Effects of disorder on modulated quantum Hall systems

The Hall conductivity and the localization length are calculated for weakly modulated two-dimensional systems within the lowest Landau level approximation. We find that the fractal character of the Hofstadter butterfly is reflected on the coincidence in the localization and the Hall conductivity among a series of fluxes φ+2n with integers n.     

Evidence for Anderson localisation in Landau level tails from the analysis of two-dimensional Shubnikov—de Haas conductivity minima

The amplitudes of the Shubnikov—de Haas conductivity minima are analysed for n-type inversion layers in Si 〈100〉 MOS devices. Thermal excitation between adjacent Landau levels, conduction through extended tail states and activated conduction from localised tail states are all detected in different magnetic field and temperature ranges. The minimum metallic conductivity found for the lowest spin extremum agrees well with theory but the values for higher Landau levels are lower than expected.     

Evolution of individual quantum Hall edge states in the presence of disorder

By using the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As demonstrated by the two-parameter renormalization group flow of the Hall and Thouless conductances, quantum Hall edge states with high Chern number n are completely different from that of the n = 1 case. Two categories of individual edge modes are evaluated in a quantum Hall system with high Chern number. Edge states from the lowest Landau level have similar eigenfunctions that are well localized at the system edge and independent of the Fermi energy. On the other hand, at fixed Fermi energy, the edge state from higher Landau levels exhibit larger expansion, which results in less stable quantum Hall states at high Fermi energies. By presenting the local current density distribution, the effect of disorder on eigenmode-resolved edge states is distinctly demonstrated.     

Density of states for high landau levels and random potential

The density of states of a two-dimensional, non-interacting electron gas under the influence of a strong perpendicular magnetic field and random impurities is examined. In the strong magnetic field the ensemble averaged Green's function can be restricted to a single Landau leveln. Using 1/n as expansion parameter we calculate first order corrections. The results for two models of disorder are compared: white-noise potential and uniformly distributed zero-range scatterers with a Lorentzian distribution of strength.     

Separable interactions and liquid 3He: II. Extrema of Landau expansion and phase diagram in the weak-coupling limit

In a previous paper we derived a Landau expansion starting from an exactly solvable model for a system of fermions with an l = 1 pairing interaction in the presence of a magnetic field. The Landau expansion, which can be used to study the phases of liquid ³He, is a complicated function of 9 complex variables, in which it is not obvious a priori that the field dependence of the coefficients of the fourth-order terms can be neglected. In the present paper the extrema of the Landau expansion are analyzed in some detail with the weak-coupling values of the coefficients. The absolute minimum of the Landau expansion can be found by minimizing a three-parameter function Φ_BW, the minimalization of which leads to three possible phases, the A1-phase, the ABM-phase (or two-dimensional 2D-phase) and the proper generalization of the BW-phase in the presence of a magnetic field. The phase diagram is compared with the one given by Ambegaokar and Mermin.     

Landau levels in a novel two-dimensional electron system interacting with charged quantum dots

Landau levels have been theoretically investigated in a two-dimensional electron gas near a quantum dot (QD) layer. By a diagrammatical method, we have formulated the self-energy for the Landau level and deduced its relation to the AC conductivity σ_loc(ω) in the QD layer. As an example, we have examined the density of states in the case where σ_loc(ω) is described by Aω^S(S=0.8). It is found that the Landau levels are broadened due to the interaction with the localized electrons in the QDs.     

Far-infrared laser oscillation due to cyclotron emission in p-type germanium

Far-infrared laser oscillation due to cyclotron emission in the light hole band of p-type germanium was observed under crossed electric and magnetic fields. The wavelength is inversely proportional to magnetic fields with a cyclotron mass ofm _c =0.048m _c . Numerical calculations based on Luttinger Hamiltonian show that mixing of wavefunctions between the light and heavy hole bands causes population inversion betweenn=0 andn=1 light-hole Landau levels. It is also shown that non-equidistant energy spacing of light-hole Landau levels is essential to yield net amplification.     

