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Physical review. B, Condensed matter

Order formation and superfluidity of excitons in type-II semiconductor quantum wells

Takuya Iida, Makoto Tsubota

Published Aug 15, 1999• 15 citations
Publisher

Abstract

The condensed state and superfluidity of excitons in type-II semiconductor quantum wells (QW's) are investigated theoretically. Since the excitons in type-II QW's have translational motion along the layer, the assembly of them is regarded as an interacting dilute quasi-two-dimensional Bose gas. This system is advantageous for our purpose because those excitons have a long lifetime of the order of ${10}^{\ensuremath{-}6}\mathrm{s},$ and their transport mechanism can be directly studied in experiments by observing electric current since the excitons consist of spatially separated electron-hole pairs. Using the exciton wave functions obtained by the variational method, the exciton-exciton interaction is calculated and found to be repulsive when the thickness of the QW is thinner than a critical value. To illustrate the situation, we carry out the numerical computation adopting a model system with material constants appropriate to GaAs/AlAs type-II QW's. The basic equation for the phase of the condensate wave function is derived when the exciton system is irradiated by a weak laser light at zero temperature. Solving the equation in the presence of the external current ${J}_{\mathrm{ex}},$ we study the stationary spatial pattern of the phase of the condensate wave function. It is shown that there appears a vortex lattice with a net supercurrent when ${J}_{\mathrm{ex}}$ is larger than a critical value; the period of the lattice is determined as a function of ${J}_{\mathrm{ex}}.$ We calculate the magnetic field induced by the current in the vortex lattice, and discuss a possibility of an experimental observation of the critical current. Such a direct observation of the exciton transport will provide unambiguous experimental evidence for the superfluidity of excitons.

