Electron-electron interactions in the 2D electron system

In this paper, we report studies of the electron-electron interaction effects in 2D electron systems. The interaction manifests in renormalization of the effective spin susceptibility, effective mass, g^∗-factor, conductivity etc. By applying in-plane magnetic field, we tuned the effective interaction between the electrons and compared with theory the temperature dependence of the conductivity. We find a good agreement with interaction corrections calculated within the Fermi liquid theory. To address the question on the origin of the metal-insulator transition (MIT) in 2D, we explored transport and magnetotransport properties in the vicinity of the MIT and compared our data with solutions of two equations of the renormalization group (RG) theory, which describes temperature evolutions of the resistivity and interaction parameters for 2D electron system. We found a good agreement between the ρ(T,B_∥) data and the RG-theory in a wide range of the in-plane fields. These results support the Fermi liquid type origin of the metallic state and the interpretation of the observed 2D MIT as the true quantum phase transition.     

Effect of interface roughness on the density of states of finite barrier height quantum wells

We calculate the density of states of a 2D electron gas in finite barrier height quantum wells with the explicit inclusion of the interface roughness effect. By using Feynman path-integral method, the analytic expression is derived. The results show that the 2D density of states is dependent on the RMS of the fluctuation potential. The interface roughness causes localized states below the subband edge. We also apply the theory to model the finite barrier height quantum wells in Al_xGa_1?xAs/GaAs.     

Electronic parameters and electronic structures in modulation-doped highly strained InxGa1−xAs/InyAl1−yAs coupled double quantum wells

Electronic parameters of a two-dimensional electron gas (2DEG) in modulation-doped highly strained In_xGa_1−xAs/In_yAl_1−yAs coupled double quantum wells were investigated by performing Shubnikov-de Haas (S-dH), Van der Pauw Hall-effect, and cyclotron resonance measurements. The S-dH measurements and the fast Fourier transformation results for the S-dH at 1.5 K indicated the electron occupation of two subbands in the quantum well. The electron effective masses of the 2DEG were determined from the cyclotron resonance measurements, and satisfied qualitatively the nonparabolicity effects in the quantum wells. The electronic subband structures were calculated by using a self-consistent method.     

Electron correlation in two-dimensional systems: CHNC approach to finite-temperature and spin-polarization effects

Applying the classical-map hypernetted-chain method (CHNC) developed recently by Dharma-wardana and Perrot, we have studied the temperature and spin-polarization effects on electron correlation in the uniform quantum two-dimensional gas (2DEG) over a wide range of temperature T and spin-polarization ζ. The quantum fluid at the temperature T is mapped to a classical fluid at the temperature T_cf given by T_cf²=T²+T_q², where the quantum temperature T_q is determined by comparing the calculated correlation energy to that of Monte Carlo results for the fully spin-polarized quantum system at zero temperature. By the iterative solution of the modified HNC equation and the Ornstein-Zernike equation, we have obtained the pair distribution function (PDF) and correlation energy for the two-component classical 2DEG with a classical fluid temperature T_cf. The anti-parallel bridge function B₁₂(r) appearing in the modified HNC equation is determined by using the Monte Carlo correlation energy at T=0 or STLS (Singwi-Tosi-Land-Sjölander) result at T>0 and the numerical solution to the Percus-Yevick (PY) equation for the system of hard disks. By calculating the Pauli potential, the bridge function, PDFs, structure factors and correlation energy, we have shown that in some cases, the properties of the uniform quantum 2DEG depend remarkably on the temperature and spin-polarization.     

Quantum magneto-transport in two-dimensional GaAs electron gases and SiGe hole gases

We have measured the low-temperature transport properties of two-dimensional (2D) GaAs electron gases and 2D SiGe hole gases. Our experimental results fall into three categories. (i) Collapse of spin-splitting and an enhanced Landé g-factor at Landau level filling factors both ν=3 and ν=1 in a 2D GaAs electron gas are observed. Our experimental results show direct evidence that the effective disorder is stronger at ν=1 than that at ν=3 over approximately the same perpendicular magnetic field range. (ii) We present evidence for spin-polarisation of a dilute 2D GaAs electron gas. The Lande g-factor of the system is estimated to be 1.66. This enhanced g value is ascribed to electron–electron interactions at ultra low carrier density limit. (iii) In a high-quality SiGe hole gas, there is a temperature-independent point in the magnetoresistivity ρ_xx and ρ_xy which is ascribed to experimental evidence for a quantum phase transition between ν=3 and ν=5. We also present a study on the temperature(T)-driven flow lines in our system.     

