Electron Gas In Magnetic Field Research Articles

High-precision measurements of terahertz polarization states with a fiber coupled time-domain THz spectrometer

We present a new method for high precision measurements of polarization rotation in the frequency range from 0.2 to 2.2 THz using a fiber coupled time-domain THz spectrometer. A free standing wire-grid polarizer splits THz light into orthogonal components that are then measured by two separate detectors simultaneously. We theoretically model the uncertainties introduced by optical component non-idealities and predict that we may expect to achieve accuracies of 0.8% when anti-symmetrizing the response with respect to an applied field. Anti-symmetrization improves accuracy by more than four orders of magnitude. We demonstrate this method on a 2D electron gas in magnetic field and show that we achieve a precision of 20 μrad (1.1 mdeg) for small polarization rotation angles. A detailed description of the technique and data analysis procedure is provided, demonstrating its capability to precisely measure polarization states in the 0.2 to 2.2 THz range.

Peculiarities of the Temperature Dependence of the Chemical Potential of a Two-dimensional Electron Gas in Magnetic Field

A numerical calculation of the temperature dependence of the chemical potential and for various values of the filling factor [Formula: see text] of the Landau level is carried out. The degree of filling of each Landau level is found as a function of temperature. Analytical calculations were carried out in the model of an ideal Fermi gas both without taking into account the broadening of the Landau levels [Formula: see text] and taking into account their broadening [Formula: see text]. An analytical formula is found that describes the dependences of [Formula: see text] at [Formula: see text] and low temperatures. A low-temperature formula for the dependence of [Formula: see text] based on the Sommerfeld expansion is also given. The influence of the intra- and interlevel thermal excitations on changes in the chemical potential with temperature is discussed.

Gated two-dimensional electron gas in magnetic field: Nonlinear versus linear regime

We study the effect of magnetic field on the properties of a high mobility gated two-dimensional electron gas in a field effect transistor with the Hall bar geometry. When approaching the current saturation when the drain side of the channel becomes strongly depleted, we see a number of unusual effects related to the magnetic field induced re-distribution of the electron density in the conducting channel. The experimental results obtained in the non-linear regime have been interpreted based on the results obtained in the linear regime by a simple theoretical model, which describes quite well our observations.

Second Order Solutions of THz Response of Gated Two-Dimensional Electron Gas in Magnetic Field

Abstract In this work, the Lifshits-Dyakonov theory for THz response of gated two-dimensional electron gas in magnetic field are analyzed and improved. Instead an approximate processing method for the response in original theory to the second order solution, the second order equations are strictly solved. The numerical results show that both first and second order solutions are damped oscillating functions of coordinate, but all amplitudes would decrease as magnetic field B increasing except for the first order solution of voltage. The variation of second order response as a function of B also shows damped oscillating variations, the agreement with experimental curves is reasonable.

Longitudinal conductivity of a three-dimensional Dirac electron gas in magnetic field

We discuss a conductivity of a three-dimensional gas of Dirac electrons in the direction of magnetic field in high magnetic fields. Analytical expressions for the zero temperature conductivity are calculated in the linear response theory using the basis of relativistic Landau levels. The impurity scattering is treated in the self-consistent Born approximation which gives Landau level broadening increasing linearly in magnetic field. We demonstrate that in the special case of zero-gap Dirac semimetal this leads to the magnetic field and temperature independent conductivity in high magnetic field limit.

Analytical thermodynamical properties of a two-dimensional electron gas in a magnetic field

Analytical expressions for the thermodynamical properties of a two-dimensional electron gas in a perpendicular magnetic field are derived. This is accomplished by first deriving the general expression for the thermodynamical potential, and then employing this result to obtain the corresponding expression for the two-dimensional gas. The chemical potential and magnetization are studied as a function of temperature and magnetic field, and shown to be in agreement with prior work. It is also shown that the results are close to those obtained by assuming a Gaussian density of states for the Landau levels.