DOI
10.1103/physrevb.60.5802

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The condensed state and superfluidity of excitons in type-II semiconductor quantum wells (QW's) are investigated theoretically. Since the excitons in type-II QW's have translational motion along the layer, the assembly of them is regarded as an interacting dilute quasi-two-dimensional Bose gas. This system is advantageous for our purpose because those excitons have a long lifetime of the order of 10\ensuremath−6s,{10}^{\ensuremath{-}6}\mathrm{s},10\ensuremath−6s, and their transport mechanism can be directly studied in experiments by observing electric current since the excitons consist of spatially separated electron-hole pairs. Using the exciton wave functions obtained by the variational method, the exciton-exciton interaction is calculated and found to be repulsive when the thickness of the QW is thinner than a critical value. To illustrate the situation, we carry out the numerical computation adopting a model system with material constants appropriate to GaAs/AlAs type-II QW's. The basic equation for the phase of the condensate wave function is derived when the exciton system is irradiated by a weak laser light at zero temperature. Solving the equation in the presence of the external current Jex,{J}_{\mathrm{ex}},Jex​, we study the stationary spatial pattern of the phase of the condensate wave function. It is shown that there appears a vortex lattice with a net supercurrent when Jex{J}_{\mathrm{ex}}Jex​ is larger than a critical value; the period of the lattice is determined as a function of Jex.{J}_{\mathrm{ex}}.Jex​. We calculate the magnetic field induced by the current in the vortex lattice, and discuss a possibility of an experimental observation of the critical current. Such a direct observation of the exciton transport will provide unambiguous experimental evidence for the superfluidity of excitons.
The ordered state and the elementary excitations are theoretically studied in an interacting dilute quasi-two-dimensional Bose gas of excitons in a type-II quantum well. This system is advantageous for studying the macroscopic quantum phenomena because those excitons have a long lifetime of the order of 10-6 s, and their transport mechanism can be directly studied in experiments by observing electric current since the excitons consist of spatially separated electron-hole pairs. Using the obtained dispersion relations for excitations, we examine the Landau criterion for exciton superflow and the temperature dependence of the off-diagonal long-range order which characterizes the quasi-Bose-Einstein condensation in two-dimensional systems.
Summary form only given. In the dilute limit excitons behave as weakly interacting Bose particles and are expected to undergo the Bose-Einstein condensation (BEC). Because the exciton mass is very small at experimentally accessible exciton densities the critical temperature for exciton BEC should reach several Kelvins, i.e., about six orders of magnitude higher than the T/sub c/ for atom BEC. To create degenerate Bose-gas of excitons we propose quasi-2D gas of indirect excitons in coupled quantum wells (CQWs) which have two primary advantages for realizing a quantum degenerate exciton gas and, ultimately, the BEC-like phase transition: (i) the long lifetime of indirect excitons and (ii) the short exciton cooling time.
Correlated electron-hole pairs, or excitons, in semiconductor nanostructures have been studied extensively over the past few decades. The optical response of excitons is complicated due to inhomogeneous broadening, presence of multiple states, and exciton-exciton interactions. In this work we bring new perspectives to exciton physics in semiconductor quantum wells (QWs) through two-dimensional coherent spectroscopy (2DCS).\nThe effect of QW growth direction on the optical properties of excitons is explored by studying (110)-oriented GaAs QWs. The homogeneous and inhomogeneous linewidths of the heavy-hole exciton resonance are measured. By probing the optical nonlinear response for polarization along the in-plane crystal axes [1-10] and [001], we measure different homogeneous linewidths for the two orthogonal directions. This difference is found to be due to anisotropic excitation-induced dephasing, caused by a crystal-axis-dependent absorption coefficient. The extrapolated zero-excitation density homogeneous linewidth exhibits an activation-like temperature dependence.\nSpectral diffusion of excitons in (001)-oriented QWs has been studied. We show that the spectral diffusion characteristics depend strongly on the sample temperature. Spectral diffusion is generally assumed to follow the strong-redistribution approximation, partly because of lack of any evidence to the contrary. We find that this assumption is violated at low sample temperatures for excitons in QWs; high-energy excitons preferentially relax due to a negligible phonon population at low temperatures. The frequency-frequency correlation function is measured through a numerical fitting procedure to quantify spectral diffusion for sample temperatures >20>20>20 K.\nExciton-exciton interactions affect the light-matter interactions in QWs significantly. We present an intuitive and simple model for these interactions by treating excitons as interacting bosons. We show that the polarization-dependent exciton dephasing rate in GaAs quantum wells is due to the bosonic character of excitons. We fit slices from simulated spectra to those from the experimentally measured spectra and show that interference between two different quantum mechanical pathways results in a slower dephasing rate for co-circular and co-linear polarization of optical excitation pulses. This interference does not exist for cross-linearly polarized excitation pulses resulting in a faster dephasing rate. Additionally, we were able to separately quantify inter- and intra-mode interactions between excitons through exciton-density-dependent measurements.
We review, aiming at an audience of final year undergraduates, the phenomena observed in, and properties of, microcavity exciton–polariton condensates. These are condensates of mixed light and matter, consisting of superpositions of photons in semiconductor microcavities and excitons in quantum wells. Because of the imperfect confinement of the photon component, exciton–polaritons have a finite lifetime, and have to be continuously re-populated. Therefore, exciton–polariton condensates lie somewhere between equilibrium Bose–Einstein condensates and lasers. We review in particular the evidence for condensation, the coherence properties studied experimentally, and the wide variety of spatial structures either observed or predicted to exist in exciton–polariton condensates, including quantised vortices and other coherent structures. We also discuss the question of superfluidity in a non-equilibrium system, reviewing both the experimental attempts to investigate superfluidity to date, and the theoretical suggestions of how it may be further elucidated.
The case of excitons as candidates for Bose–Einstein condensation is discussed, and experimental results in CuCl and Cu 2 O are presented. In CuCl, spectral analysis of the luminescence from biexcitons as a function of their density reveals a gradual evolution from classical statistics towards a quantum degenerate regime. The appearance of a sharp emission line below a critical temperature and above a critical density is attributed to the presence of a laser-induced Bose–Einstein condensate of excitonic molecules. This interpretation is supported by pump-probe experiments which show that additional particles injected in the presence of a biexciton condensate are drawn into it. In Cu 2 O, free exciton luminescence spectral analysis of ortho- and paraexcitons reveals a gradual evolution from a classical to a Bose quantum degenerate regime with increasing particle densities. Orthoexciton densities close to the critical density for condensation are obtained at high incoherent excitation. Under similar pumping, paraexciton densities exceeding the critical value are inferred from luminescence intensity ratios. Anomalous transport properties of paraexcitons, such as ballistic propagation over macroscopic distances and formation of soliton-like excitonic packets are discussed as evidence for excitonic superfluidity. Introduction Excitons The lowest electronically excited state of a non-metallic crystal corresponds to the promotion of one electron from the top of the highest fully occupied valence band to the bottom of the next empty conduction band. A correct evaluation of the required energy must include the Coulomb correlation between the promoted electron and all other electrons left behind in the valence band.
Summary form only given. The optical properties of semiconductor quantum wells (QW) and, in particular, the coherent dynamics of excitons following resonant excitation with ultrafast laser pulses have attracted much attention in recent years. It is generally accepted that there is a transfer of coherence between the optical field and the QW that disappears in a characteristic time T/sub 2/ (picoseconds for GaAs) after the laser is turned off. However, the questions as to how the coherence is actually induced and that of the nature of the coherent state of the solid are poorly understood. In this work we address these points by re-examining the longstanding problem of the (classical vs. quantum) nature of the ubiquitous beats associated with the light-hole (LX) heavy-hole (HX) excitons, which are observed in transient optical experiments on QW. To this end, we consider the coherent behavior of excitons using the simplest albeit non-trivial model where they are treated as non-interacting bosons. Our results bear directly on studies for which nonlinear effects are not important and are not aimed directly at explaining the fourwave-mixing (FWM) experiments that dominate the field. Nevertheless, since nonlinear effects are, typically, weak compared with harmonic contributions, the free boson picture provides in all cases the correct lowest order wavefunction of the photoexcited solid.