PLE studies of two-dimensional hole systems in the quantum Hall regime

We report a spectroscopic investigation of the densities of both occupied and unoccupied states of a high-quality two-dimensional hole system, in the regime of the quantum Hall effects (QHEs). Photoluminescence and photoluminescence excitation spectroscopies are used to elucidate the complicated valence band structure of the holes, and to establish their optical response to the QHEs.     

Exact results for systems of electrons in the fractional quantum Hall regime

There has been a great deal of interest over the last two decades on the fractional quantum Hall effect, a novel quantum many-body liquid state of strongly correlated two-dimensional electronic systems in a strong perpendicular magnetic field. The most pronounced fractional quantum Hall states occur at odd denominator filling factors of the lowest Landau level and are described by the Laughlin wave function. It is well known that exact closed-form solutions for many-body wave functions, including the Laughlin wave function, are generally very rare and hard to obtain. In this work we present some exact results corresponding to small systems of electrons in the fractional quantum Hall regime at odd denominator filling factors. Use of Jacobi coordinates is the key tool that facilitates the exact calculation of various quantities. Expressions involving integrals over many variables are considerably simplified with the help of Jacobi coordinates allowing us to calculate exactly various quantities corresponding to systems with several electrons.     

Mesoscopic effects in the quantum Hall regime

We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to the corresponding magnetic subbands. In finite-size systems, we find that mesoscopic effects often dominate, leading to apparent non-universal scaling behavior in higher Landau levels. This is because localization length, which grows exponentially with Landau level index, exceeds the system sizes amenable to the numerical study at present. When band mixing between multiple Landau levels is present, mesoscopic effects cause a crossover from a sequence of quantum Hall transitions for weak disorder to classical behavior for strong disorder. This behavior may be of relevance to experimentally observed transitions between quantum Hall states and the insulating phase at low magnetic fields.     

Electronic correlation in the quantum Hall regime

Two‐dimensional interacting electron systems become strongly correlated if the electrons are subject to a perpendicular high magnetic field. After introducing the physics of the quantum Hall regime the incompressible many‐particle ground state and its excitations are studied in detail at fractional filling factors for spin‐polarized electrons. The spin degree of freedom whose importance was shown in recent experiments is considered by studying the thermodynamics at filling factor one and near one.     

Electron localization in the quantum Hall regime

The theory of the insulating state discriminates between insulators and metals by means of a localization tensor, which is finite in insulators and divergent in metals. In absence of time-reversal symmetry, this same tensor acquires an off-diagonal imaginary part, proportional to the dc transverse conductivity, leading to quantization of the latter in two-dimensional systems. I provide evidence that electron localization--in the above sense--is the common cause for both vanishing of the dc longitudinal conductivity and quantization of the transverse one in quantum Hall fluids.     

Exact results for systems of electrons in the fractional quantum Hall regime II

In a previous work [O. Ciftja, Physica B 404 (2009) 227] we reported the exact calculation of energies for the fractional quantum Hall Laughlin state at filling factor for systems with up to N=4 electrons in a disk geometry. The purpose of this brief extension of the earlier work is to report similar exact results for the other Laughlin state at filling factor . We use the same method of orthogonal Jacobi variables adopted in the earlier work.     

Gate-defined graphene quantum point contact in the quantum Hall regime

We investigate transport in a gate-defined graphene quantum point contact in the quantum Hall regime. Edge states confined to the interface of p and n regions in the graphene sheet are controllably brought together from opposite sides of the sample and allowed to mix in this split-gate geometry. Among the expected quantum Hall features, an unexpected additional plateau at 0.5h/e2 is observed. We propose that chaotic mixing of edge channels gives rise to the extra plateau.     

Identifying the closeness of eigenstates in quantum many-body systems

We propose a quantity called modulus fidelity to measure the closeness of two quantum pure states. We use it to investigate the closeness of eigenstates in one-dimensional hard-core bosons. When the system is integrable, eigenstates close to their neighbor or not, which leads to a large fluctuation in the distribution of modulus fidelity. When the system becomes chaos, the fluctuation is reduced dramatically, which indicates all eigenstates become close to each other. It is also found that two kind of closeness, i.e., closeness of eigenstates and closeness of eigenvalues, are not correlated at integrability but correlated at chaos. We also propose that the closeness of eigenstates is the underlying mechanism of eigenstate thermalization hypothesis(ETH) which explains the thermalization in quantum many-body systems.     

Inhomogeneous Hall-geometry sample in the quantum Hall regime

A generalization of the known theory describing the Hall channels with integer filling factors in inhomogeneous 2D electronic samples to the case of a stationary nonequilibrium state (with a nonzero Hall voltage V _H across the 2D system) is proposed. For the central strip located near the extremum of the electron density, the theory predicts a change in its width and a shift of the whole strip from the equilibrium position as functions of V _H . The theoretical results are used to interpret recent experiments on measuring the local electric fields along the Hall samples both in equilibrium conditions and in the presence of transport in the quantum Hall regime.     

Conductivity peaks broadening in the quantum Hall regime

We argue that it is the hopping transport that is responsible for broadening of the σ_xx peaks. Explicit expressions for the width Δν of a peak as a function of the temperature T, current J and frequency ω are found. It is shown that Δν grows with T as (T/T₁)^κ, where κ is the inverse localization-length exponent. The current J is shown to act like the effective temperature T_eff(J) ∝ J^1/2 if . Broadening of the ohmic ac-conductivity peaks with frequency ω is found to be determined by the effective temperature      

Edge physics of graphene in the quantum Hall regime

We study the electronic edge states of graphene in the quantum Hall regime. For non-interacting electrons, graphene supports both electron-like and hole-like edge states. We find there are half as many edge states of each type in the lowest Landau level compared to higher Landau levels, leading to a quantization of the Hall conductance that is shifted relative to standard two dimensional electron gases. We also consider the effect of quantum Hall ferromagnetism on this edge structure, and find an unusual Luttinger liquid at the edge in undoped graphene. This arises due to a domain wall that forms near the edge between partially spin-polarized and valley-polarized regions. The domain wall has a U(1) degree of freedom which generates both collective and charged gapless excitations, whose consequences for tunneling experiments are discussed.