We investigate the transport of dipolar indirect excitons along the growth plane of polar (Al,Ga)N/GaN quantum well structures by means of spatially- and time-resolved photoluminescence spectroscopy. The transport in these strongly disordered quantum wells is activated by dipole-dipole repulsion. The latter induces an emission blue shift that increases linearly with exciton density, whereas the radiative recombination rate increases exponentially. Under continuous, localized excitation, we measure a continuous red shift of the emission, as excitons propagate away from the excitation spot. This shift corresponds to a steady-state gradient of exciton density, measured over several tens of micrometers. Time-resolved micro-photoluminescence experiments provide information on the dynamics of recombination and transport of dipolar excitons. We account for the ensemble of experimental results by solving the nonlinear drift-diffusion equation. Quantitative analysis suggests that in such structures, exciton propagation on the scale of 10 to 20 microns is mainly driven by diffusion, rather than by drift, due to the strong disorder and the presence of nonradiative defects. Secondary exciton creation, most probably by the intense higher-energy luminescence, guided along the sample plane, is shown to contribute to the exciton emission pattern on the scale up to 100 microns. The exciton propagation length is strongly temperature dependent, the emission being quenched beyond a critical distance governed by nonradiative recombination.
The nonlinear dynamics of a Bose-Einstein condensate (BEC) of dipolar excitons trapped in an external confining potential in coupled quantum wells is analysed. It is demonstrated that under typical experimental conditions the dipolar excitons BEC can be described by a generalized Gross-Pitaevskii equation with the local interaction between the excitons, which depends on the exciton distribution function. It is shown that, if the system is pumped at sufficiently high frequencies, a steady turbulent state can be formed.
In this paper we suggest a method to observe remote interactions of spatially separated dipolar quantum fluids, and in particular of dipolar excitons in GaAs bilayer based devices. The method utilizes the static electric dipole moment of trapped dipolar fluids to induce a local potential change on spatially separated test dipoles. We show that such an interaction can be used for a model- independent, objective fluid density measurements, an outstanding problem in this field of research, as well as for inter-fluid exciton flow control and trapping. For a demonstration of the effects on realisti…
Van der Waals heterostructures composed of transition metal dichalcogenide monolayers (TMDs) are characterized by their truly rich excitonic properties which are determined by their structural, geometric and electronic properties: In contrast to pure monolayers, electrons and holes can be hosted in different materials, resulting in highly tunable dipolar manyparticle complexes. However, for genuine spatially indirect excitons, the dipolar nature is usually accompanied by a notable quenching of the exciton oscillator strength. Via electric and magnetic field dependent measurements, we demonstra…
While the interaction potential between two dipoles residing in a single plane is repulsive, in a system of two vertically adjacent layers of dipoles it changes from repulsive interaction in the long range to attractive interaction in the short range. Here we show that for dipolar excitons in semiconductor heterostructures, such a potential may give rise to bound states if two such excitons are excited in two separate layers, leading to the formation of vertically coupled dipolar exciton molecules. Our calculations prove the existence of such bound states and predict their binding energy as a …
In this paper we show experimental evidence of a few correlation regimes of a cold dipolar exciton fluid, created optically in a semiconductor bilayer heterostructure. In the higher temperature regime, the average interaction energy between the particles shows a surprising temperature dependence which is an evidence for correlations beyond the mean field model. At a lower temperature, there is a sharp increase in the interaction energy of optically active excitons, accompanied by a strong reduction in their apparent population. This is an evidence for a sharp macroscopic transition to a dark s…
Correlations of luminescence intensity have been studied under Bose-Einstein condensation of dipolar excitons in the temperature range of 0.45-4.2 K. Photoexcited dipolar excitons were collected in a lateral trap in GaAs/AlGaAs Schottky-diode heterostructure with single wide (25 nm) quantum well under applied electric bias. Two-photon correlations were measured with the use of a classical Hanbury Brown - Twiss intensity interferometer (time resolution ~0.4 ns). Photon "bunching" has been observed near the Bose condensation threshold of dipolar excitons determined by the appearance of a narrow …
Dipolaritons are a three-way superposition of photon, a direct exciton, and an indirect exciton that are formed in coupled quantum well microcavities. As is the case with exciton-polaritons, dipolaritons have a self-interaction due to direct and exchange effects of the underlying electrons and holes. Here we present a theoretical description of dipolaritons and derive simple formulas for their basic parameters. In particular, we derive the effective dipolariton-dipolariton interaction taking into account of exchange effects between the excitons. We obtain a simple relation to describe the effe…
