Non-interacting Two-dimensional Electron Gas Research Articles

Quantum heat machines enabled by twisted geometry

In this paper, we analyze the operation of an Otto cycle heat machine driven by a non-interacting two-dimensional electron gas on a twisted geometry. We show that due to both the energy quantization on this structure and the adiabatic transformation of the number of complete twists per unit length of a helicoid, the machine performance in terms of output work, efficiency, and operation mode can be altered. We consider the deformations as in a spring, which is either compressed or stretched from its resting position. The realization of classically inconceivable Otto machines, with an incompressible sample, can be realized as well. The energy-level spacing of the system is the quantity that is being either compressed or stretched. These features are due to the existence of an effective geometry-induced quantum potential which is of pure quantum-mechanical origin.

Residual bulk viscosity of a disordered two-dimensional electron gas

Nonzero bulk viscosity signals breaking of the scale invariance. We demonstrate that disorder in a two-dimensional noninteracting electron gas in a perpendicular magnetic field results in nonzero disorder-averaged bulk viscosity. We derive an analytic expression for the bulk viscosity within the self-consistent Born approximation. This residual bulk viscosity provides the lower bound for the bulk viscosity of 2D interacting electrons at low enough temperatures.

Theory of the nonlinear Rashba-Edelstein effect: The clean electron gas limit

It is well known that a current driven through a two-dimensional electron gas with Rashba spin-orbit coupling induces a spin polarization in the perpendicular direction (Edelstein effect). This phenomenon has been extensively studied in the linear response regime, i.e., when the average drift velocity of the electrons is a small fraction of the Fermi velocity. Here we investigate the phenomenon in the nonlinear regime, meaning that the average drift velocity is comparable to or exceeds the Fermi velocity. This regime is realized when the electric field is very large or when electron-impurity scattering is very weak. We consider the limiting case of a two-dimensional noninteracting electron gas with no impurities. In this case, the quantum kinetic equation for the density matrix is exactly and analytically solvable, reducing to a problem of spin dynamics for ``unpaired'' electrons near the Fermi surface. The crucial parameter is $\ensuremath{\gamma}=eE{L}_{s}/{E}_{F}$, where $E$ is the electric field, $e$ is the absolute value of the electron charge, ${E}_{F}$ is the Fermi energy, and ${L}_{s}=\ensuremath{\hbar}/(2m\ensuremath{\alpha})$ is the spin-precession length in the Rashba spin-orbit field with coupling strength $\ensuremath{\alpha}$. If $\ensuremath{\gamma}\ensuremath{\ll}1$, the evolution of the spin is adiabatic, resulting in a spin polarization that grows monotonically in time and eventually saturates at the maximum value $n(\ensuremath{\alpha}/{v}_{F})$, where $n$ is the electron density and ${v}_{F}$ is the Fermi velocity. If $\ensuremath{\gamma}\ensuremath{\gg}1$ the evolution of the spin becomes strongly nonadiabatic and the spin polarization is progressively reduced and eventually suppressed for $\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\infty}$. We also predict an inverse nonlinear Edelstein effect, in which an electric current is driven by a magnetic field that grows linearly in time. The ``conductivities'' for the direct and the inverse effects satisfy generalized Onsager reciprocity relations, which reduce to the standard ones in the linear response regime.

Band of critical States in anderson localization in a strong magnetic field with random spin-orbit scattering.

The Anderson localization problem for a noninteracting two-dimensional electron gas subject to a strong magnetic field, disordered potential, and spin-orbit coupling is studied numerically on a square lattice. The nature of the corresponding localization-delocalization transition and the properties of the pertinent extended states depend on whether the spin-orbit coupling is uniform or fully random. For uniform spin-orbit coupling (such as Rashba coupling due to a uniform electric field), there is a band of metallic extended states in the center of a Landau band as in a "standard" Anderson metal-insulator transition. However, for fully random spin-orbit coupling, the familiar pattern of Landau bands disappears. Instead, there is a central band of critical states with definite fractal structure separated at two critical energies from two side bands of localized states. Moreover, finite size scaling analysis suggests that for this novel transition, on the localized side of a critical energy E_{c}, the localization length diverges as ξ(E)∝exp(α/sqrt[|E-E_{c}|]), a behavior which, together with the emergence of a band of critical states, is reminiscent of a Berezinskii-Kosterlitz-Thouless transition.

Transport properties of a 2DEG in the presence of tilted magnetic field: the influence of a 1D modulation

The effect of 1D periodic modulation on the transport and thermodynamic properties of a non-interacting two-dimensional electron gas (2DEG) is investigated. The Hamiltonian used also includes a tilted magnetic field, Rashba, and Dresselhauss spin-orbit interactions. The 1D periodic modulation introduces non-quantized regions on Hall conductivity and a non-zero diffusive conductivity. A method to estimate the modulation periodicity is given using the periodicity of Weiss oscillations on the diffusive conductivity.

