Relaxation time of a chiral quantum R-L circuit

We report on the GHz complex admittance of a chiral one-dimensional ballistic conductor formed by edge states in the quantum Hall regime. The circuit consists of a wide Hall bar (the inductor L) in series with a tunable resistor (R) formed by a quantum point contact. Electron interactions between edges are screened by a pair of side gates. Conductance steps are observed on both real and imaginary parts of the admittance. Remarkably, the phase of the admittance is transmission independent. This shows that the relaxation time of a chiral R -L circuit is resistance independent. A current and charge conserving scattering theory is presented that accounts for this observation with a relaxation time given by the electronic transit time in the circuit.     

From magnetically doped topological insulator to the quantum anomalous Hall effect

Quantum Hall effect （QHE）, as a class of quantum phenomena that occur in macroscopic scale, is one of the most important topics in condensed matter physics. It has long been expected that QHE may occur without Landau levels so that neither external magnetic field nor high sample mobility is required for its study and application, Such a QHE free of Landau levels, can appear in topological insulators （TIs） with ferromagnetism as the quantized version of the anomalous Hall effect, i.e., quantum anomalous Hall （QAH） effect. Here we review our recent work on experimental realization of the QAH effect in magnetically doped TIs. With molecular beam epitaxy, we prepare thin films of Cr-doped （Bi,Sb）2Te3 TIs with well- controlled chemical potential and long-range ferromagnetic order that can survive the insulating phase. In such thin films, we eventually observed the quantization of the Hall resistance at h/e2 at zero field, accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect provides a foundation for many other novel quantum phenomena predicted in TIs, and opens a route to practical applications of quantum Hall physics in low-power-consumption electronics.     

Multiple phases with the same quantized Hall conductance in a two-subband system

In a two-dimensional electron system with two occupied subbands, the experimentally determined phase diagram in the density-magnetic field plane exhibits rich topological features. Ringlike structures are observed at even integer filling factors in the phase diagram. Even with the identical quantized Hall resistance values as those given by the ordinary integer quantum Hall effect due to the Landau level quantization, the activation energies of these states within the rings are much smaller. These ring structures cannot be accounted for by the simple single particle picture. We argue that ferromagnetic quantum Hall states, due to the interaction of two energy levels with opposite spin and different subband indices, are responsible for these unusual structures.     

Fractional quantization of Hall resistance as a consequence of mesoscopic feedback

A nonlinear single-particle model is introduced, which captures the characteristic of systems in the quantum Hall regime. The model involves the magnetic Schrödinger equation with spatially variable magnetic flux density. The distribution of flux is prescribed via the postulates of the mesoscopic mechanics (MeM) introduced in my previous articles (cf. [9, 10]). The model is found to imply exact integer and fractional quantitzation of the Hall conductance. In fact, Hall resistance is found to be R _H = (h/e ²)(M/N) at the filling factor value N/M. The assumed geometry of the Hall plate is rectangular. Special properties of the magnetic Schrödinger equation with the mesoscopic feedback loop allow us to demonstrate quantization of Hall resistance as a direct consequence of charge and flux quantization. I believe results presented here shed light at the overall status of the MeM in quantum physics, confirming its validity.     

Quantum hall effect at low magnetic fields

The temperature and scale dependence of resistivities in the standard scaling theory of the integer quantum Hall effect is discussed. It is shown that recent experiments, claiming to observe a discrepancy with the global phase diagram of the quantum Hall effect, are in fact in agreement with the standard theory. The apparent low-field transition observed in the experiments is identified as a crossover due to weak localization and a strong reduction of the conductivity when Landau quantization becomes dominant.     

Quantum Hall effect of massless dirac fermions in a vanishing magnetic field

The effect of strong long-range disorder on the quantization of the Hall conductivity sigma{xy} in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in sigma{xy} except the plateaus at sigma{xy}=-/+e{2}/2h (per valley and per spin). The critical state at the Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.     

Observation of intrinsic inverse spin Hall effect

We report observation of intrinsic inverse spin Hall effect in undoped GaAs multiple quantum wells with a sample temperature of 10 K. A transient ballistic pure spin current is injected by a pair of laser pulses through quantum interference. By time resolving the dynamics of the pure spin current, the momentum relaxation time is deduced, which sets the lower limit of the scattering time between electrons and holes. The transverse charge current generated by the pure spin current via the inverse spin Hall effect is simultaneously resolved. We find that the charge current is generated well before the first electron-hole scattering event. Generation of the transverse current in the scattering-free ballistic transport regime provides unambiguous evidence for the intrinsic inverse spin Hall effect.     

Fractional charge revealed in computer simulations of resonant tunneling in the fractional quantum Hall regime

The concept of fractional charge is central to the theory of the fractional quantum Hall effect. Here I use exact diagonalization as well as configuration space renormalization to study finite clusters which are large enough to contain two independent edges. I analyze the conditions of resonant tunneling between the two edges. The "computer experiment" reveals a periodic sequence of resonant tunneling events consistent with the experimentally observed fractional quantization of electric charge in units of e/3 and e/5.     

Universal periods in quantum Hall droplets

Using the hierarchy picture of the fractional quantum Hall effect, we study the ground-state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is periodically modulated with flux through the droplet and will lead to a periodic variation in the conductance of a nearby point contact, such as occurs in some quantum Hall interferometers. Our model is consistent with experiment and predicts that superperiods can be observed in geometries where no interfering trajectories occur. The model may also provide an experimentally feasible method of detecting elusive neutral modes and otherwise obtaining information about the microscopic edge structure in fractional quantum Hall states.     

