Pattern formation as a signature of quantum degeneracy in a cold exciton system

Exciton condensation in quantum wells with defects of macroscopic sizes

Formation of the excitonic condensed phase in quantum wells with defects of macroscopic size is investigated in the case of a specific kind of defect arising in local areas of planar quantum wells where the wells are thicker or thinner by an atomic monolayer or two. The excitonic system in the wells is non-equilibrium as the excitons are constantly created by an irradiation and decay due to the finite lifetime. The condensation considered in the paper is not the Bose-Einstein condensation but rather the classical condensation due an interaction between excitons with additional peculiarities caused by non-equilibrium conditions. The main contribution to the exciton's energy in the defect's area comes from the energy of the exciton's confinement along the growth axis and the respective quantization of the exciton's levels. The condensation manifests itself by an enhancement the exciton accumulation in the defect's area with increasing pumping and by an appearance of different types of structures in the exciton density distribution when the defect's size is large. The condensed phase may appear in the form of islands or in the form of rings on the defect's boundary. It is shown, that the value of the exciton's lifetime plays an important role in the spatial distribution of the exciton density. The similarity and the difference of density structures for wells with the extra or lacking atomic monolayer in the defect's area are investigated. The specific features of the manifestation of the exciton luminescence at the condensation in the defect's region is analyzed.

Exciton Diffusion and Halo Effects in Monolayer Semiconductors

We directly monitor exciton propagation in freestanding and SiO_{2}-supported WS_{2} monolayers through spatially and time-resolved microphotoluminescence under ambient conditions. We find a highly nonlinear behavior with characteristic, qualitative changes in the spatial profiles of the exciton emission and an effective diffusion coefficient increasing from 0.3 to more than 30  cm^{2}/s, depending on the injected exciton density. Solving the diffusion equation while accounting for Auger recombination allows us to identify and quantitatively understand the main origin of the increase in the observed diffusion coefficient. At elevated excitation densities, the initial Gaussian distribution of the excitons evolves into long-lived halo shapes with μm-scale diameter, indicating additional memory effects in the exciton dynamics.

Bose-Einstein condensation and indirect excitons: a review

We review recent progress on Bose-Einstein condensation (BEC) of semiconductor excitons. The first part deals with theory, the second part with experiments. This Review is written at a time where the problem of exciton Bose-Einstein condensation has just been revived by the understanding that the exciton condensate must be dark because the exciton ground state is not coupled to light. Here, we theoretically discuss this missed understanding before providing its experimental support through experiments that scrutinize indirect excitons made of spatially separated electrons and holes. The theoretical part first discusses condensation of elementary bosons. In particular, the necessary inhibition of condensate fragmentation by exchange interaction is stressed, before extending the discussion to interacting bosons with spin degrees of freedom. The theoretical part then considers composite bosons made of two fermions like semiconductor excitons. The spin structure of the excitons is detailed, with emphasis on the crucial fact that ground-state excitons are dark: indeed, this imposes the exciton Bose-Einstein condensate to be not coupled to light in the dilute regime. Condensate fragmentations are then reconsidered. In particular, it is shown that while at low density, the exciton condensate is fully dark, it acquires a bright component, coherent with the dark one, beyond a density threshold: in this regime, the exciton condensate is 'gray'. The experimental part first discusses optical creation of indirect excitons in quantum wells, and the detection of their photoluminescence. Exciton thermalisation is also addressed, as well as available approaches to estimate the exciton density. We then switch to specific experiments where indirect excitons form a macroscopic fragmented ring. We show that such ring provides efficient electrostatic trapping in the region of the fragments where an essentially-dark exciton Bose-Einstein condensate is formed at sub-Kelvin bath temperatures. The macroscopic spatial coherence of the photoluminescence observed in this essentially dark region confirms this conclusion.

Interplay between periodicity and nonlinearity of indirect excitons in coupled quantum wells

Inspired by a recent experiment of localization-delocalization transition (LDT) of indirect excitons in lateral electrostatic lattices (Remeika et al 2009 Phys. Rev. Lett. 102 186803), we theoretically investigate the interplay between periodic potential and nonlinear interactions of indirect excitons in coupled quantum wells. It is shown that the model involving both attractive two-body and repulsive three-body interactions can lead to a natural account for the LDT of excitons across the lattice when reducing lattice amplitude or increasing particle density. In addition, the observations that the smooth component of the photoluminescent energy increases with increasing exciton density and that the exciton interaction energy is close to the lattice amplitude at the transition are also qualitatively explained. Our model provides an alternative way of understanding the underlying physics of the exciton dynamics in lattice potential wells.

