Zener tunneling between the landau levels in quasi-two-dimensional electronic Corbino disks at large filling factors

The magnetotransport characteristics of quasi-two-dimensional electronic Corbino disks based on a wide GaAs quantum well with two filled subbands of size quantization are studied. At low temperatures and high magnetic fields, the Corbino disks exhibit the oscillations of differential conductivity, which are periodic with respect to dc electric field E _dc. It is shown that the observed oscillations are related to the Zener tunneling induced by E _dc. The tunneling occurs between the filled and empty Landau levels under conditions corresponding to the absence of the Hall field.     

Cyclotron-resonance harmonics in the ac response of a 2D electron gas with smooth disorder

The frequency-dependent conductivity sigma(xx)(omega) of 2D electrons subjected to a transverse magnetic field and smooth disorder is calculated. The interplay of Landau quantization and disorder scattering gives rise to an oscillatory structure that survives in the high-temperature limit. The relation to recent experiments on photoconductivity by Zudov et al. and Mani et al. is discussed.     

Theory of the transverse static magnetoconductivity in a two-dimensional electron-phonon system

The theory of the transverse static magnetoconductivity (σ_xx) in a two-dimensional system under the simultaneous influence of electron-phonon and electron-impurity interactions is presented. The memory function technique is employed to obtain explicit expression for σ_xx under conditions appropriate for typical Shubnikov-deHaas measurements. It is shown that σ_xx involves two different effective masses and scattering times, of which one is the scattering time in the absence of the magnetic field. In addition, the Landau level width appears in σ_xx, thus providing an experimental means for extracting the same from a study of the background conductivity.     

Giant quantum oscillations of the skin layer in semimetals

We study theoretically the effect of electron energy quantization in a magnetic field on the penetration of radio waves into a semimetal in a geometry in which a constant magnetic field H is directed along the trigonal axis of a crystal. In this geometry, strong magnetic Landau damping in semimetals prevents wave propagation and is responsible for the skin effect. It is shown that quantization of the transverse energy of electrons considerably influences the effectiveness of collisionless absorption of the wave. As a result, the magnetic Landau damping and the skin depth experience giant oscillations upon a change in magnetic field H.     

The c-axis fluctuation conductivity in layered superconductors in a strong electric field under a magnetic field

The effect of a high electric field on the c-axis fluctuation conductivity in layered superconductors near the superconducting transition is investigated by the time-dependent Ginzburg-Landau equation. The c-axis fluctuation conductivity is calculated in self-consistent Gaussian approximation for an arbitrarily strong electric field and a magnetic field perpendicular to the layers. Our results include all Landau levels and have refined analytical form. The results in linear response are in good agreement with the experimental data in a wide region around T _c in high T _c superconductor. We also show that high electric fields can be effectively used to suppress the c-axis fluctuation conductivity in high-temperature superconductors.     

Sliding Abrikosov lattice in a superconductor with a regular array of artificial pinning centers: AC conductivity and criticality at small frequencies

Dynamics of the flux lattice in the mixed state of strongly type-II superconductor near the upper critical field subjected to AC field and interacting with a periodic array of short range pinning centers is considered. The superconductor in a magnetic field in the absence of thermal fluctuations on is described by the time-dependent Ginzburg–Landau equations. For a special case of the δ-function shaped pinning centers and for pinning array commensurate with the Abrikosov lattice (so that vortices outnumber pinning centers) an analytic expression or the AC conductivity is obtained. It is found that below a certain critical pinning strength and for sufficiently low frequencies there exists a sliding Abrikosov lattice, which vibrates nearly uniformly despite interactions with the pinning centers. At very small frequencies the conductivity diverges at the critical pinning strength.     

Landau Levels on a Torus

Landau levels have represented a very rich field of research, which has gained widespread attention after their application to the quantum Hall effect. In a particular gauge, the holomorphic gauge, they give a physical implementation of Bargmann's Hilbert space of entire functions. They have also been recognized as a natural bridge between Feynman's path integral and geometric quantization. We discuss here some mathematical subtleties involved in the formulation of the problem when one tries to study quantum mechanics on a finite strip of sides L₁, L₂ with a uniform magnetic field and periodic boundary conditions. There is an apparent paradox here: infinitesimal translations should be associated to canonical operators [þ_x, þ_y] iB, and, at the same time, live in a Landau level of finite dimension BL₁L₂/(hc/e), which is impossible from Wintner's theorem. The paper shows the way out of this conundrum.     

