克科学院物理研究所）；Georg-August-Universität Göttingen（哥廷根大学）；Donostia International Physics Center（多诺斯蒂亚国际物理中心）；Ikerbasque, Basque Foundation for Science（伊克尔巴斯克科学基金会）
Excitonic and vibronic spectra of Frenkel excitons (FEs) in a two-dimensional (2D) lattice with one molecule per unit cell have been studied and their manifestation in the linear absorption is simulated. We use the Green function formalism, the vibronic approach (see Lalov and Zhelyazkov [Phys. Rev. B \textbf{75}, 245435 (2007)]), and the nearest-neighbor approximation to find expressions of the linear absorption lineshape in closed form (in terms of the elliptic integrals) for the following 2D models: (a) vibronic spectra of polyacenes (naphthalene, anthracene, tetracene); (b) vibronic spectr…
The concept of quantum plasmonic excitations in plasmonic lattices, which similarly to Frenkel excitons in molecular crystals propagate by hopping from one nanoparticle to another, is introduced. A consistent quantum theory of such plasmonic excitons, beginning with the quantization of localized surface plasmons in a metal nanoparticle and including the radiative relaxation in both 1D and 2D lattices near a reflective substrate surface, is developed. A possible room-temperature Bose-Einstein condensation in the quantum gas of plasmonic excitons is also discussed.
In this work electronic structures and optical properties of organic-inorganic exciton and polaritons in two-dimensional heterostructures combining both organic and semiconductor materials are studied. In those systems, Wannier-Frenkel hybrid exciton has unique and interesting properties that can improve the efficiency of optical materials. When an organic-semiconductor combined heterostructure is illuminated by high-intensity electromagnetic radiation with the frequency of the photons at or near the resonance frequency of the Wannier-Frenkel exciton, we obtain a macroscopically occupied syste…
Frenkel polaritons, hybrid light-matter quasiparticles, offer promises for the designing of new opto-electronic devices. However, their technological implementations are hindered by sensitivity to imperfections. Topology has raised as a way to circumvent defects and fabrication limitations. Here, we propose a lattice of cavities to realize the one-dimensional Su-Schrieffer-Heeger model (SSH) for topological Frenkel polaritons. By engineering the configuration of the cavities we demonstrate that the SSH topological and trivial phases can be accessed, which we unravel by complementary classical …
This paper introduces a new quantum object, the ``coboson'', for composite particles, like the excitons, which are made of two fermions. Although commonly dealed with as elementary bosons, these composite bosons -- ``cobosons'' in short -- differ from them due to their composite nature which makes the handling of their many-body effects quite different from the existing treatments valid for elementary bosons. Due to this composite nature, it is not possible to correctly describe the interaction between cobosons as a potential $V$. Consequently, the standard Fermi golden rule, written in terms …
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 …
We have recently constructed a many-body theory for composite excitons, in which the possible carrier exchanges between $N$ excitons can be treated exactly through a set of dimensionless ``Pauli scatterings'' between two excitons. Many-body effects with excitons turn out to be rather simple because excitons are the exact one-electron-hole-pair eigenstates of the semiconductor Hamiltonian, thus forming a complete orthogonal set for one-pair states. It can however be of interest to extend this new many-body theory to more complicated composite bosons, \emph{i. e.}, ``cobosons'', which are not ne…
The control of exciton transport in organic materials is of fundamental importance for the development of efficient light-harvesting systems. This transport is easily deteriorated by traps in the disordered energy landscape. Here, we propose and analyze a system that supports topological Frenkel exciton edge states. Backscattering of these chiral Frenkel excitons is prohibited by symmetry, ensuring that the transport properties of such a system are robust against disorder. To implement our idea, we propose a two-dimensional periodic array of tilted porphyrins interacting with a homogenous magn…
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 …
Charged excitons of composite fermions (CFs) are considered in the fractional quantum Hall effect. Energies of the charged CF excitons are computed at $ν=1/3$ as a function of the size of exciton. We show that the charged CF exciton with size of roton is lower in energy than the unbound state of a neutral roton and a lone charge. Therefore we propose that the lowest-energy excitation of the fractional quantum Hall effect is in fact due to the charged excitons of composite fermions composed of two CF-particles and one CF-hole. We believe that charged excitons of composite fermions shed new ligh…