Density of one-particle states for 2-D electron gas in magnetic field

The density of states of a particle in a 2D area is independent both of the energy and form of the area only at the region of large values of energy. If energy is small, the density of states in the rectangular potential well essentially depends on the form of the area. If the bottom of the potential well has a potential relief, it can define the small eigenvalues as the discrete levels. In this case, dimensions and form of the area would not have any importance. If the conservation of zero value of the angular momentum is taken into account, the effective one-particle Hamiltonian for the 2D electron gas in the magnetic field in the circle is the Hamiltonian with the parabolic potential and the reflecting bounds. It is supposed that in the square, the Hamiltonian has the same view. The 2D density of states in the square can be computed as the convolution of 1D densities. The density of one-particle states for 2D electron gas in the magnetic field is obtained. It consists of three regions. There is a discrete spectrum at the smallest energy. In the intervening region the density of states is the sum of the piecewise continuous function and the density of the discrete spectrum. At great energies, the density of states is a continuous function. The Fermi energy dependence on the magnetic field is obtained when the field is small and the Fermi energy is located in the region of continuous spectrum. The Fermi energy has the oscillating correction and in the average it increases proportionally to the square of the magnetic induction. Total energy of electron gas in magnetic field also oscillates and increases when the magnetic field increases monotonously.

Energy spectra for quantum wires and two-dimensional electron gases in magnetic fields with Rashba and Dresselhaus spin-orbit interactions

We introduce an analytical approximation scheme to diagonalize parabolically confined two dimensional electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and non-crossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength k_Rl of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e.g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the n^th Landau-level g_n-factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g-factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.

Photovoltaic effect in a gated two-dimensional electron gas in magnetic field

The photovoltaic effect induced by terahertz radiation in a gated two-dimensional electron gas in magnetic field is considered theoretically. It is assumed that the incoming radiation creates an ac voltage between the source and gate and that the gate length is long compared to the damping length of plasma waves. In the presence of pronounced Shubnikov-de Haas oscillations, an important source of non-linearity is the oscillating dependence of the mobility on the ac gate voltage. This results in a photoresponse oscillating as a function of magnetic field, which is enhanced in the vicinity of the cyclotron resonance, in accordance with recent experiments. Another, smooth component of the photovoltage, unrelated to SdH oscillations, has a maximum at cyclotron resonance.

Quantum statistical mechanics of electron gas in magnetic field

Electron eigenstates in a magnetic field are considered. Density of the electrical current and an averaged magnetic moment are obtained. Density of states is investigated for two-dimensional electron in a circle that is bounded by the infinite potential barrier. The present study shows that the common quantum statistical mechanics of electron gas in a magnetic field leads to incorrect results. The magnetic moment of electron gas can be computed as the sum of averaged moments of the occupied states. The computations lead to the results that differ from the ones obtained as the derivative of the thermodynamical potential with respect to the magnetic field. Other contradictions in common statistical thermodynamics of electron gas in a magnetic field are pointed out. The conclusion is done that these contradictions arise from using the incorrect statistical operator. A new quantum function of distribution is derived from the basic principles, taking into account the law of conservation of an angular momentum. These results are in accord with the theory that has been obtained within the framework of classical statistical thermodynamics in the previous work.

The conductivity tensor and frequency of electron momentum relaxation in the case of scattering by ionized impurities in a magnetic field: The density matrix method

A solution to the Liouville equation for a one-electron density matrix in relation to a homogeneous semiconductor in a magnetic field is obtained using perturbation theory. Expressions for the conductivity tensor and electron-momentum relaxation rate are obtained for the case of scattering by ionized impurities. These expressions provide a sufficiently accurate description of the concentration and magnetic field dependences of the longitudinal conductivity of a nondegenerate electron gas in the quantum limit that have been observed in some studies. No explanation for these dependences is found in the context of the current theory of magnetoresistivity. An explanation of the temperature dependences of the components of the conductivity tensor is suggested for a degenerate electron gas in magnetic fields that correspond to the quantum limit.

Conductivity of a two-dimensional electron gas in magnetic field in the presence of microwave radiation

The experimental observations of novel behavior of the kinetic properties of a two-dimensional electron gas in the presence of microwave radiation are reviewed, and the various theoretical models that have been proposed for explaining them are described.

Longitudinal dielectric behavior of a harmonically bound two-dimensional electron gas in a uniform magnetic field

We have employed random-phase approximation to determine the inverse dielectric function for a harmonically confined two-dimensional electron gas in a magnetic field. We examine the plasmon dispersion relation and show the results for the variation of plasmon frequency with the magnetic field strength and confinement energy.

