Pseudospin soliton in the nu=1 bilayer quantum Hall state

We investigate a domain structure of pseudospins, a soliton lattice in the bilayer quantum Hall state at total Landau level filling factor nu = 1, in a tilted magnetic field, where the pseudospin represents the layer degree of freedom. An anomalous peak in the magnetoresistance Rxx appears at the transition point between the commensurate and incommensurate phases. The Rxx at the peak is highly anisotropic for the angle between the in-plain magnetic field B parallel and the current, and indicates a formation of the soliton lattice aligned parallel to B parallel. The temperature dependence of the Rxx peak reveals that the dissipation is caused by thermal fluctuations of pseudospin solitons. We also study a phase diagram of the bilayer nu = 1 system, and the effects of density imbalance between the two layers.     

Particle-hole symmetry and the Pfaffian state

We show that the particle-hole conjugate of the Pfaffian state-or "anti-Pfaffian" state-is in a different universality class from the Pfaffian state, with different topological order. The two states can be distinguished easily by their edge physics: their edges differ in both their thermal Hall conductance and their tunneling exponents. At the same time, the two states are exactly degenerate in energy for a nu=5/2 quantum Hall system in the idealized limit of zero Landau level mixing. Thus, both are good candidates for the observed sigma_{xy}=5/2(e;{2}/h) quantum Hall plateau.     

Signatures of non-Abelian statistics in nonlinear Coulomb blockade transport

Signatures of the non-Abelian statistics of quasiparticles in the ν=5/2 quantum Hall state are predicted to be present in the current-voltage characteristics of tunneling through one or two quantum Hall puddles of Landau filling ν(a) embedded in a bulk of filling ν(b) with (ν(a),ν(b))=(2,5/2) and (ν(a),ν(b))=(5/2,2).     

Transition from an electron solid to the sequence of fractional quantum Hall states at very low Landau level filling factor

At low Landau level filling of a two-dimensional electron system, typically associated with the formation of an electron crystal, we observe local minima in Rxx at filling factors nu = 2/11, 3/17, 3/19, 2/13, 1/7, 2/15, 2/17, and 1/9. Each of these developing fractional quantum Hall (FQHE) states appears only above a filling-factor-specific temperature. This can be interpreted as the melting of an electron crystal and subsequent FQHE liquid formation. The observed sequence of FQHE states follows the series of composite fermion states emanating from nu = 1/6 and nu = 1/8.     

Effect of Landau level mixing on braiding statistics

We examine the effect of Landau level mixing on the braiding statistics of quasiparticles of Abelian and non-Abelian quantum Hall states. While path dependent geometric phases can perturb the Abelian part of the statistics, we find that the non-Abelian properties remain unchanged to an accuracy that is exponentially small in the distance between quasiparticles.     

Influence of interactions on flux and back-gate period of quantum Hall interferometers

In quantum Hall systems with two narrow constrictions, tunneling between opposite edges can give rise to quantum interference and Aharonov-Bohm-like oscillations of the conductance. When there is an integer quantized Hall state within the constrictions, a region between them, with higher electron density, may form a compressible island. Electron tunneling through this island can lead to residual transport, modulated by Coulomb-blockade-type effects. We find that the coupling between the fully occupied lower Landau levels and the higher-partially occupied level gives rise to flux subperiods smaller than one flux quantum. We generalize this scenario to other geometries and to fractional quantum Hall systems, and compare our predictions to experiments.     

Non-Abelian Chern-Simons particles in an external magnetic field

The quantum mechanics and thermodynamics of SU(2) non-Abelian Chern-Simons particles (non-Abelian anyons) in an external magnetic field are addressed. We derive the N-body Hamiltonian in the (anti-) holomorphic gauge when the Hilbert space is projected onto the lowest Landau level of the magnetic field. In the presence of an additional harmonic potential, the N-body spectrum depends linearly on the coupling (statistics) parameter. We calculate the second virial coefficient and find that in the strong magnetic field limit it develops a step-wise behavior as a function of the statistics parameter, in contrast to the linear dependence in the case of Abelian anyons. For small enough values of the statistics parameter we relate the N-body partition functions in the lowest Landau level to these of SU(2) bosons and find that the cluster (and virial) coefficients dependence on the statistics parameter cancels.     