Magneto-absorption in CdS

We have investigated the 2°K absorption spectra of CdS between 4700 Å and 4860 Å for magnetic fields up to 100 kG. We find that excitonic effects are important for the two lowest Landau levels but not for the third or higher Landau levels. The most interesting feature of the data is that the higher excited states (n ? 3) of the exciton are associated with the two lowest Landau levels. These results are discussed and compared with those in other materials. A reduced effective mass of 0.18m₀ has been deduced.     

Magneto-optics of monolayer and bilayer graphene

The optical conductivity of graphene and bilayer graphene in quantizing magnetic fields is studied. Both dynamical conductivities, longitudinal and Hall’s, are analytically evaluated. The conductivity peaks are explained in terms of electron transitions. Correspondences between the transition frequencies and the magneto-optical features are established using the theoretical results. The main optical transitions obey the selection rule Δn = 1 with the Landau number n. The Faraday rotation and light transmission in the quantizing magnetic fields are calculated. The effects of temperatures and magnetic fields on the chemical potential are considered.     

Shubnikov-de Haas oscillations in n-channel silicon 〈100〉 MOSFETS in magnetic fields up to 35 T

Shubnikov-de Haas oscillations have been studied in n-channel silicon 〈100〉 MOSFETS in magnetic fields up to 35 T. At high magnetic fields the shape of the conductivity peaks becomes asymmetric and the conductivity from whole regions of the Landau level spectrum is suppressed by the magnetic field. The asymmetry is thought to arise from the low effective density of scatterers which occurs for high magnetic fields, as predicted by Ando. These effects may also be related to the presence of phenomena such as Wigner crystallisation or Anderson localisation.     

Interband resonant tunneling in superconductor heterostructures in a quantizing magnetic field

The resonant tunneling of electrons through quasistationary levels in the valence band of a quantum well in double-barrier structures based on III–V materials with type-II heterojunctions is considered in a quantizing magnetic field directed perpendicularly to the interfaces. The transmission coefficients of the tunnel structure for transitions from states corresponding to different Landau levels are calculated using the Kane model. It is shown that transitions with a unit change in the Landau level index n as a result of mixing of the wave functions of states with opposite spin orientations are possible on the interfaces due to spin-orbit coupling. The probability of such transitions can be comparable to the probability of transitions without a change in the Landau level index for InAs/AlGaSb/GaSb resonant-tunneling structures. Fiz. Tverd. Tela (St. Petersburg) 40, 2121–2126 (November 1998)     

The stability of the fractional quantum Hall effect in topological insulators

With the recent observation of graphene-like Landau levels at the surface of topological insulators, the possibility of fractional quantum Hall effect, which is a fundamental signature of strong correlations, has become of interest. Some experiments have reported intra-Landau level structure that is suggestive of fractional quantum Hall effect. This paper discusses the feasibility of fractional quantum Hall effect from a theoretical perspective, and argues that while this effect should occur, ideally, in the n=0 and |n|=1 Landau levels, it is ruled out in higher |n| Landau levels. Unlike graphene, the fractional quantum Hall effect in topological insulators is predicted to show an interesting asymmetry between n=1 and n=−1 Landau levels due to spin-orbit coupling.     

Resonant tunneling transport through GaAs/AlGaAs superlattices in strong tilted magnetic field

An analysis is presented of the transverse resonant tunneling transport through GaAs/AlGaAs superlattices due to tunneling between Landau levels in quantum wells in a strong tilted magnetic field. A high tunneling rate is demonstrated between Landau levels with Δn ≠ 0 in a magnetic field with a nonzero in-plane component. This leads to substantial broadening and shift of the tunneling resonance and significant changes in the current-voltage characteristics of superlattices. The predicted behavior of the current-voltage characteristics of superlattices in tilted magnetic fields is demonstrated experimentally.     