Dissipative phase fluctuations in superconducting wires capacitively coupled to diffusive metals

We study the screening of the Coulomb interaction in a quasi one-dimensional superconductor given by the presence of either a one- or a two-dimensional non-interacting electron gas. To that end, we derive an effective low-energy phase-only action, which amounts to treating the Coulomb and superconducting correlations in the random-phase approximation. We concentrate on the study of dissipation effects in the superconductor, induced by the effect of Coulomb coupling to the diffusive density-modes in the metal, and study its consequences on the static and dynamic conductivity. Our results point towards the importance of the dimensionality of the screening metal in the behavior of the superconducting plasma mode of the wire at low energies. In absence of topological defects, and when the screening is given by a one-dimensional electron gas, the superconducting plasma mode is completely damped in the limit $q\to 0$, and consequently superconductivity is lost in the wire. In contrast, we recover a Drude-response in the conductivity when the screening is provided by a two-dimensional electron gas.

Transport and thermodynamic properties of a 2DEG in the presence of tilted magnetic field: the influence of Rashba interaction

The effects of Rashba spin-orbit coupling on the physical properties of a non-interacting two-dimensional electron gas (2DEG) in presence of a tilted magnetic field are investigated. The spin-orbit and Zeeman interactions depend on the intensity and direction of the external magnetic field and we study their influence on the physical properties of the system. We obtain the energy spectrum, the density of states, the Fermi energy, and we analyze the combined effect of the Zeeman and Rashba Spin-Orbit Interaction on the transport and thermodynamic properties.

Magnetic field dependence of the transverse plasmon in SmLa(0.8)Sr(0.2)CuO(4-delta).

The magnetic field and temperature dependence of the transverse and longitudinal plasmons in SmLa(0.8)Sr(0.2)CuO(4-delta) have been investigated. A transition between a vortex-glass and a vortex-liquid regime, which revealed different field dependencies of the resonance frequencies, could be clearly observed. The positions and the spectral weights of the plasmons were successfully described using the multilayer model [Phys. Rev. B 64, 024530 (2001)], which takes the compressibility of the electronic liquid into account. The absolute value of the compressibility is close to that of a two-dimensional noninteracting electron gas.

Anisotropic scattering and quantum magnetoresistivities of a periodically modulated two-dimensional electron gas

We calculate the longitudinal conductivities of a two-dimensional noninteracting electron gas in a uniform magnetic field and a lateral electric or magnetic periodic modulation in one spatial direction, in the quantum regime. We consider the effects of the electron-impurity scattering anisotropy through the vertex corrections on the Kubo formula, which are calculated with the Bethe-Salpeter equation, in the self-consistent Born approximation. We find that due to the scattering anisotropy the band conductivity increases, and the scattering conductivities decrease and become anisotropic. Our results are in qualitative agreement with recent experiments.

Disorder and localization in the lowest Landau level in the presence of dilute point scatterers

We study the localization properties of a two-dimensional noninteracting electron gas in the presence of randomly distributed short-range scatterers in very high magnetic fields. We evaluate the participation number of the eigenstates obtained by exact diagonalization technique. At low impurity concentrations we obtain self-averaged values showing that all states, except those exactly at the Landau level, are localized with finite localization length. We conclude that in this dilute regime the localization length does not diverge. We also find that the maximum localization length increases exponentially with impurity concentration. Our calculations suggest that scaling behavior may be absent even for higher concentrations of scatterers.

Kosterlitz-Thouless-Type Metal-Insulator Transition of a 2D Electron Gas in a Random Magnetic Field

We study the localization property of a two-dimensional noninteracting electron gas in the presence of a random magnetic field. The localization length is directly calculated using a transfer matrix technique and finite size scaling analysis. We show strong numerical evidence that the system undergoes a disorder-driven Kosterlitz-Thouless-type metal-insulator transition. We develop a mean field theory which maps the random field system into a two-dimensional $\mathrm{XY}$ model. The vortex and antivortex excitations in the $\mathrm{XY}$ model correspond to two different kinds of magnetic domains in the random field system.

Quantum magnetic confinement and transport in spherical two-dimensional electron gases.

We present results from a theoretical study of a ballistic electron confined to move in either a spherical or hemispherical noninteracting two-dimensional electron gas in a nonuniform magnetic field, arising as a result of an applied axial field. We calculate the ground-state energy as a function of magnetic-field strength and the dispersion relation for isolated systems. We then discuss quantum ballistic transport on a contacted sphere, a system which is topologically equivalent to a Corbino disk, as a function of Fermi energy and magnetic-field strength.

Stopping power of a two-dimensional electron gas for heavy particles.

The velocity dependence of the stopping power of a two-dimensional noninteracting electron gas for heavy in-plane ions is calculated. The transport cross section required in the kinetic treatment is determined for a bare Coulomb potential. Detailed analytical and illustrative numerical results are derived. The problem of screening is also discussed.

