Evidence for Coulomb staircase in tunneling through an antidot island in the quantum Hall regime

We studied the – characteristics of tunneling devices, defined by two trench fingers and an antidot island patterned on Corbino rings in the quantum Hall plateau regime. Well-developed current steps were observed at filling factors near , which we interpret as a Coulomb staircase phenomenon due to charging of compressible strips around the antidot. The evolution of the current steps with filling factor is explained in the quasi-elastic inter landau level scattering model.     

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.     

Manifestations of incompressible strips in the edge magnetoplasmon spectrum in the quantum Hall effect regime

The behavior of the main edge magnetoplasmon mode in the quantum Hall effect (QHE) regime has been analyzed by the method of optical detection of resonance microwave absorption. Near a filling factor of 2 at a temperature of about 0.3 K, the main edge mode splits into two modes seemingly due to broadening of the incompressible strip at the edge of the two-dimensional electron gas under such conditions.     

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.     

Excitations in a quantum Hall ferromagnet with strong Coulomb interaction

A quantum Hall ferromagnet is considered at integer fillings ν, provided typical Coulomb interaction energy E _c is large compared to the cyclotron energy ω_H. Low-energy collective modes consist of a magnetoplasmon exciton and a gapless spin exciton. All charged excitations have a gap. The activation energy gap for a pair of charged topological excitations—skyrmion and antiskyrmion—is small, i.e., Δ< vω_H. The electric charge of a skyrmion is the multiple q=eνQ, where Q is the integer topological charge.     

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.