Coulomb blockade and the thermopower of a suspended quantum dot

On the basis of the 2D electron gas in an AlGaAs/GaAs membrane separated from a wafer, a one-electron transistor is created that operates on the Coulomb blockade effect—a two-barrier structure with a quantum dot. The separation of the sample from the wafer, which has a large dielectric constant, leads to a sharp decrease in the total capacity C of the quantum dot and, as a result, to high charge energy E _C = e ²/C and critical temperature T _C = E _C/k _B ≈ 40 K. The dependence of the conductance of the quantum dot on the driving and gate voltages includes a rhombic structure characteristic of the Coulomb blockade effect. The phonon-drag thermopower is found in this system. This thermopower exhibits an anomalous alternating dependence on the gate voltage and intensity of the phonon flux. Possible mechanisms are proposed for explaining the indicated anomalies in the thermopower.     

Edge current switch of two-dimensional electron gas using carrier density control

We have investigated the effects of electron density discontinuity on the transports of edge currents of two-dimensional electron gas (2DEG). The electric field applied to a gate, which covers the 2DEG partially, gives rise to change in the carrier density and results in a density gradient, which deforms the edge currents. The transverse and longitudinal resistances were measured as functions of gate voltage V_G in the quantum Hall regime. The deviations of the longitudinal resistances from the normal quantum Hall resistances are attributed to the reflections of the edge currents under the influence of the abrupt density discontinuity. A switching behavior of the transverse resistance by controlling the gate voltage was observed when V_G=−2.2 and −2.0 V for magnetic field H=5 and 7.2 T, respectively.     

Compressibility of a two-dimensional electron gas in a parallel magnetic field

The thermodynamic compressibility of a two-dimensional electron system in the presence of an in-plane magnetic field is calculated. We use accurate correlation energy results from quantum Monte Carlo simulations to construct the ground state energy and obtain the critical magnetic field B_c required to fully spin polarize the system. Inverse compressibility as a function of density shows a kink-like behavior in the presence of an applied magnetic field, which can be identified as B_c. Our calculations suggest an alternative approach to transport measurements of determining full spin polarization.     

Scattering times in AlGaN/GaN two-dimensional electron gas from magnetotransport measurements

The various scattering times of two-dimensional electron gas were investigated in modulation-doped Al_0.22Ga_0.78N/GaN quantum wells by means of magnetotransport measurements. The ratio of transport and quantum scattering times, τ_t/τ_q∼1, shows that the dominant mobility-limiting mechanisms are short-range scattering potentials. The low-field magnetoresistance shows the weak antilocalization and localization phenomenon from which the spin-orbit scattering and inelastic scattering times are obtained. The inelastic scattering time is found to follow the T⁻¹ law, indicating that electron-electron scattering with small energy transfer is the dominant inelastic process.     

Inter and intrasubband transitions via LO phonons in quantum wires

We investigate the effects of the finite confining potential V₀ on the absorption and emission scattering rates of electrons interacting with LO phonons for a cylindrical GaAs quantum wire. The emission rates are qualitatively similar to those of the 2D case. The absorption rates on the other hand exhibit two different regimes: 1) for a wire radius smaller than a certain value (80 Å in the case where V₀ = 190 meV) the behavior is similar to the 2D and 3D analogues, but 2) for larger radius the absorption rates initially increase with increasing energy, reach a maximum value and then decrease monotonicaly. A complete study is made as a function of wire radius, and electron energy.     

