Two-dimensional Electron-hole System Research Articles

Hot luminescence of two-dimensional electron hole systems in modulation-doped silicon

Modulation doping of silicon has great potential for miniaturization, surface passivation, and third generation photovoltaics (PV). At a modulation-doped silicon surface, we observe the formation of a 2D hole layer at the silicon surface at low temperatures by means of photoluminescence (PL) measurements. A line shape analysis of band–band and hot luminescence reveals the hole density (which is equal to the modulation-doped acceptor density). A high excitation intensity leads to a Fermi edge singularity of the band–band and hot PL emission. While the 2D layer can be characterized by the observed luminescence, the spectral region of twice the bandgap is fully dominated by emission from this surface layer, impeding the measurement of bulk hot luminescence, e.g., from Auger electrons or from nonthermalized carriers in a hot carrier PV device.

Two-Dimensional Electron-Hole System under the Influence of the Chern–Simons Gauge Field Created by the Quantum Point Vortices

In the present work the Chern-Simons(C-S) gauge field theory developed by Jackiw and Pi [1] and widely used to explain the fractional quantum Hall effects, was applied to describe the two-dimensional (2D) electron-hole (e-h) system in a strong perpendicular magnetic field under the influence of the quantum point vortices creating the Chern-Simons(C-S) gauge field. The composite particles formed by electrons and by holes with equal integer positive numbers of the attached quantum point vortices are described by the dressed field operators, which obey to the Fermi or to the Bose statistics depending on the even or odd numbers . It is shown that the phase operators as well as the vector and the scalar potentials of the C-S gauge field depend on the difference of the electron and of the hole density operators. They vanish in the mean field approximation, when the average values of the electron and of the whole densities coincide. Nevertheless, even in this case, the quantum fluctuations of the C-S gauge field lead to new physics of the 2D e-h system.

Metal-insulator transitions in bilayer electron-hole systems in transition metal dichalcogenides

We investigated metal-insulator transitions for double layer two-dimensional electron hole systems in transition metal dicalcogenides (TMDC) stacked on opposite sides of thin layers of boron nitride (BN). The interparticle interaction is calculated by including the screening due to the polarization charges at different interfaces, including that at the encapsultion and the substrate of experimental structures. We compute and compare the energies of the metallic electron-hole plasma and the newly proposed insulating exciton solid with fixed-node diffusion Monte Carlo simulation including the high valley degeneracy of the electron bands. We found that for some examples of current experimental structures, the transition electron/hole density is in an accessible range of g x 10^12 /cm*2 with g between 4.1 and 14.5 for spacer thicknesses between 2.5 and 7.5 nm. Our result raise the possibility of exploiting this effect for logic device applications.

Anderson Localization in a Two-Dimensional Electron–Hole System

Anderson Localization in a Two-Dimensional Electron–Hole System

Thermo emf in a two-dimensional electron-hole system in HgTe quantum wells in the presence of magnetic field. The role of the diffusive and the phonon-drag contributions

We present an experimental study of the thermo emf of a two-dimensional electron-hole system in a 21 nm HgTe quantum well in the presence of magnetic field. The first experimental observation of Nernst-Ettingshausen effect in a 2D semimetal is reported. The comparison between theory and experiment shows that the thermo emf is determined by two contributions: the diffusion and the phonon drag, with the latter contribution several times greater than the first. The conclusion is drawn about the important role of electron-hole scattering in the formation of both thermoelectric power mechanisms.

Quantum exciton solid in bilayer two-dimensional electron-hole systems

We propose a state of excitonic solid for double layer two dimensional electron hole systems in transition metal dicalcogenides stacked on opposite sides of thin layers of BN. Properties of the exciton lattice such as its Lindemann ratio and possible supersolid behaviour are studied. We found that the solid can be stabilized relative to the fluid by the potential due to the BN.

Extremely imbalanced two-dimensional electron-hole-photon systems

We investigate the phases of two-dimensional electron-hole systems strongly coupled to a microcavity photon field in the limit of extreme charge imbalance. Using variational wave functions, we examine the competition between different electron-hole paired states for the specific cases of semiconducting III-V single quantum wells, electron-hole bilayers, and transition metal dichalcogenide monolayers embedded in a planar microcavity. We show how the Fermi sea of excess charges modifies both the electron-hole bound state (exciton) properties and the dielectric constant of the cavity active medium, which in turn affects the photon component of the many-body polariton ground state. On the one hand, long-range Coulomb interactions and Pauli blocking of the Fermi sea promote electron-hole pairing with finite center-of-mass momentum, corresponding to an excitonic roton minimum. On the other hand, the strong coupling to the ultra-low-mass cavity photon mode favors zero-momentum pairs. We discuss the prospect of observing different types of electron-hole pairing in the photon spectrum.