Correlated tunneling and the instability of the fractional quantum Hall edge

We consider a class of interaction terms that describes correlated tunneling of composite fermions between effective Landau levels. Despite being generic and of similar strength to that of the usual density-density couplings, these terms are not included in the accepted theory of the edges of fractional quantum Hall systems. Here we show that they may lead to an instability of the edge towards a new reconstructed state with additional channels, and thereby demonstrate the incompleteness of the traditional edge theory.     

Transition from Abelian to non-Abelian FQHE states

We study the transition from the Abelian multi-component (3, 3, 1) quantum Hall state to the non-Abelian one component Pfaffian state in bilayer two dimensional electron systems. We show that tunneling between layers can induce this transition. At the transition points part of the degrees of freedom that describe the (3, 3, 1) state disappear from the spectrum, and the system is correctly described by the Pfaffian state, with quasi-particles that satisfy non-Abelian statistics. The mechanism described in this work provides for a physical Hamiltonian interpretation of the algebraic projection from the (3, 3, 1) to the Pfaffian state that has been discussed in the literature. Received 12 September 2000     

Acoustic properties of amorphous silica between 1 and 500 mK

We have made reliable measurements of the sound velocity delta v/v(0) and internal friction Q(-1) in vitreous silica at 1.03, 3.74, and 14.0 kHz between 1 mK and 0.5 K. In contrast with earlier studies that did not span as wide a temperature and frequency range, our measurements of Q(-1) reveal a crossover (as T decreases) only near 10 mK from the T(3) dependence predicted by the standard tunneling model to a T dependence predicted if interactions are accounted for. We find good fits at all frequencies using a single interaction parameter, the prefactor of the interaction-driven relaxation rate, in contrast to earlier claims of a frequency dependent power law. We also show that the discrepancy in the slopes d(delta v/v(0))/d(log(10)T) below and above the sound velocity maximum (1: -1 observed, 1: -2 predicted) can be resolved by assuming a modified distribution of tunneling states.     

Carrier kinetics and population inversion in Landau level system in cascade GaAs/AlGaAs quantum well structures

The carrier distribution over Landau levels was studied in resonant tunneling GaAs/AlGaAs quantum well structures under tunneling pumping of the upper subband. The numerical calculations of the Landau levels population for various values of pumping intensity (tunneling time), magnetic field and the structure doping were carried out. The effect of various scattering mechanisms, as two-electron (electron–electron scattering) as single-electron (acoustic phonon and interface roughness scattering) ones on level population was studied. The population inversion between the zeroth Landau level of the upper subband and the first Landau level of the lowest subband was shown to exist in wide range of the magnetic field strength thus providing the possibility of wide range tunable stimulated terahertz emission.     

Carrier dynamics and stimulated radiative terahertz transitions between Landau levels in cascade GaAs/AlGaAs quantum well structures

The carrier distribution over Landau levels was studied in resonant tunneling GaAs/AlGaAs quantum well structures under tunneling pumping of the upper subband. The numerical calculations of the Landau level populations for various values of pumping intensity (tunneling time), magnetic field and structure doping were carried out. The population inversion between zeroth Landau level of the upper subband and the first Landau level of the lowest subband was shown to exist in wide range of the magnetic field strength. The effect of various scattering mechanisms, both two-particle (electron-electron scattering) and single-particle (acoustic phonon and interface roughness scattering) ones, on level population was studied. The way of lifting the selection rule forbidding the inter-Landau level terahertz transitions of interest and achieving considerable values of the dipole matrix element is proposed.     

Magneto-optical studies of ballistic electron transport in single barrier heterostructures

We report an investigation of ballistic electron transport in GaAs/AlGaAs p-i-n single barrier structures with magnetic fields of up to 14T applied parallel to the tunneling direction (B//z). The energy distribution and relaxation processes of the non-equilibrium electron population injected into the p-doped collector from the Landau levels of the emitter accumulation layer are studied by means of electroluminescence (EL) spectroscopy. The observation of emitter Landau level structure in the ballistic electron EL spectra shows that the 2D to 3D tunneling process is elastic. In addition to the ballistic electron EL, cross-barrier recombination between the electron and hole accumulation layers is observed. This allows a precise determination of the initial energy distribution of the injected electrons.     

