Influence of excited Landau levels on a two-dimensional electron-hole system in a strong perpendicular magnetic field

The study of the quantum states of a two-dimensional electron-hole system in a strong perpendicular magnetic field is carried out with special attention to the influence of virtual quantum transitions of interacting particles between the Landau levels. These virtual quantum transitions from the lowest Landau levels to excited Landau levels with arbitrary quantum numbers n and m and their reversion to the lowest Landau levels in second order perturbation theory result in an indirect attraction between the particles. The influence of the indirect interaction on the magnetoexciton ground state, on the chemical potential of the Bose-Einstein condensed magnetoexcitons, and on the ground state energy of the metallic-type electron-hole liquid is investigated in the Hartree-Fock approximation. The coexistence of different phases is suggested.     

Excitons and magnetoexcitons in coupled quantum nanostructures: the role of a dirty environment

The effect of a random field caused by impurities, interface roughness and so on, on the optical properties and superfluidity of a quasi-two-dimensional system of excitons is studied. The influence of a random field on the density of the superfluid component of excitonic systems at low temperatures is investigated. For quasi-two-dimensional excitonic systems in a random field the Kosterlitz–Thouless temperature in the superfluid state is calculated. The superfluidity and Bose–Einstein condensation of indirect excitons in coupled quantum dots are studied. Magnetoexciton light absorption in the disordered quantum wells is considered. The two-particle problem of the magnetoexciton motion in the external field depending on the external magnetic field is reduced to the one-particle motion with effective magnetic mass in some effective field. The energy and optical absorption of the magnetoexciton in a single and coupled quantum dots are studied using the effective-magnetic-mass Hamiltonian. In the coherent potential approximation the coefficient of magnetoexciton optical absorption in single and coupled quantum wells is calculated. In the strong magnetic fields the exciton peak decreases with magnetic field increasing in accordance with the experimental data. The localization of direct and indirect magnetoexcitons is investigated. Received: 14 April 2000 / Accepted: 17 April 2000 / Published online: 6 September 2000     

Linear polarization of luminescence in Bose-Einstein condensation of indirect excitons and spontaneous symmetry breaking

The linear polarization of luminescence from the Bose-Einstein condensate of dipolar (indirect) excitons accumulated in the ring lateral traps in GaAs/AlGaAs Schottky-diode heterostructures with a wide single quantum well has been observed. Luminescence from direct excitons remains unpolarized under the same experimental conditions. It has been shown that the linear polarization of the exciton condensate may arise from the anisotropic electron-hole (e–h) exchange interaction associated with the lateral anisotropy of the confining potential. The interaction mixes and splits the ground state of optically active excitons on heavy holes (with angular momentum projections of m=±1). The split spectral components from the corresponding angular momentum projections are linearly polarized in mutually orthogonal directions. Under this e–h exchange, the condensate component of excitons should appear in the lowest of the split states and luminescence from the Bose-Einstein condensate of excitons in such a split state becomes linearly polarized along the 〈110〉 crystallographic direction in the quantum well plane. The observed effect is a manifestation of spontaneous symmetry breaking in Bose-Einstein condensation of excitons.     

Quantum phase transitions across a p-wave Feshbach resonance

We study a single-species polarized Fermi gas tuned across a narrow p-wave Feshbach resonance. We show that in the course of a Bose-Einstein condensation (BEC)-BCS crossover, the system can undergo a magnetic-field-tuned quantum phase transition from a px-wave to a px+ipy-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological px+ipy to px+ipy transition at zero chemical potential mu. In two dimensions, for mu > 0 it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.     

Rotons in a hybrid Bose-Fermi system

We calculate the spectrum of elementary excitations in a two-dimensional exciton condensate in the vicinity of a two-dimensional electron gas. We show that attraction of excitons due to their scattering with free electrons may lead to formation of a roton minimum. The energy of this minimum may go below the ground state energy which manifests breaking of the superfluidity. The Berezinsky-Kosterlitz-Thouless phase transition temperature decreases due to the exciton-exciton attraction mediated by electrons.     