Simplification of the electron-ion many-body problem: N -representability of pair densities obtained via a classical map for the electrons

The classical map hypernetted-chain (CHNC) method for interacting electrons uses a kinetic energy functional in the form of a classical-fluid temperature. Here, we show that the CHNC generated two-body densities and pair-distribution functions (PDFs) correspond to $N$-representable densities. Comparisons of results from CHNC with quantum Monte Carlo (QMC) and path-integral Monte Carlo (PIMC) are used to validate the CHNC results. Since the PDFs are sufficient to obtain the equation of state or linear response properties of electron-ion systems, we apply the CHNC method for fully classical calculations of electron-ion systems in the quantum regime, using hydrogen at 4000 K and 350 times the solid density as an example since QMC comparisons are available. We also present neutral pseudoatom (NPA) calculations which use rigorous density functional theory (DFT) to reduce the many nuclear problem to an effective one-ion problem. The CHNC PDFs and NPA results agree well with the ion-ion, electron-ion, and electron-electron PDFs from QMC, PIMC, or DFT coupled to molecular dynamics simulations where available. The PDFs of a two-dimensional (2D) electron-hole system at 5 K are given as an example of 2D ``warm dense'' matter where the electrons and the counterparticles (holes) are all in the quantum regime. Basic methods such as QMC, PIMC, or even DFT become prohibitive while CHNC methods, being independent of the number of particles or the temperature, prove to be easily deployable.

Terahertz Cyclotron Photoconductivity in a Highly Unbalanced Two-Dimensional Electron–Hole System

Terahertz cyclotron-resonance photoconductivity in a two-dimensional electron–hole system under conditions where the cyclotron resonance occurs owing to the absorption of radiation by electrons whose density is one to three orders of magnitude lower than the hole density is experimentally investigated for the first time. Information on the behavior of the main parameters (i.e., amplitude and broadening) characterizing resonance photoconductivity as a function of wavelength, temperature, and electron density is obtained. On this basis, it is concluded that resonance photoconductivity in the system under study results from cyclotron resonance caused by transitions between the partially filled zeroth Landau level and the first Landau level of electrons, and resonance broadening is caused by scattering on a short-range screened impurity potential. It is found that a decrease in the electron density by an order of magnitude does not lead to a significant reduction of the photoconductivity signal; moreover, at a wavelength of 432 μm, the signal even grows slightly. This fact can be associated with the effective enhancement of the field of the incident radiation in the system under study.

On the phase diagram of a two-dimensional electron–hole system

The phase diagram for a system of spatially separated electrons and holes in coupled quantum wells or graphene double layers is studied in the framework of a BCS-like mean-field approach and a Landau expansion in terms of the pairing order parameter. We find a second order transition between an electron–hole plasma and a BCS phase, as well as a first-order transition between the BCS phase and a bosonic Mott phase of tightly bound electron–hole pairs without phase coherence. The electron–hole plasma exists at low and at high densities for weak interaction, the BCS phase at moderate density and the Mott phase at high density and strong interaction.

Exciton–Mott Physics in Two-Dimensional Electron–Hole Systems: Phase Diagram and Single-Particle Spectra

Exciton Mott physics in two-dimensional electron-hole (e-h) systems is studied in the quasiequilibrium, which is the crossovers or phase transitions between the insulating exciton gas and the metallic e-h plasma. By developing a self-consistent screened T-matrix approximation, we succeed in obtaining the "global" phase diagram on the plane of the e-h density and the temperature as a contour plot of the exciton ionization ratio. The detailed features of the exciton-Mott crossover at high temperature are figured out beyond the conventionally used concept of the Mott density. At low temperature, we find not only the region unstable toward the inhomogeneity but the pure Mott transition point characterized by the discontinuity in the ionization ratio. The single particle spectra also exhibit interesting features reflecting the excitonic correlations.

Nonlinear optical rectification in a two-dimensional system

The optical rectification (OR) in the two-dimensional electron–hole system is investigated theoretically. An analytical expression formula of the OR coefficient is obtained via the framework of compact density matrix approach and the iterative method. The results show that the OR coefficient depends strongly on the system׳s size and the relaxation time. A more obvious OR coefficient should be found by adjusting an appropriate choice of the system parameters.