Time domain capacitance spectroscopy of tunneling electrons in the two-dimensional electron gas

We have developed a technique capable of measuring the tunneling current into both localized and conducting states in a 2D electron system (2DES). The method yields I-V characteristics for tunneling with no distortions arising from low 2D in-plane conductivity. We have used the technique to determine the pseudogap energy spectrum for electron tunneling into and out of a 2D system and, further, we have demonstrated that such tunneling measurements reveal spin relaxation times within the 2DEG. Pseudogap: In a 2DEG in perpendicular magnetic field, a pseudogap develops in the tunneling density of states at the Fermi energy. We resolve a linear energy dependence of this pseudogap at low excitations. The slopes of this linear gap are strongly field dependent. No existing theory predicts the observed behavior. Spin relaxation: We explore the characteristics of equilibrium tunneling of electrons from a 3D electrode into a high mobility 2DES. For most 2D Landau level filling factors, we find that electrons tunnel with a single, well-defined tunneling rate. However, for spin-polarized quantum Hall states (ν=1, 3 and 1/3) tunneling occurs at two distinct rates that differ by up to two orders of magnitude. The dependence of the two rates on temperature and tunnel barrier thickness suggests that slow in-plane spin relaxation creates a bottleneck for tunneling of electrons.     

Localization of quantum states at the cyclotron resonance

Tunneling of a quantum particle to the classically inaccessible region in an intrinsically degenerate system is investigated here by means of quasienergy eignestates. The exact resonance (δω=ω−ω₀=0) and near resonance (δω ≠ 0) cases are explored numerically. It is shown that in both cases all quantum states are localized. Correspondence of the quantum dynamical barriers to the classical invariant curves is demonstrated. The phenomena considered can be observed when an ultrasound wave propagates perpendicularly to a magnetic field and interacts with a 2D electron gas in a semiconductor heterostructure.     

Coulomb oscillations of the current through spin-nondegenerate <Emphasis Type="Italic">p</Emphasis> states of InAs quantum dots

The electron transport is studied in split-gate structures fabricated on the basis of a modulation-doped heterostructure that contains a single quantum well and self-assembled InAs quantum dots near the 2D electron gas regions. The current passing through the channel with a denumerable set of InAs quantum dots is found to exhibit Coulomb oscillations as a function of the gate voltage. The oscillations are associated with the excited p states of InAs quantum dots, which are characterized by opposite spins and caused by lifting of the spin degeneracy of the p state due to the Coulomb interaction. The Coulomb oscillations of the current are observed up to a temperature of ～20 K. The Coulomb energy is found to be ΔE_c = 12.5 meV, which agrees well with the theoretical estimates for the p states of quantum dots in the structures under study.     

Magneto-optics of strongly correlated two-dimensional electrons in single heterojunctions

Investigations of two-dimensional (2D) electron systems in semiconductors subjected to a strong perpendicular magnetic field with the use of photoluminescence are reviewed. The foundation of the optical spectroscopy method using the radiative recombination of 2D electrons with photoexcited holes bound to acceptors in a δ-doped monolayer in GaAs/Al _x Ga_1-x As single heterojunctions is presented. Optical spectroscopy studies of the energy spectra of 2D electrons imposed on transverse magnetic fields in the regimes of the integer and fractional quantum Hall effects are discussed. The relationship between the mean energy of the 2D electron gas and the first moment of their radiative recombination is analysed. It is shown that the magnetic field dependence of the first moment provides a method to measure the cyclotron, enhanced spin and quasiparticle energy gaps at the same time. Therefore it is shown how magneto-optics ‘see’ the ground state of interacting 2D electrons in the extreme quantum limit and how an optical ‘tool’ is efficient for the determination of Coulomb gaps of incompressible Fermi fluids in the fractional quantum Hall effect. Finally optical observations and studies of the Wigner crystallization of 2D electrons are presented. The corresponding liquid-solid phase diagram is discussed.     

Inhomogeneous Hall-geometry sample in the quantum Hall regime

A generalization of the known theory describing the Hall channels with integer filling factors in inhomogeneous 2D electronic samples to the case of a stationary nonequilibrium state (with a nonzero Hall voltage V _H across the 2D system) is proposed. For the central strip located near the extremum of the electron density, the theory predicts a change in its width and a shift of the whole strip from the equilibrium position as functions of V _H . The theoretical results are used to interpret recent experiments on measuring the local electric fields along the Hall samples both in equilibrium conditions and in the presence of transport in the quantum Hall regime.     