Drift-diffusion model of the fragmentation of the external ring structure in the photoluminescence pattern emitted by indirect excitons in coupled quantum wells

Under optical excitation, coupled quantum wells are known to reveal fascinating features in the photoluminescence pattern originating from dipole orientated indirect excitons. The appearance of an external ring has been attributed to macroscopic charge separation in the quantum well plane. We present a classical model of nonlinear diffusion to account for the observed fragmentation of the external ring into a periodic array of islands. The model incorporates the Coulomb interactions between electrons, holes, and indirect excitons. At low temperatures, these interactions lead to pattern formation similar to the experimentally observed ring fragmentation. The fragmentation is found to persist to temperatures above the quantum degeneracy temperature of indirect excitons.

Exciton phase transitions in semiconductor quantum wells with disc-shaped electrode

Phase transitions in a system of indirect excitons in semiconductor double quantum wells are studied for a set-up when one of the electrodes is of finite size and, in particular, has the shape of a disc. At voltage a region under the rim of the disc is created where excitons have lower energy, thus providing a macroscopic trap attractive for excitons while being repulsive for charged particles. The theory of the formation of patterns of the excitonic condensed phase under the disc is built based on the assumption of the existence of the inter-exciton range where the interaction between them is attractive. The finite value of the exciton lifetime is taken into account serving as a limiting factor for the size of the islands of the condensed phase. The calculations reveal complex restructuring of the patterns of the spatial distribution of exciton density with increasing pumping intensity: from the structureless gaseous phase to separate islands of the condensed phase within the gaseous phase, then to islands of the gaseous phase in the bulk of the condensed phase and finally to the continuous condensed phase.

Ordered structures of exciton condensed phases in the presence of an inhomogeneous potential

A theory of the separation of a system of indirect excitons into a condensed and a gaseous phase with the formation of regular patterns of alternating phases in inhomogeneous external fields is developed. The model of spinodal decomposition of phase transitions, generalized for systems of unstable particles, is used. The theory is applied to the study of the non-uniform distribution of the exciton density in a double quantum well under a slot cut in a metallic electrode. It is shown that in a certain range of exciton generation rates a chain of light-emitting islands periodically localized along the slot is developed. With increasing width of the slot, the chain splits into two parallel chains shifted by a half period with respect to each other. By creating a biased external potential along the slot, the periodical pattern could be forced to move along the slot. The effect of the motion of the islands should manifest itself as time oscillations of the intensity of the light emitted from a fixed point.

Exciton storage in a nanoscale Aharonov-Bohm ring with electric field tuning

We study analytically the optical properties of a simple model for an electron-hole pair on a ring subjected to perpendicular magnetic flux and in-plane electric field. We show how to tune this excitonic system from optically active to optically dark as a function of these external fields. Our results offer a simple mechanism for exciton storage and readout.

Long-range coherence of interacting Bose gas of dipolar excitons

Experiments connected with dipolar exciton Bose condensation in lateral traps are reviewed. Observations of long-range coherence of condensate in ring electrostatic traps in Schottky-diode heterostructures with double and single quantum wells are presented and discussed.

Experimental methods and analysis of cold and dense dipolar exciton fluids

We review various aspects of our recent work on dipolar excitons in double quantum well systems. We describe and analyse different possible avenues for obtaining high density and cold dipolar exciton fluids that may enable an observation of quantum phase transitions in excitonic systems. These avenues include free dipolar exciton fluids, dipolar exciton fluids in electrostatic traps and in excitonic rings. We present our experimental and modelling work on the exciton dynamics in such systems, and discuss our current view of the advances made and the challenges that remain in this fast evolving and promising field of research.

Cold exciton gases in coupled quantum well structures

Cold exciton gases can be implemented in coupled quantum well structures. In this contribution, we review briefly the recent works on spontaneous coherence of cold excitons and on trapping of cold excitons with laser light.

Coherence length of cold exciton gases in coupled quantum wells

A Mach-Zehnder interferometer with spatial and spectral resolution was used to probe spontaneous coherence in cold exciton gases, which are implemented experimentally in the ring of indirect excitons in coupled quantum wells. A strong enhancement of the exciton coherence length is observed at temperatures below a few Kelvin. The increase of the coherence length is correlated with the macroscopic spatial ordering of excitons. The coherence length at the lowest temperature corresponds to a very narrow spread of the exciton momentum distribution, much smaller than that for a classical exciton gas.

Ring-shaped luminescence pattern in biased quantum wells studied as a steady-state reaction front

Under certain conditions, focused laser excitation in semiconductor quantum well structures can lead to a charge separation and a circular reaction front, which is visible as a ring-shaped photoluminescence pattern. The diffusion-reaction equations governing the system are studied here with the aim of a detailed understanding of the steady state. The qualitative asymmetry in the sources for the two carriers is found to lead to unusual effects which dramatically affect the steady-state configuration. Analytic expressions are derived for carrier distributions and interface positions for a number of cases. These are compared with steady-state information obtained from simulations of the diffusion-reaction equations.