Coherence of two-dimensional electron-hole systems: Spontaneous breaking of continuous symmetries: A review

The spontaneous breaking of the continuous symmetries of a two-dimensional electron-hole system in a strong magnetic field perpendicular to the plane leads to the formation of new ground states and determines the energy spectrum of collective elementary excitations that appear above these new ground states. In this review, the main attention is paid to the electron-hole system formed from coplanar magnetoexcitons under conditions of Bose-Einstein condensation in the ground state with the wave vector k = 0 taking into account the influence of excited Landau levels, when exciton-type elementary excitations coexist with plasmon-type oscillations. At the same time, the properties of a two-component system consisting of a two-dimensional electron gas and a two-dimensional hole gas spatially separated in a double quantum well under conditions of the fractional quantum Hall effect are of great interest, because these properties can affect the quantum states of magnetic excitons that are formed when the distance between the layers tends to zero. Bilayer electron systems are also considered under conditions of the fractional quantum Hall effect with the one-half filling factor for each layer and the total filling factor equal to unity for both layers. The coherence between the electron states in the two layers is equivalent to the formation of excitons in a macroscopic coherent state. This makes it possible to compare the energy spectrum of collective elementary excitations of Bose-Einstein condensed excitons under conditions of the quantum Hall effect and coplanar magnetoexcitons. The breaking of the global gauge symmetry or of the continuous rotational symmetry leads to the formation of a gapless spectrum of the Nambu-Goldstone type, whereas the breaking of the local gauge symmetry is accompanied by the appearance of a gap in the energy spectrum (Higgs phenomenon). These phenomena are equivalent to the formation of massless and massive particles in the relativistic physics. The application of the Nielsen-Chadha theorem, which determines the number of Nambu-Goldstone modes as a function of the number of broken symmetry operators, is demonstrated using the example of Bose-Einstein condensation of spinor atomic gases in an optical trap. This example is presented for a better understanding of the results obtained in the case of a Bose-Einstein condensation of coplanar magnetoexcitons. The Higgs phenomenon leads to the formation of composite particles under conditions of the fractional quantum Hall effect. Their description is given in terms of the Ginzburg-Landau theory. The possibilities for the appearance of spontaneous coherence in a system of indirect excitons in structures with a double quantum well are analyzed. The experimental attempts to create these conditions, the main results obtained in this field, and the accumulated knowledge are reviewed. The basic properties of the energy spectrum of magnetoexciton polaritons in a microcavity are formulated. A hypothesis is put forward about the possibility of forming two-dimensional magnetoexcitons and two-dimensional magnetoexciton polaritons of high density with attached point quantum vortices, i.e., about the possibility of forming new composite particles.

The Plasma Oscillations in a Two-Dimensional Electron–Hole Liquid Under Influence Rashba Spin-Orbit Coupling

The plasma oscillations of the two-dimensional electron-hole system in the presence of a Rashba spin-orbit coupling are studied. Only the intra-Landau level excitations are taken into account when the electrons and holes are situated on their lowest Landau levels, the filling factor $v^{2}$ being less than 1. The ground state of the two-dimensional electron-hole system is supposed to be the electron-hole liquid. The dispersion relations for the optical and acoustical plasmon modes were obtained. The acoustical plasmon branch has a linear dispersion law in the range of small wave vectors and monotonically increases with saturation at higher values of wave vectors. The optical plasmon branch has a quadratic dependence in the range of long wavelength and a monotonic increasing with saturation as in the case of acoustical branch.

Spontaneous Symmetry Breaking and Coherence in Two-Dimensional Electron–Hole and Exciton Systems

The spontaneous breaking of the continuous symmetries of the two-dimensional(2D) electron-hole systems in a strong perpendicular magnetic field leads to the formation of new ground states and determines the energy spectra of the collective elementary excitations appearing over these ground states. In this review the main attention is given to the electron-hole systems forming coplanar magnetoexcitons in the Bose-Einstein condensation(BEC) ground state with the wave vector k=0, taking into account the excited Landau levels, when the exciton-type elementary excitations coexist with the plasmon-type oscillations. At the same time properties of the two-dimensional electron gas(2DEG) spatially separated as in the case of double quantum wells(DQWs) from the 2D hole gas under conditions of the fractional quantum Hall effect(FQHE) are of great interest because they can influence the quantum states of the coplanar magnetoexcitons when the distance between the DQW layers diminishes. We also consider in this review the bilayer electron systems under conditions of the FQHE with the one half filling factor for each layer and with the total filling factor for two layers equal to unity because the coherence between the electron states in two layers is equivalent to the formation of the quantum Hall excitons(QHExs) in a coherent macroscopic state. The breaking of the global gauge symmetry as well as of the continuous rotational symmetries leads to the formation of the gapless Nambu-Goldstone(NG) modes while the breaking of the local gauge symmetry gives rise to the Higgs phenomenon characterized by the gapped branches of the energy spectrum. The conditions in which the spontaneous coherence could appear in a system of indirect excitons in a double quantum well structures are discussed. The experimental attempts to achieve these conditions, the main results and the accumulated knowledge are reviewed.