Dipolar excitons offer a rich playground for both design of novel optoelectronic devices and fundamental many-body physics. Wide GaN/(AlGa)N quantum wells host a new and promising realization of dipolar excitons. We demonstrate the in-plane confinement and cooling of these excitons, when trapped in the electrostatic potential created by semitransparent electrodes of various shapes deposited on the sample surface. This result is a prerequisite for the electrical control of the exciton densities and fluxes, as well for studies of the complex phase diagram of these dipolar bosons at low temperatu…
We report on the exciton propagation in polar (Al,Ga)N/GaN quantum wells over several micrometers and up to room temperature. The key ingredient to achieve this result is the crystalline quality of GaN quantum wells (QWs) grown on GaN template substrate. By comparing microphotoluminescence images of two identical QWs grown on sapphire and on GaN, we reveal the twofold role played by GaN substrate in the transport of excitons. First, the lower threading dislocation densities in such structures yield higher exciton radiative efficiency, thus limiting nonradiative losses of propagating excitons. …
The Mott transition from a dipolar excitonic liquid to an electron-hole plasma is demonstrated in a wide GaN/(Al,Ga)N quantum well at $T=7$K by means of spatially-resolved magneto-photoluminescence spectroscopy. Increasing optical excitation density we drive the system from the excitonic state, characterized by a diamagnetic behavior and thus a quadratic energy dependence on the magnetic field, to the unbound electron-hole state, characterized by a linear shift of the emission energy with the magnetic field. The complexity of the system requires to take into account both the density-dependence…
We study laterally trapped dipolar exciton ensembles in coupled GaAs quantum wells at high magnetic fields in the Faraday configuration. In photoluminescence experiments, we identify three magnetic field regimes. At low fields, the exciton density is increased by a reduced charge carrier escape from the trap, and additionally, the excitons' emission energy is corrected by a positive diamagnetic shift. At intermediate fields, magnetic field dependent correction terms apply which follow the characteristics of a neutral magnetoexciton. Due to a combined effect of an increasing binding energy and …
We describe the behavior of a repulsively interacting Bose-Einstein condensate of indirect dipolar exciton gas in a double quantum well (QW) system under external static or dynamic electric fields at finite temperatures. Electrostatic perturbation is considered to be created by an impurity atom or shot-range defect of QW fluctuation. The screening of this defect potential by an exciton condensate is studied. We find asymptotic spatial dependence of the screened potential and analyse its dependence on the temperature and exciton concentration. It is shown that the asymptotic of the screened pot…
The possible phases and the nano-scale particle correlations of two-dimensional interacting dipolar particles is a long-sought problem in many-body physics. Here we observe a spontaneous condensation of trapped two-dimensional dipolar excitons with internal spin degrees of freedom from an interacting gas into a high density, closely packed liquid state made mostly of dark dipoles. Another phase transition, into a bright, highly repulsive plasma is observed at even higher excitation powers. The dark liquid state is formed below a critical temperature $T_c \approx 4.8K$, and it is manifested by …
Photogenerated excitonic ensembles confined in coupled GaAs quantum wells are probed by a complementary approach of emission spectroscopy and resonant inelastic light scattering. Lateral electrostatic trap geometries are used to create dense systems of spatially indirect excitons and excess holes with similar densities in the order of 10$^{11}$ cm$^{-2}$. Inelastic light scattering spectra reveal a very sharp low-lying collective mode that is identified at an energy of 0.44 meV and a FWHM of only ~50 $μ$eV. This mode is interpreted as a plasmon excitation of the excess hole system coupled to t…
The interaction between aligned dipoles is long-ranged and highly anisotropic: it changes from repulsive to attractive depending on the relative positions of the dipoles. We report on the observation of the attractive component of the dipolar coupling between excitonic dipoles in stacked semiconductor bilayers. We show that the presence of a dipolar exciton fluid in one bilayer modifies the spatial distribution and increases the binding energy of excitonic dipoles in a vertically remote layer. The binding energy changes are explained by a many-body polaron model describing the deformation of t…
The formation of the roton-maxon excitation spectrum and the roton instability effect for a weakly correlated Bose gas of dipolar excitons in a semiconductor layer are predicted. The stability diagram is calculated. According to our numerical estimations, the threshold of the roton instability for Bose-Einstein condensed exciton gas with roton-maxon spectrum is achievable experimentally, e.g., in GaAs semiconductor layers.
We introduce a confocal shift-interferometer based on optical fibers. The presented spectroscopy allows measuring coherence maps of luminescent samples with a high spatial resolution even at cryogenic temperatures. We apply the spectroscopy onto electrostatically trapped, dipolar excitons in a semiconductor double quantum well. We find that the measured spatial coherence length of the excitonic emission coincides with the point spread function of the confocal setup. The results are consistent with a temporal coherence of the excitonic emission down to temperatures of 250 mK.