Interacting electrons on a two-dimensional surface: planar vs. spherical geometries

The center-of-mass excitations are identified in the spectrum of electrons on a two-dimensional surface in the lowest Landau level. The correspondence between the quantum numbers labeling electron states on a sphere and on a plane is drawn. The excitation spectrum on a sphere with increasing radius is shown to converge to that on a plane. In particular, in the presence of a lateral confinement (i.e. for the case of quantum dots), identical series of magic states appear in both cases. Also, a class of interaction potentials which lead to the fractional quantum Hall effect in an extended system are identified.     

Coherent ultrafast dynamics in the quantum Hall effect regime

We review recent investigations of the femtosecond non-linear optical response of the two-dimensional electron gas (2DEG) in the quantum Hall effect regime. We find that the time and frequency profile of the four-wave-mixing non-linear optical spectrum is strongly influenced by Coulomb correlations between the photoexcited electron-hole pairs and the 2DEG collective excitations. We discuss experimental and theoretical results showing non-Markovian memory effects in the polarization dephasing, and an optically induced time-dependent coupling between the two lowest Landau level magnetoexcitons.     

Observation of nonconventional spin waves in composite-fermion ferromagnets

We find unexpected low energy excitations of fully spin-polarized composite-fermion ferromagnets in the fractional quantum Hall liquid, resulting from a complex interplay between a topological order manifesting through new energy levels and a magnetic order due to spin polarization. The lowest energy modes, which involve spin reversal, are remarkable in displaying unconventional negative dispersion at small momenta followed by a deep roton minimum at larger momenta. This behavior results from a nontrivial mixing of spin-wave and spin-flip modes creating a spin-flip excitonic state of composite-fermion particle-hole pairs. The striking properties of spin-flip excitons imply highly tunable mode couplings that enable fine control of topological states of itinerant two-dimensional ferromagnets.     

Signatures of fractional statistics in noise experiments in quantum Hall fluids

The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics. Yet, this fundamental prediction has remained an open experimental challenge. Here we show that the cross-current noise in a three-terminal tunneling experiment of a two dimensional electron gas in the FQH regime can be used to detect directly the statistical angle of the excitations of these topological quantum fluids. We show that the noise also reveals signatures of exclusion statistics and of fractional charge. The vortices of Laughlin states should exhibit a bunching effect, while for higher states in the Jain sequences they should exhibit an "antibunching" effect.     

Electron fractionalization in two-dimensional graphenelike structures

Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. In this Letter, we show that fractionally charged topological excitations exist on graphenelike structures, where quasiparticles are described by two flavors of Dirac fermions and time-reversal symmetry is respected. The topological zero modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics.     

Condensation effects of excitons

The theory of the electronic excitations in a highly excited semiconductor is presented. The relaxation processes, the formation of excitons and excitonic molecules, the interaction among the various forms of electronic excitations, as well as their optical and thermodynamical properties are analyzed. At low temperatures one expects condensations into the quantum statistically degenerate phases of the excitonic molecules and of the electron-hole plasma. The physical properties of these low temperature phases are investigated. Possibilities and previous attempts to observe the Bose-Einstein condensation in excitonic systems are discussed critically. The experimental observations of the electron-hole liquid phase transition are reviewed.     

Polariton-mode lasing and Bose condensate of dipolar excitons in heterostructures

The analysis of the polariton modes in 2D traps based on heterostructures with quantum wells for Bose-Einstein condensation of dipolar excitons is presented. The characteristic equation of such modes is derived with allowance for the polarization relaxation of excitons and radiative losses from the trap. The spectrum and structure of high-quality modes are analytically and numerically studied. It is demonstrated that several modes become unstable at a high enough density of excitons and a long relaxation time of the exciton polarization. In accordance with the estimations, such an instability can be reached in the experiments on the Bose-Einstein condensation of dipolar excitons and can be used to interpret the corresponding coherent emission.     