Semiclassical theory of magnetization for a two-dimensional non-interacting electron gas

We compute the semiclassical magnetization and susceptibility of non-interacting electrons, confined by a smooth two-dimensional potential and subjected to a uniform perpendicular magnetic field, in the general case when their classical motion is chaotic. It is demonstrated that the magnetization per particle m(B) is directly related to the staircase function N(E), which counts the single-particle levels up to energy E. Using Gutzwiller's trace formula for N, we derive a semiclassical expression for m. Our results show that the magnetization has a non-zero average, which arises from quantum corrections to the leading-order Weyl approximation to the mean staircase and which is independent of whether the classical motion is chaotic or not. Fluctuations about the average are due to classical periodic orbits and do represent a signature of chaos. This behaviour is confirmed by numerical computations for a specific system.

Influence of a periodic potential on the integer quantum Hall effect

We calculate the Hall conductivity for a disordered non-interacting two-dimensional electron gas in a strong magnetic field under the influence of a periodic potential. We investigate under which experimental conditions the unusual behavior of the Hall effect in the system could be observed.

Electronic conductance of a multi-channel point contact in a magnetic field

We present the numerical results of the electronic conductanceG of a quantum wire with a multichannel point contact structure in a perpendicular external magnetic fieldH at zero temperature, based on the rigorous quantum mechanics of a two-dimensional noninteracting electron gas. Computational results show the approximate quantization of the electronic conductance. WheH is weak,G≅integer multiples of 2e2/h; and whenH is trong, G≅integer multiples of 2ne2/h, wheren is the number of channels in the point contact structure of the quantum wire. Quantum leaps take place whenH≅±2m*EF/[ħe(2j+1)], wherej is either zero or a positive integer small enough for the external magnetic fieldH to be strong, andm* is the effective mass of an electron in the device. To our knowledge, no report on this quantization of electronic conductance has been published. Oscillations are manifest in theG∼H curves for comparatively narrow channels because of the quantum size effect.

Efficiency of determinantal transport theory in the integer quantum Hall effect.

A steady-state solution of the density matrix, capable of properly handling a quasi-infinite density of states, is applied to the integer quantum Hall effect in a noninteracting two-dimensional electron gas, on the basis of unperturbed Landau's states. The width of the Landau subbands due to the crystal periodic potential is taken as an infinitely small quantity tending to zero, and the initial many-body density matrix at equilibrium is calculated up to first order of this bandwidth. This allows us to extract the finite principal part of the conductivity-tensor components from the statistical average of the current density. The quantized plateaus of the Hall conductivity are shown to result from both the very large relaxation parameters due to the quasi-infinite density of states in the Landau subbands and the effect of disorder on the center-of-orbit motion. These are responsible for the vanishing of the diagonal conductivity, except in the intermediate regions between the plateaus, where the density of states is strongly reduced and additional interband transitions take place. The present treatment formally amounts to a change of basis and explains that the underlying physical content is found to be in agreement with prevailing interpretations. The salient experimental features are obtained without an explicit knowledge of localized-extended states, nor with the use of gauge or topological invariants. Owing to its efficiency and simplicity, such an approach offers attractive promise in further quantitative developments.

Quantum transmission in a junction of crossed wires with a box resonator.

We report the results of quantum-mechanical calculations of the transmission properties of a two-dimensional noninteracting electron gas through a ballistic cross, where a box resonator is placed at the center of the junction. The transmission and reflection probabilities, and therefore the bend resistance, fluctuate irregularly as a function of energy. The oscillation is discussed in terms of the cavity resonances.

Resonant conductance of two-dimensional electron systems in a long-wave approximation

A simple method for the description of resonant phenomena in the ballistic quantum transport of the non-interacting two-dimensional electron gas has been developed. The method is based on the analogies to the theory of diffraction by small holes and is of use when the quantum electronic device consists of some parts separated by apertures the dimensions of which are small compared with the electron wavelength. The conductance of the narrow ring with the magnetic flux through the hole has been calculated and the magnetic field influence on the conductance resonant structure has been considered.

Conductance of Fabry-Pérot and two-slit electronic waveguides.

We study the quantum-mechanical ballistic propagation of a two-dimensional noninteracting electron gas within waveguide structures similar to a Fabry-P\'erot interferometer and to the Young two-slit interference structure. The novel features in the Fabry-P\'erot setup are the following: (1) possibility of tuning the conductance to very small values; (2) universal conductance fluctuations (in ballistic propagation) of order 2${\mathit{e}}^{2}$/h (which are characteristic of disordered systems); (3) approximate periodicity of the conductance as a function of geometrical parameters, in agreement with a recent experiment. In the two-slit configuration, the structure of both the conductance and the intensity is not similar to the optical Young interference pattern (due to the presence of reflecting walls on all sides) and, quite surprisingly, may show a minimum at the center of the waveguide.