Quadrupolar and dipolar phases of excitons in transition-metal dichalcogenide trilayer heterostructures
The Racah Institute of Physics, The Hebrew University of Jerusalem（拉卡物理研究所，耶路撒冷希伯来大学）；Department of Physics, Technion（理工学院物理系）；The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem（分子动力学弗里茨·哈伯研究中心，耶路撒冷希伯来大学）
Emergence of algebraic quasi-long-range order is a key feature of superfluid phase transitions at two dimensions. For this reduced dimensionality interactions prevent Bose-Einstein condensation with true long range order, at any finite temperature. Here, we report the occurence of algebraic order in a strongly interacting quantum liquid formed by dipolar excitons confined in a bilayer semiconductor heterostructure. We observe a transition from exponential to algebraic decay of the excitons temporal coherence, accompanied by a universal scaling behaviour of the equation of state. Our results pr…
We develop the autolocalization hypothesis suggested recently in [Andreev, Phys. Rev. Lett. 110, 146401 (2013)] to explain the formation of the macroscopically ordered exciton state (MOES) in semiconductor quantum wells [L. V. Butov et al., Nature (London) 418, 751 (2002)]. We argue that the onset of a periodical localizing potential having a macroscopic spatial period is possible in the systems where in addition to long-range dipolar repulsion the excitons exhibit resonant pairing at short distances. Our theory suggests, that the central incoherent part of each condensate in the MOES may repr…
We study ultra-cold dipolar excitons confined in a 10$μ$m trap of a double GaAs quantum well. Based on the local density approximation, we unveil for the first time the equation of state of excitons at pure thermodynamic equilibrium. In this regime we show that, below a critical temperature of about $1$ Kelvin, a superfluid forms in the inner region of the trap at a local exciton density $n \sim 2-3 \, 10^{10} \text{cm}^{-2}$, encircled by a more dilute and normal component in the outer rim of the trap. Remarkably, this spatial arrangement correlates directly with the concentration of defects …
The formation of a dense Bose-Einstein condensate in dark spin states of two-dimensional dipolar excitons is shown to be driven by a dynamical transition to the long-lived dark states. The condensate is stabilized by strong dipole-dipole interactions up to densities high enough for a dark quantum liquid to form. The persistence of dark condensation was observed in recent experiments. A model describing the non-equilibrium dynamics of externally driven coupled dark and bright condensates reproduces the step-like dependence of the exciton density on the pump power or on temperature. This unique …
We consider quantum phase transitions in a system of bright dipolar excitons which can form bound pairs (dipolar biexcitons). We assume a narrow resonance in the interaction of excitons with opposite spins. At sufficiently large density a resonant exciton superfluid transforms into a superfluid of biexcitons. The transition may be either of the first or the second kind. The average relative momenta of excitons in the pairs being beyond the light cone, the transition should be accompanied by reduction of the photoluminescence intensity. Effective magnetic fields due to the long-range exchange s…
We study anisotropies of helicity modulus, excitation spectrum, sound velocity and angle-resolved luminescence spectrum in a two-dimensional system of interacting excitons in a periodic potential. Analytical expressions for anisotropic corrections to the quantities characterizing superfluidity are obtained. We consider particularly the case of dipolar excitons in quantum wells. For GaAs/AlGaAs heterostructures as well as MoS$_2$/hBN/MoS$_2$ and MoSe$_2$/hBN/WSe$_2$ transition metal dichalcogenide bilayers estimates of the magnitude of the predicted effects are given. We also present a method t…
We measure the spin-resolved transport of dipolar excitons in a biased GaAs double quantum well structure. From these measurements we extract both spin lifetime and mobility of the excitons. We find that below a temperature of $4.8$K, there is a sharp increase in the spin lifetime of the excitons, together with a sharp reduction in their mobility. Below a critical power the spin lifetime increases with increasing mobility and density, while above the critical power the opposite trend is observed. We interpret this transition as an evidence of the interplay between two different spin dephasing …
Trimer superfluidity of antiparallel dipolar excitons in a bilayer heterostructure
Racah Institute of Physics, The Hebrew University of Jerusalem（拉卡物理研究所，耶路撒冷希伯来大学）；The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem（弗里茨·哈伯分子动力学研究中心，耶路撒冷希伯来大学）
We discuss a possible link between the recently observed macroscopic ordering of ultra cold dipolar excitons (MOES) and the phenomenon of supersolidity. In the dilute limit we predict a stable supersolid state for a quasi-one-dimensional system of bosonic dipoles characterized by two- and three-body contact repulsion. We phenomenologically extend our theory to the strongly-correlated regime and find a critical value of the contact interaction parameter at which the supersolid exhibits a quantum phase transition to a fragmented state. The wavelength of the fragmented-condensate solid is defined…