Point impurities remove degeneracy of the Landau levels in a two-dimensional electron gas

We study the density of states of two-dimensional electron gas in magnetic field with scattering on point-like impurities that are uniformly distributed along the sample. We show that the electron-impurity interaction completely lifts the degeneracy of the Landau levels even at low impurity concentration. This statement is in contradiction with the previous results obtained in the unphysical approximation of two-dimensional impurities. There is a large region of the electron energy $\omega $, counted from the Landau level, where the density of states $\rho (\omega)$ is inversely proportional to $|\omega|$ and proportional to the impurity concentration. Our results are applicable to different 2D electron systems as heterostructures, inversion layers and interfaces.

Nematic phase of the two-dimensional electron gas in a magnetic field

The two-dimensional electron gas (2DEG) in moderate magnetic fields in ultraclean AlAs-GaAs heterojunctions exhibits transport anomalies suggestive of a compressible anisotropic metallic state. Using scaling arguments and Monte Carlo simulations, we develop an order parameter theory of an electron nematic phase. The observed temperature dependence of the resistivity anisotropy behaves like the orientational order parameter if the transition to the nematic state occurs at a finite temperature T(c) approximately 65 mK, and is slightly rounded by a small background microscopic anisotropy. We propose a light scattering experiment to measure the critical susceptibility.

Characteristic energy losses of electrons in a two-dimensional electron gas in a magnetic field

The electron energy loss function is calculated in the random phase approximation for a two-dimensional electron gas in a quantizing magnetic field. Local states of electrons at impurity atoms are taken into consideration. The energy losses due to one-particle and collective excitations of two-dimensional electrons are determined. The activation of electrons localized at impurities leads to the emergence of steps on the dependence of loss function on the energy of an incident electron. Cerenkov losses associated with emission of magnetoplasmons appear starting from a threshold velocity of the electron. When the velocity exceeds the threshold value significantly, the losses are due only to spontaneous emission of magnetoplasmons. The corresponding loss function decreases in inverse proportion to the electron velocity.

Optical signatures from magnetic two-dimensional electron gases in magnetic fields to 60 T

We present experiments in the 60 T long-pulse magnet at the Los Alamos National High Magnetic Field Lab focusing on the high-field, low temperature photoluminescence (PL) from modulation-doped ZnSe/Zn(Cd,Mn)Se single quantum wells. High-speed charge-coupled array detectors and the long (2 s) duration of the magnet pulse permit continuous acquisition of optical spectra throughout a single magnet shot. High-field PL studies of the magnetic two-dimensional electron gases at temperatures down to 350 mK reveal clear intensity oscillations corresponding to integer quantum Hall filling factors, from which we determine the density of the electron gas. At very high magnetic fields, steps in the PL energy are observed which correspond to the partial unlocking of antiferromagnetically bound pairs of Mn2+ spins.

Negative Electron Drag and Holelike Behavior in the Integer Quantum Hall Regime

Electron drag between two two-dimensional electron gases in magnetic fields has been observed with a polarity opposite that for zero field. This negative drag requires that the electrons have a hole-like dispersion. Density dependence measurements in the integer quantum Hall regime show that drag is negative only when the upper Landau level of one layer is more than half filled while the other is less than half filled, indicating that hole-like dispersion is present in a half of each Landau level. Negative drag is argued to be a consequence of disorder.

Exchange-correlation energy for a two-dimensional electron gas in a magnetic field.

We present the results of a variational Monte Carlo calculation of the exchange-correlation energy for a spin-polarized two-dimensional electron gas in a perpendicular magnetic field. These energies are a necessary input to the recently developed current-density functional theory. Landau-level mixing is included in a variational manner, which gives the energy at finite density at finite field, in contrast to previous approaches. Results are presented for the exchange-correlation energy and excited-state gap at $\nu =$ 1/7, 1/5, 1/3, 1, and 2. We parameterize the results as a function of $r_s$ and $\nu$ in a form convenient for current-density functional calculations.

Inelastic light scattering from a modulated two-dimensional electron gas in magnetic fields.

We study inelastic light scattering from a two-dimensional electron gas subject to a weak in-plane one-dimensional periodic potential modulation and a perpendicular magnetic field. Electronic Raman scattering is considered for (i) inter-Landau-level transitions, which result in a Raman shift of \ensuremath{\sim}2${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$, and (ii) transitions involving collective excitations at the hybridized magnetoplasmon frequency and a modulation-indued, low-frequency intra-Landau-level plasmon. Raman cross sections and their dependencies on the magnetic field strength and the modulation potential/density are examined.