The simulation of the optical properties of supramolecular aggregates requires the development of methods, which are able to treat a large number of coupled chromophores interacting with the environment. Since it is currently not possible to treat large systems by quantum chemistry, the Frenkel exciton model is a valuable alternative. In this work we show how the Frenkel exciton model can be extended in order to explain the excitonic spectra of a specific double-walled tubular dye aggregate explicitly taking into account dispersive energy shifts of ground and excited states due to van der Waal…
The aim of this paper is to clarify the conceptual difference which exists between the interactions of composite bosons and the interactions of elementary bosons. A special focus is made on the physical processes which are missed when composite bosons are replaced by elementary bosons. Although what is here said directly applies to excitons, it is also valid for bosons in other fields than semiconductor physics. We in particular explain how the two basic scatterings -- Coulomb and Pauli -- of our many-body theory for composite excitons can be extended to a pair of fermions which is not an Hami…
Molecular materials have emerged as highly tunable materials for photovoltaic and light-harvesting applications. The most severe challenge of this class of materials is the trapping of charge carriers in bound electron-hole pairs, which severely limits the free charge carrier generation. Here, we demonstrate a significant modification of the exciton dynamics of thin films of endohedral metallofullerene complexes upon alkali metal intercalation. For the exemplary case of Sc$_3$N@C$_{80}$ thin films, we show that potassium intercalation results in an additional relaxation channel for the optical…
We present a quantitative microscopic analysis of the formation of exciton-polaritons, the composite particles possessing light and material components, polariton-polariton interactions, and resonant pumping dynamics in cylindrical semiconductor micropillars. We discuss how the redistribution effect can be used in devices generating photons with non zero orbital angular momenta.
We consider a nanostructure consisting of a semiconductor quantum dot coupled to a metal nanoparticle, and show with numerical simulations that the exciton state of the quantum dot can be robustly generated from the ground state even for small interparticle distances, using conventional chirped pulses with Gaussian and hyperbolic secant envelopes. The asymmetry observed in the final exciton population with respect to the chirp sign of the applied pulses is explained using the nonlinear density matrix equations describing the system, and is attributed to the real part of the parameter emerging …
Half-filled Landau levels admit the theoretically powerful fermion-vortex duality but longstanding puzzles remain in their experimental realization as $ν_T=1$ quantum Hall bilayers, further complicated by Zheng et al's recent numerical discovery of an unknown phase at intermediate layer spacing. Here we propose that half-filled quantum Hall bilayers ($ν_T=1$) at intermediate values of the interlayer distance $d/\ell_B$ enter a phase with \textit{paired exciton condensation}. This phase shows signatures analogous to the condensate of interlayer excitons (electrons bound to opposite-layer holes)…
Exact diagonalization studies have revealed that the energy spectrum of interacting electrons in the lowest Landau level splits, non-perturbatively, into bands, which is responsible for the fascinating phenomenology of this system. The theory of nearly free composite fermions has been shown to be valid for the lowest band, and thus to capture the low temperature physics, but it over-predicts the number of states for the excited bands. We explain the state counting of higher bands in terms of composite fermions with an infinitely strong short range interaction between an excited composite-fermi…
We compute the exciton transfer (ET) rate between semiconducting single-wall carbon nanotubes (SWNTs). We show that the main reasons for the wide range of measured ET rates reported in the literature are 1) exciton confinement in local quantum wells stemming from disorder in the environment and 2) exciton thermalization between dark and bright states due to intratube scattering. The SWNT excitonic states are calculated by solving the Bethe-Salpeter equation using tight-binding basis functions. The ET rates due to intertube Coulomb interaction are computed via Fermi's golden rule. In pristine s…
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 bosoniz…