Unconventional Hall effect near charge neutrality point in a two-dimensional electron-hole system

The transport properties of the two-dimensional system in HgTe-based quantum wells containing simultaneously electrons and holes of low densities are examined. The Hall resistance, as a function of perpendicular magnetic field, reveals an unconventional behavior, different from the classical N-shaped dependence typical for bipolar systems with electron-hole asymmetry. The quantum features of magnetotransport are explained by means of numerical calculation of the Landau level spectrum based on the Kane Hamiltonian. The origin of the quantum Hall plateau {\sigma}xy = 0 near the charge neutrality point is attributed to special features of Landau quantization in our system.

Nonlocal Transport Near Charge Neutrality Point in a Two-Dimensional Electron-Hole System

Nonlocal resistance is studied in a two-dimensional system with a simultaneous presence of electrons and holes in a 20 nm HgTe quantum well. A large nonlocal electric response is found near the charge neutrality point in the presence of a perpendicular magnetic field. We attribute the observed nonlocality to the edge state transport via counterpropagating chiral modes similar to the quantum spin Hall effect at a zero magnetic field and graphene near a Landau filling factor ν=0.

Two-dimensional electron-hole system in HgTe-based quantum wells with surface orientation (112)

A two-dimensional electron-hole system has been shown to exist in 20 nm thick HgTe quantum wells (QWs) with the orientation (112). This finding proves that the semimetallic state is a universal property of wide HgTe-based quantum wells with an inverted energy band structure that is independent of surface orientation. Calculation of the energy band structure in these QWs shows that the strain caused by the lattice mismatch of HgTe and CdTe is likely to be a key reason for the formation of the overlap of the conduction and valence bands that leads to a semimetallic state. In the vicinity of the charge neutrality point (i.e., the point where the electron and hole densities are equal), the system is found to be in an insulating state with an anomalously weak power-law temperature dependence of the resistivity.

Magneto-infrared modes in InAs-AlSb-GaSb coupled quantum wells

We have studied a series of InAs/GaSb coupled quantum wells using magneto-infrared spectroscopy for high magnetic fields up to 33 T within temperatures ranging from 4 to 45 K in both Faraday and tilted field geometries. This type of coupled quantum wells consists of an electron layer in the InAs quantum well and a hole layer in the GaSb quantum well, forming the so-called two-dimensional electron-hole bilayer system. Unlike the samples studied in the past, the hybridization of the electron and hole subbands in our samples is largely reduced by having narrower wells and an AlSb barrier layer interposed between the InAs and the GaSb quantum wells, rendering them weakly hybridized. Previous studies have revealed multiple absorption modes near the electron cyclotron resonance of the InAs layer in moderately and strongly hybridized samples while only a single absorption mode was observed in the weakly hybridized samples. We have observed a pair of absorption modes occurring only at magnetic fields higher than 14 T, which exhibited several interesting phenomena. Among which we found two unique types of behavior that distinguish this work from the ones reported in the literature. This pair of modes is very robust against rising thermal excitations and increasing magnetic fields aligned parallel to the heterostructures. While the previous results were aptly explained by the antilevel crossing due to the hybridization of the electron and hole wave functions, i.e., conduction-valence Landau-level mixing, the unique features reported in this paper cannot be explained within the same concept. The unusual properties found in this study and their connection to the known models for InAs/GaSb heterostructures will be discussed; in addition, several alternative ideas will be proposed in this paper and it appears that a spontaneous phase separation can account for most of the observed features.

Quantum Hall Effect near the Charge Neutrality Point in a Two-Dimensional Electron-Hole System

We study the transport properties of HgTe-based quantum wells containing simultaneously electrons and holes in a magnetic field B. At the charge neutrality point (CNP) with nearly equal electron and hole densities, the resistance is found to increase very strongly with B while the Hall resistivity turns to zero. This behavior results in a wide plateau in the Hall conductivity sigma(xy) approximately = 0 and in a minimum of diagonal conductivity sigma(xx) at nu = nu(p) - nu(n) = 0, where nu(n) and nu(p) are the electron and hole Landau level filling factors. We suggest that the transport at the CNP point is determined by electron-hole "snake states" propagating along the nu = 0 lines. Our observations are qualitatively similar to the quantum Hall effect in graphene as well as to the transport in a random magnetic field with a zero mean value.