Nonequilibrium Green's Function Approach to Resonant Magnetotunneling Through a Quantum Dot

Keldysh's nonequilibrium Green's function is applied to studying resonant magnetotunneling through a quantum dot. We propose a microscopic Anderson-impurity-like Hamiltonian in which two kinds of the on-site Coulomb interactions are introduced:the interaction of two electrons at the same Landau level with different spins, U₁ and the interaction for the electrons between different Landau levels, U₁. I-V curves are obtained under different magnetic fields in asymmetrical structures which can display both the energy quantization and singleelectron charging effect. The theoretical results are in good agreement with the experiments qualitatively. The linear-response conductance is also discussed.     

On the current compensation in the integer quantum Hall effect

A system of independent electrons in a random potential on the surface of a finite cylinder is considered in the presence of a perpendicular magnetic field. It is shown that the spectral stability condition which essentially asserts that the range of variation of the electrostatic energy in an external electric field is independent of disorder, and which is sufficient to prove the integer quantization of the Hall conductivity is also sufficient to prove the exact compensation of current loss brought about by bound states by current gain in extended states for completely filled Landau bands. Furthermore, the spectral stability condition is shown to be both sufficient and necessary to prove Levinson's theorem which was used by some authors to demonstrate compensation.     

Quantum galvanomagnetic properties of n-type inversion layers on Si(100) MOSFET

Transverse magnetoconductivity σ_xx and Hall effect in n-type inversion layers of Si(100) MOSFET are measured for various source-drain fields between 0.08 and 40 V/cm under magnetic fields up to 150 kOe at 1.4 K. Conductivity peaks in low Landau levels are in good agreement with theory. Effect of the source-drain field in the magnetoconductivity is found to be very important in higher Landau levels as well as in the appearance of the lowest Landau level peak. Immobile electrons are clearly observed in conductivity bottoms. Electrode geometry effect for Hall effect measurement under strong magnetic fields is discussed.     

Clear experimental evidence for boundary and impurity scattering related crossover field scales in GaAs/AlGaAs split-gate wires

We study the magnetic field dependence of the correlation field ΔB_cand amplitude δgof the conductance fluctuations, observed in the low temperature magnetoresistance of GaAs/AlGaAs split-gate wires. Near zero field, universality of quantum interference is retained and the magnetoresistance shows universal conductance fluctuations. At high magnetic fields, although the discrete Landau level quantization becomes resolved. ΔB_cand δgare found to increase linearly with magnetic field, with a slope which depends upon the nature of electron scatterings in the wire.     

Magneto-dimensional resonance. Pseudospin phase and hidden quantum number

The Schrödinger operator for a spinless charge inside a layer with parabolic confinement profile and homogeneous magnetic field is considered. The Lorentz (cyclotron) and the confinement frequencies are assumed to be equal to each other. After inclination of the layer normal from the magnetic field direction there appears a pseudospin su(2)-field removing the resonance degeneracy of Landau levels. Under deviations of the layer surface from the plane shape, a longitudinal geometric current is created. In circulations around surface warping, there is a nontrivial quantum phase transition generated by an element of the π₁-homotopy group and a hidden degree of freedom (spectral degeneracy) associated with a “charge” of geometric poles on the layer. The quantization rule contains an additional parity index related to the algebraic number of geometric poles and the Landau level number. The resonance pseudospin phase-shift represents an example of general Aharonov–Bohm type topologic phenomena in quantum (semiclassical or adiabatic) systems with delta-function singularities in symplectic structure.     

Effect of a transverse electric field on the Landau bands in a Weyl semimetal

The Landau bands in crossed magnetic and electric fields are studied for the case of a Weyl semimetal. The expression for the energy spectrum of such a system is obtained using an approach based on the Lorentz shift. It is shown that the electric field leads to a substantial transformation of the Landau bands. At the electric field equal to v_F H/c, the collapse of the Landau levels occurs and the motion becomes completely linear. Under this condition, the wavefunction is nonzero only for the states with p _z = 0. This significantly affects the phenomena related to the unusual surface states, which are characteristic of such materials.     