Ground-state properties of jellium metals with low electron densities

The ground state of a three-dimensional electron gas is theoretically investigated within the framework of the local spin density approximation with the Perdew–Zunger exchange-correlation energy. The system has been found to be in a one- or two-dimensional crystal state, when the Wigner sphere radius r_s has an intermediate value. At r_s=60, a triangular lattice with the lattice spacing 96.10 is the lowest energy state among fluids, 1D, 2D, and 3D crystals.     

A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

It is previously found that the two-dimensional (2D) electron-pair in a homogeneous magnetic field has a set of exact solutions for a denumerably infinite set of magnetic fields. Here we demonstrate that as a function of magnetic field a band-like structure of energy associated with the exact pair states exists. A direct and simple connection between the pair states and the quantum Hall effect is revealed by the band-like structure of the hydrogen “pseudo-atom”. From such a connection one can predict the sites and widths of the integral and fractional quantum Hall plateaus for an electron gas in a GaAs-Al _x Ga_1−x As heterojunction. The results are in good agreement with the existing experimental data.     

Impurity effects on the magnetization and magnetic susceptibility of an electron confined in a quantum ring under the presence of an external magnetic field

The magnetization and the magnetic susceptibility of a single electron confined in a two-dimensional (2D) parabolic quantum ring under the effect of external uniform magnetic field and in the presence of an acceptor impurity have been studied. The shifted 1/N expansion method was used to solve the Hamiltonian quantum ring within the effective mass approximation. The computed energy spectra, the magnetization and magnetic susceptibility have been displayed as a function of the quantum ring parameters: confinement strength ω₀, magnetic field strength (ω_c), and temperature (T). The obtained energy results show level-crossings, in the absence and presence of acceptor impurity, which are manifested as oscillations in the magnetization and magnetic susceptibility curves.     

One-electron spin-dependent transport in split-gate structures containing self-organized InAs quantum dots

The paper presents the results obtained in a study of electron transport in split-gate structures prepared from heterostructures with self-organizing InAs quantum dots situated close to a two-dimensional electron gas. Coulomb oscillations of current through InAs quantum dots depending on the voltage on the gate were observed. Coulomb current oscillations persisted up to about 20 K. The Coulomb energy ΔE _C = 12.5 meV corresponding to theoretical estimates for the p-states of quantum dots in our structures was determined.     

Potential Energies of the Orbitally Degenerate Atmospheric Rydberg Complexes

A method was developed for calculating the vibronic potential energy surfaces (PESs) of atmospheric complexes consisting of orbitally degenerate Rydberg nitrogen and oxygen molecules and the molecules of a neutral medium in the ground electronic state. The degenerate states are formed as a result of l-mixing in the D and E layers of the atmosphere during the periods of increased solar activity. The complexes are populated in the nonequilibrium two-temperature plasma and are responsible for the incoherent additional background radiation in the decimeter (microwave) and terahertz (IR) bands at an altitude of 80–110 km from the Earth’s surface. To describe the interaction of a weakly bound electron with a singly charged molecular ion and a neutral molecule of a gas medium, the formalism of the multichannel quantum defect (MCD) theory was used. Quantum-chemical calculations of the dependences of the scattering lengths, polarizabilities, and quadrupole moments of the main atmospheric molecules N₂ and O₂ on the interatomic distance were performed. The specific features of the behavior of vibronic PESs of Rydberg complexes for large values of the principal quantum number (n ? 1) were analyzed. The vibronic PESs of orbitally degenerate states were constructed. They are necessary for determining the positions and shape of the vibronic minima of the l-mixing cross sections of the N₂ and O₂ Rydberg molecules in the D and E layers of the Earth’s atmosphere, where the delay times of satellite positioning signals should be minimum. The possibility of “quantum chaos” appearing in the Rydberg complexes at sufficiently large n values and angular momenta of the weakly bound electron was noted.