Virial coefficients of non-abelian anyons

We study a system of non-Abelian anyons in the lowest Landau level of a strong magnetic field. Using diagrammatic techniques, we prove that the virial coefficients do not depend on the statistics parameter. This is true for all representations of all non-Abelian groups for the statistics of the particles and relies solely on the fact that the effective statistical interaction is a traceless operator.     

Gauge fields, geometric phases, and quantum adiabatic pumps

Quantum adiabatic pumping of charge and spin between two reservoirs (leads) has recently been demonstrated in nanoscale electronic devices. Pumping occurs when system parameters are varied in a cyclic manner and sufficiently slowly that the quantum system always remains in its ground state. We show that quantum pumping has a natural geometric representation in terms of gauge fields (both Abelian and non-Abelian) defined on the space of system parameters. Tunneling from a scanning tunneling microscope tip through a magnetic atom could be used to demonstrate the non-Abelian character of the gauge field.     

Coulomb drag as a probe of the nature of compressible States in a magnetic field

Magnetodrag reveals the nature of compressible states and the underlying interplay of disorder and interactions. At nu=3/2 clear T(4/3) dependence is observed, which signifies the metallic nature of the N=0 Landau level. In contrast, drag in higher Landau levels reveals an additional contribution, which anomalously grows with decreasing T before turning to zero following a thermal activation law. The anomalous drag is discussed in terms of electron-hole asymmetry arising from disorder and localization, and the crossover to normal drag at high fields as due to screening of disorder.     

Electrically controlled nuclear spin polarization and relaxation by quantum-Hall states

We study interactions between electrons and nuclear spins by using the resistance ( Rxx) peak which develops near the Landau-level filling factor nu = 2/3 as a probe. Temporarily tuning nu to a different value, nu(temp), with a gate demonstrates that the Rxx peak regenerates even after complete depletion ( nu(temp) = 0), while it rapidly relaxes on either side of nu(temp) = 1. This indicates that the nu = 2/3 domain morphology is memorized by the nuclear spins which can be rapidly depolarized by Skyrmions. An additional enhancement in the nuclear spin relaxation around nu = 1/2 and 3/2 suggests a Fermi sea of partially polarized composite fermions.     

Universal and measurable entanglement entropy in the spin-boson model

We study the entanglement between a qubit and its environment from the spin-boson model with Ohmic dissipation. Through a mapping to the anisotropic Kondo model, we derive the entropy of entanglement of the spin E(alpha,Delta,h), where alpha is the dissipation strength, Delta is the tunneling amplitude between qubit states, and h is the level asymmetry. For 1-alpha>Delta/omegac and (Delta,h)TK, E vanishes as (TK/h)2-2alpha, up to a logarithmic correction. For a given h, the maximum entanglement occurs at a value of alpha which lies in the crossover regime h approximately TK. We emphasize the possibility of measuring this entanglement using charge qubits subject to electromagnetic noise.     

Incompressible paired hall state, stripe order, and the composite fermion liquid phase in half-filled landau levels

We consider the two lowest Landau levels at half filling. In the higher Landau level (nu = 5/2), we find a first-order phase transition separating a compressible striped phase from a paired quantum Hall state, which is identified as the Moore-Read state. The critical point is very near the Coulomb potential and the transition can be driven by increasing the width of the electron layer. We find a much weaker transition (either second-order or a crossover) from pairing to the composite fermion Fermi-liquid behavior. A very similar picture is obtained for the lowest Landau level, but the transition point is not near the Coulomb potential.     

Spatial fluctuations of the density of states in magnetic fields observed with scanning tunneling spectroscopy

Scanning tunneling spectroscopy images on n-InAs(110) exhibit a strong magnetic field dependent contrast on the 50 nm length scale, indicating fluctuations in the density of states of the sample. The contrast is correlated to previously observed Landau oscillations in dI/dV curves. Its origin is a spatial fluctuation of the Landau level energy of 3-4 meV caused by the inhomogeneous distribution of dopant atoms. Besides inducing large-scale fluctuations in the density of states, dopants preserve their ability to scatter electron waves. The resulting wave pattern is found to depend on the magnetic field. It is suggested that the dependence is guided by the condensation of the electronic states on Landau tubes.