Induced Chern-Simons term of a paired electron state in the quantum Hall system

The induced Chern-Simons term for a paired electron state is calculated in the quantum Hall system by using a field theory on the von Neumann lattice. The coefficient of the Chern-Simons term, which is the Hall conductance, has not only the usual term proportional to a filling factor due to P (parity) & T (time reversal) symmetry breaking but also correction terms due to P & T & U(1) symmetry breaking. The correction term essentially comes from the Nambu-Goldstone mode and depends on an infrared limit. It is shown that the correction term is related to a topological number of a gap function in the momentum space.     

to -12pt [-12pt]to 16ptRapid Note Wavefunctions for the Luttinger liquid

Standard bosonization techniques lead to phonon-like excitations in a Luttinger liquid (LL), reflecting the absence of Landau quasiparticles in these systems. Yet in addition to the above excitations some LL are known to possess solitonic states carrying fractional quantum numbers (e.g. the spin 1/2 Heisenberg chain). We have reconsidered the zero modes in the low-energy spectrum of the Gaussian boson LL Hamiltonian both for fermionic and bosonic LL: in the spinless case we find that two elementary excitations carrying fractional quantum numbers allow to generate all the charge and current excited states of the LL. We explicitly compute the wavefunctions of these two objects and show that one of them can be identified with the 1D version of the Laughlin quasiparticle introduced in the context of the Fractional Quantum Hall effect. For bosons, the other quasiparticle corresponds to a spinon excitation. The eigenfunctions of Wen's chiral LL Hamiltonian are also derived: they are quite simply the one dimensional restrictions of the 2D bulk Laughlin wavefunctions. Received 26 January 1999 and Received in final form 21 April 1999     

Theory of four-dimensional fractional quantum Hall states

We propose a pseudo-potential Hamiltonian for the Zhang-Hu’s generalized fractional quantum Hall states to be the exact and unique ground states. Analogously to Laughlin’s quasi-hole (quasi-particle), the excitations in the generalized fractional quantum Hall states are extended objects. They are vortex-like excitations with fractional charges +(−)1/m³ in the total configuration space CP³. The density correlation function of the Zhang-Hu states indicates that they are incompressible liquid.     

耦合量子阱中激子凝聚的研究进展

近年来，半导体量子阱中激子的玻色一爱因斯坦凝聚研究取得了很大进展．实验上利用耦合量子阱间接激子中电子和空穴在空间上的分离，显著提高了激子的冷却速度和寿命，成功地把激子冷却到1K以下，观察到了激子的准凝聚状态，并且在强激光照射下，发现了随光照强度增强而增大的激子发光环和环上形成的有规则斑点图案，引起了广泛的兴趣和重视．理论研究表明，发光环的出现是电子和空穴在量子阱中的反常输运行为造成的，但环上形成规则斑点的物理机理目前尚不清楚．文章介绍了这方面的实验背景和形成激子环的物理图像，指出了理论研究中存在的问题，并对解决问题的方案进行了讨论．     

Magnetoabsorption spectra of magnetoexciton transitions in GaAs/Ga0.7Al0.3As quantum wells

The internal transitions and absorption spectra of confined magnetoexcitons in GaAs/Ga0.TA10.aAs quan- tum wells have been theoretically investigated under magnetic fields along the growth direction of the semiconductor heterostructure. The magnetoexciton states are obtained within the effective-mass ap- proximation by using a variational procedure. The trial exciton-envelope wavefunctions are described as hydrogeniclike polynomial functions. The internal transition energies are investigated by studying the allowed magnetoexcitonic transitions using terahertz radiation circularly polarized in the plane of the quantum well. The intraexcitonic magnetoabsorption to 2p^± like magnetoexciton states as functions of the coefficients are obtained for transitions from 1s-like applied magnetic field.     

Entanglement spectrum of non-Abelian anyons

Non-Abelian anyons can emerge as fractionalized excitations in two-dimensional systems with topological order. One important example is the Moore—Read fractional quantum Hall state. Its quasihole states are zero-energy eigenstates of a parent Hamiltonian, but its quasiparticle states are not. Both of them can be modeled on an equal footing using the bipartite composite fermion method. We study the entanglement spectrum of the cases with two or four non-Abelian anyons. The counting of levels in the entanglement spectrum can be understood using the edge theory of the Moore—Read state, which reflects the topological order of the system. It is shown that the fusion results of two non-Abelian anyons is determined by their distributions in the bipartite construction.