Quantum theory of the Hall effect

We discuss a model of both the classical and the integer quantum Hall effect which is based on a semiclassical Schrödinger-Chern-Simons action, where the Ohm equations result as equations of motion. The quantization of the classical Chern-Simons part of action under typical quantum Hall conditions results in the quantized Hall conductivity. We show further that the classical Hall effect is described by a theory which arises as the classical limit of a theory of the quantum Hall effect. The model also explains the preference and the domain of the edge currents on the boundary of samples.     

Hall quantum Hamiltonians and electric 2D-curvature

For the Dirac 2D-operator in a constant magnetic field with perturbing electric potential, we derive Hamiltonians describing the quantum quasiparticles (Larmor vortices) at Landau levels. The discrete spectrum of this Hall-effect quantum Hamiltonian can be computed to all orders of the semiclassical approximation by a deformed Planck-type quantization condition on the 2D-plane; the standard magnetic (symplectic) form on the plane is corrected by an ??electric curvature?? determined via derivatives of the electric field. The electric curvature does not depend on the magnitude of the electric field and vanishes for homogeneous fields (i.e., for the canonical Hall effect). This curvature can be treated as an effective magnetic charge of the inhomogeneous Hall 2D-nanosystem.     

Self-assembled nanocrystalline CdSe thin films

The topic of this contribution is the investigation of quantum states and quantum Hall effect in electron gas subjected to a periodic potential of the lateral lattice. The potential is formed by triangular quantum antidots located on the sites of the square lattice. In such a system the inversion center and the four-fold rotation symmetry are absent. The topological invariants which characterize different magnetic subbands and their Hall conductances are calculated. It is shown that the details of the antidot geometry are crucial for the Hall conductance quantization rule. The critical values of lattice parameters defining the shape of triangular antidots at which the Hall conductance is changed drastically are determined. We demonstrate that the quantum states and Hall conductance quantization law for the triangular antidot lattice differ from the case of the square lattice with cylindrical antidots. As an example, the Hall conductances of magnetic subbands for different antidot geometries are calculated for the case when the number of magnetic flux quanta per unit cell is equal to three.     

On the theory of the integral quantized Hall effect

Summary In the present paper the integral quantum Hall effect is studied using the Schrauben functions which are suitable eigenfunctions to describe the quantum transport in uniform electric and magnetic fields. The effect of Landau band structure on the Hall quantization is investigated. A model calculation of the conductivities σ_xy and σ_yy is presented and the onset of a Hall current dissipation is discussed. Also, the quantum oscillations of a free-electron gas into the quantum Hall regime are studied, including the electric-field effect.     

Number-Phase Quantization Scheme and the Quantum Effects of a Mesoscopic Electric Circuit at Finite Temperature

For L-C circuit, a new quantized scheme has been proposed in the context of number-phase quantization. In this quantization scheme, the number n of the electric charge q(q=en) is quantized as the charge number operator and the phase difference θ across the capacity is quantized as phase operator. Based on the scheme of number-phase quantization and the thermo field dynamics (TFD), the quantum fluctuations of the charge number and phase difference of a mesoscopic L-C circuit in the thermal vacuum state, the thermal coherent state and the thermal squeezed state have been studied. It is shown that these quantum fluctuations of the charge number and phase difference are related to not only the parameters of circuit, the squeezing parameter, but also the temperature in these quantum states. It is proven that the number-phase quantization scheme is very useful to tackle with quantization of some mesoscopic electric circuits and the quantum effects.     

Coherent electron transport in a Si quantum dot dimer

We show that the coherence of charge transfer through a weakly coupled double-dot dimer can be determined by analyzing the statistics of the conductance pattern, and does not require a large phase coherence length in the host material. We present an experimental study of the charge transport through a small Si nanostructure, which contains two quantum dots. The transport through the dimer is shown to be coherent. At the same time, one of the dots is strongly coupled to the leads, and the overall transport is dominated by inelastic cotunneling processes.     

Effective Maxwell equations for finite planar samples in QHE regime

Effective Maxwell equations for the mean quantum electromagnetic field in planar samples in QHE regime are investigated. Boundary conditions to be satisfied by the mean field intensities at the filamentary boundaries (edges) are determined. For ideal strictly 2D samples embedded in real 3D space, these constraints imply that the total filamentary charge at the boundaries (the free plus polarization terms) and current densities identically vanish at all times. In the static limit the exact quantization of the Hall resistance of samples of arbitrary form, directly follows from the boundary condition. The equations for the electromagnetic response in a neighborhood of the edge of a half-plane in QHE regime are solved. The system exhibits a weak diamagnetic response and inhomogeneous charge and current distributions develop in the sample.     

Quantum coherence in a one-electron semiconductor charge qubit

We study quantum coherence in a semiconductor charge qubit formed from a GaAs double quantum dot containing a single electron. Voltage pulses are applied to depletion gates to drive qubit rotations and noninvasive state readout is achieved using a quantum point contact charge detector. We measure a maximum coherence time of ～7 ns at the charge degeneracy point, where the qubit level splitting is first-order insensitive to gate voltage fluctuations. We compare measurements of the coherence time as a function of detuning with numerical simulations and predictions from a 1/f noise model.     

Giant charge relaxation resistance in the Anderson model

We investigate the dynamical charge response of the Anderson model viewed as a quantum RC circuit. Applying a low-energy effective Fermi liquid theory, a generalized Korringa-Shiba formula is derived at zero temperature, and the charge relaxation resistance is expressed solely in terms of static susceptibilities which are accessible by Bethe ansatz. We identify a giant charge relaxation resistance at intermediate magnetic fields related to the destruction of the Kondo singlet. The scaling properties of this peak are computed analytically in the Kondo regime. We also show that the resistance peak fades away at the particle-hole symmetric point.