Conductivity of 2D multi-component electron gas partially-quantized by magnetic field

The 2D semimetal consisting of heavy holes and light electrons is studied. The consideration is based on the assumption that electrons are quantized by magnetic field while holes remain classical. We assume also that the interaction between components is weak and the conversion between components is absent. The kinetic equation for holes colliding with quantized electrons is utilized. It has been stated that the inter-component friction and corresponding correction to the dissipative conductivity σ _xx do not vanish at zero temperature due to degeneracy of the Landau levels. This correction arises when the Fermi level crosses the Landau level. The statement will keep in force until the degeneracy remains. The limits of kinetic equation applicability were found. We also study the situation of kinetic memory when particles repeatedly return to their meeting points.     

Influence of excited Landau levels on a two-dimensional electron-hole system in a strong perpendicular magnetic field

The study of the quantum states of a two-dimensional electron-hole system in a strong perpendicular magnetic field is carried out with special attention to the influence of virtual quantum transitions of interacting particles between the Landau levels. These virtual quantum transitions from the lowest Landau levels to excited Landau levels with arbitrary quantum numbers n and m and their reversion to the lowest Landau levels in second order perturbation theory result in an indirect attraction between the particles. The influence of the indirect interaction on the magnetoexciton ground state, on the chemical potential of the Bose-Einstein condensed magnetoexcitons, and on the ground state energy of the metallic-type electron-hole liquid is investigated in the Hartree-Fock approximation. The coexistence of different phases is suggested.     

Strongly anisotropic electronic transport in higher Landau levels

Low-temperature, electronic transport in higher Landau levels (N>1) in a two-dimensional electron system is strongly anisotropic. At half-filling of either spin level of such Landau levels ( etc.) the magnetoresistance either collapses to form a deep minimum or is peaked in a sharp maximum, depending on the in-plane current direction. The anisotropic axis can be reoriented by applying an in-plane magnetic field of 1–2 T strength. The magnetoresistance at and (N=1) is initially isotropic but an in-plane field induces a strong anisotropy. Our observations are strong evidence for a new many-electron phase in higher Landau levels, which forms spontaneously or can be induced by an in-plane field.     

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.     

Density–driven superfluid transition of the constrained bosons on a lattice

We formulate the Landau theory and study its consequences for lattice bosons, which are stabilized by a three-body on-site constraint. This is relevant for experiments with cold atoms in optical lattices, where the presence of three-body dissipative loss processes renders the occupation number n for bosons on short timescales effectively constrained to $n\le 2$. We elaborate on the Landau free energy expansion resulting from the Hamiltonian of bosons in the restricted Hilbert space, and present the phase diagram of the constrained Bose lattice gas.     

Quantum magneto-optics of the graphite family

The optical conductivity of graphene, bilayer graphene, and graphite in quantizing magnetic fields is studied. Both dynamical conductivities, longitudinal and Hall’s, are evaluated analytically. The conductivity peaks are explained in terms of electron transitions. Correspondences between the transition frequencies and the magneto-optical features are established using the theoretical results. We show that trigonal warping can be considered within the perturbation theory for strong magnetic fields larger than 1 T. The semiclassical approach is applied for weak fields when the Fermi energy is much larger than the cyclotron frequency. The main optical transitions obey the selection rule with Δn = 1 for the Landau number n, but the Δn = 2 transitions due to the trigonal warping are also possible. The Faraday/Kerr rotation and light transmission/reflection in quantizing magnetic fields are calculated. Parameters of the Slonczewski-Weiss-McClure model are used in the fit taking the previous de Haas-van Alphen measurements into account and correcting some of them in the case of strong magnetic fields.     

Free energy and structural phase transitions in mixed crystals: A microscopic derivation

We consider mixed crystals of the form(MY) _x (MX) _1–x , whereY is an active component which drives a structural phase transition, while the componentX has no active internal degree of freedom. We describe this system by a compressible Ising model, including the dilution of the spinsY and the elastic strain fields caused by the componentX. We derive a Landau expansion of the free energy for this system, within molecular field theory. The coefficients of this expansion depend on temperature, pressure, spin concentrationx and the strain fields. This simple model exhibits a rich phase diagram. At sufficiently high concentrationsx, the phase transition is first order. Decreasingx, the transition passes through a tricritical point and eventually becomes second order. For lowx or high strain fields, no transition occurs.