Hofstadter butterfly and integer quantum hall effect in three dimensions

For a three-dimensional (3D) lattice in magnetic fields we have shown that the hopping along the third direction, which normally smears out the Landau quantization gaps, can rather give rise to a Hofstadter's butterfly specific to 3D when a criterion is fulfilled by anisotropic (quasi-one-dimensional) systems. In 3D the angle of the magnetic field plays the role of the field intensity in 2D, so that the butterfly can occur in much smaller fields. We have also calculated the Hall conductivity in terms of the topological invariant in the Kohmoto-Halperin-Wu formula, and each of sigma(xy),sigma(zx) is found to be quantized.     

Magnetic Bloch states and Hall conductivity of a two-dimensional electron gas in a periodic potential without inversion center

Quantum states of 2D electrons are studied in a periodic potential without inversion center in the presence of a magnetic field. It is shown that the energy spectrum in magnetic subbands is not symmetric about the center of magnetic Brillouin zone E(k)≠E(?k). Singularities (phase branching points) of the electron wave function, which determine the quantization law of Hall conductivity σ_xy, are studied in the k space. It is found that a sharp change takes place in the number of points in the magnetic Brillouin zone and in the corresponding values of topological invariants determining the Hall conductivity of filled subbands. It is noted that the longitudinal conductivity of a lattice without inversion center placed in a magnetic field is not invariant with respect to a change in sign of the electric field, and a photovoltaic effect must arise in an ac electromagnetic field.     

Magnetic bloch states and carrier transport in two-dimensional semiconductor lattice structures with spin-orbit interaction

Quantization rules have been obtained for the Hall conductance of fully occupied Landau subbands of the two-dimensional electron gas with the Dresselhaus spin-orbit interaction in a periodic electrostatic field of a superlattice and a transverse magnetic field. The spin-orbit interaction mixes states of different magnetic subbands and changes the quantization rule for the Hall conductance compared to spinless particles. The calculations have been performed for the two-dimensional electrons in the structures with both a weak (AlGaAs/GaAs) and sufficiently strong (GaAs/In_0.23Ga_0.77As) spin-orbit interaction and Zeeman splitting. It has been found that the distribution of the Hall conductance among the magnetic subbands depends on the geometric parameters of the superlattices and promptly changes upon the touching of the adjacent subbands in the spectrum. The quantization rule for the Hall conductance in real semiconductor structures with relatively strong spin-orbit interaction has been shown to differ from that calculated by Thouless et al. [Phys. Rev. Lett. 49, 405 (1982)] for the systems without the spin-orbit interaction and Zeeman effect.     

Landau quantization for an induced electric dipole in the presence of topological defects

In this contribution we investigate the non-relativistic quantum dynamics of induced electric dipoles in the presence of a topological defect. We propose an analog of Landau quantization for neutral atoms, where a electric dipole is induced by the electromagnetic field configuration. We investigate this system in the presence of a topological defect and show that it breaks the infinite degeneracy of Landau levels.     

Nonlocal surface plasmon spectrum in quantizing magnetic field: Surface Bernstein mode branch (n=2)

The nonlocal surface plasmon spectrum in a quantizing magnetic field perpendicular to the surface has been found to have branches analogous to ‘Bernstein’ modes near multiples of the cyclotron frequency. The n=2 nonlocal surface ‘Bernstein’ mode is evaluated for low wavenumber, incorporating Landau quantization effects for degenerate and nondegenerate cases.     

Localization and the integer-quantized Hall effect: Diffusion constant for high Landau levels and white noise potential

The diffusion constant and the diagonal conductivity for non-interacting electrons in a two-dimensional, disordered system are studied. A homogeneous magnetic field perpendicular to the electron system is assumed. For weak short-range random potentials and high fields the Landau quantum numbern can be used as expansion parameter. In the limit of high Landau levels the system shows metallic behaviour. Corrections for finiten decrease the conductivity and indicate localized states in the whole energy band. A breakdown of the expansion and stronger localization are observed only for the lowest Landau levels if the typical experimental length scale of the quantized Hall effect is used.     

Influence of magnetic quantization on the debye screening length in degenerate semiconductors having parabolic energy bands

The Debye screening length in degenerate semiconductors having parabolic energy bands is shown for the first time to have an oscillatory dependence on magnetic field under the influence of Landau quantization when the higher lying sub-bands are occupied.The authors are indebted to Professor J. N.Bhar for his keen interest in the work.