The Hubbard model constitutes one of the most celebrated theoretical frameworks of condensed-matter physics. It describes strongly correlated phases of interacting quantum particles confined in lattice potentials. For bosons, the Hubbard Hamiltonian has been deeply scrutinised for short-range on-site interactions. However, accessing longer-range couplings has remained elusive experimentally. This marks the frontier towards the extended Bose-Hubbard Hamiltonian that allows insulating ordered phases at fractional lattice fillings. Here we implement this Hamiltonian by confining semiconductor dip…
Spatially indirect excitons in semiconducting double quantum wells have been shown to exhibit rich collective many-body behavior that result from the nature of the extended dipole-dipole interactions between particles. For many spectroscopic studies of the emission from a system of such indirect excitons, it is crucial to separate the single particle properties of the excitons from the many-body effects arising from their mutual interactions. In particular, knowledge of the relation between the emission energy of indirect excitons and their radiative lifetime could be highly beneficial for con…
We consider a bilayer system of two-dimensional Bose-Einstein-condensed dipolar dark excitons (upper layer) and bright ones (bottom layer). We demonstrate that the interlayer interaction leads to a mixing between excitations from different layers. This mixing leads to the appearance of a second spectral branch in the spectrum of bright condensate. The excitation spectrum of the condensate of dark dipolar excitons then becomes optically accessible during luminescence spectra measurements of the bright condensate, which allows one to probe its kinetic properties. This approach is relevant for ex…
Recently we reported on the condensation of cold, electrostatically trapped dipolar excitons in GaAs bilayer heterostructure into a new, dense and dark collective phase. Here we analyze and discuss in detail the experimental findings and the emerging evident properties of this collective liquid-like phase. We show that the phase transition is characterized by a sharp increase of the number of non-emitting dipoles, by a clear contraction of the fluid spatial extent into the bottom of the parabolic-like trap, and by spectral narrowing. We extract the total density of the condensed phase which we…
A giant built-in electric field in the growth direction makes excitons in wide GaN/(Al, Ga)N quantum wells spatially indirect even in the absence of any external bias. Significant densities of indirect excitons can accumulate in electrostatic traps imprinted in the quantum well plane by a thin metal layer deposited on top of the heterostructure. By jointly measuring spatially-resolved photoluminescence and photo-induced current, we demonstrate that exciton density in the trap can be controlled via an external electric bias, which is capable of altering the trap depth. Application of a negative…
Layered bosonic dipolar fluids have been suggested to host a condensate of interlayer molecular bound states. However, its experimental observation has remained elusive. Motivated by two recent experimental works [Hubert et al., Phys. Rev. X 9, 021026 (2019) and D. J. Choksy et al., Phys. Rev. B 103 045126 (2021)], we theoretically study, using numerically exact quantum Monte Carlo calculations, the experimental signatures of collective interlayer pairing in vertically stacked indirect exciton (IX) layers. We find that IX energy shifts associated with each layer evolve non trivially as a funct…
Supersolid crystals of dipolar excitons in a lattice
Université Côte d’Azur, CNRS, CRHEA（蔚蓝海岸大学）；Université de Strasbourg, CNRS, ISIS（斯特拉斯堡大学）；Dipartimento di Fisica e Astronomia ”G. Galilei” and Padua Quantum Technologies Research Center, Università degli Studi di Padova（帕多瓦大学伽利略物理与天文系及帕多瓦量子技术中心）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；PRISM, Princeton Institute for the Science and Technology of Materials, Princeton University（普林斯顿大学材料科学与技术研究所）
Excitons in semiconductors may form correlated phases at low temperatures. We report the observation of an exciton liquid in GaAs/AlGaAs coupled quantum wells. Above a critical density and below a critical temperature the photogenerated electrons and holes separate into two phases, an electron-hole plasma and an exciton liquid, with a clear sharp boundary between them. The two phases are characterized by distinct photoluminescence spectra and by different electrical conductance. The liquid phase is formed by the repulsive interaction between the dipolar excitons, and exhibits a short range ord…
Interlayer excitons (IXs) in hetero-bilayers of transition metal dichalcogenides (TMDs) represent an exciting emergent class of long-lived dipolar composite bosons in an atomically thin, near-ideal two-dimensional (2D) system. The long-range interactions that arise from the spatial separation of electrons and holes can give rise to novel quantum, as well as classical multi-particle correlation effects. In order to acquire a detailed understanding of the possible many-body effects, the fundamental interactions between individual IXs have to be studied. Here, we trap a tunable number of dipolar …
