Related papers: Quantum Hall Effect on the Hofstadter Butterfly
An integer Quantum Hall effect transition is studied in a modulation doped p-SiGe sample. In contrast to most examples of such transitions the longitudinal and Hall conductivities at the critical point are close to 0.5 and 1.5 (e^2/h), the…
Motivated by surprises in recent experimental findings, we study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a…
A two-dimensional quantum Hall system is studied for a wide class of potentials including single-body random potentials and repulsive electron-electron interactions. We assume that there exists a non-zero excitation gap above the ground…
The integer quantum Hall effect features a paradigmatic quantum phase transition. Despite decades of work, experimental, numerical, and analytical studies have yet to agree on a unified understanding of the critical behavior. Based on a…
When a two-dimensional electron gas is exposed to a perpendicular magnetic field and an in-plane electric field, its conductance becomes quantized in the transverse in-plane direction: this is known as the quantum Hall (QH) effect. This…
The magnetotransport of a high-mobility two-dimensional electron gas coupled to a hovering split-ring resonator with controllable distance is studied in the quantum Hall regime. The measurements reveal an enhancement by more than a factor 2…
We theoretically investigate electrical transport in a quantum Hall system hosting bulk and edge current carrying states. Spatially varying magnetic and electric confinement creates pairs of current carrying lines that drift in the same or…
In the fractional quantum Hall effect regime we measure diagonal ($\rho_{xx}$) and Hall ($\rho_{xy}$) magnetoresistivity tensor components of two-dimensional electron system (2DES) in gated GaAs/Al$_{x}$Ga$_{1-x}$As heterojunctions,…
We study the properties of quantum cusp and butterfly catastrophes from an algebraic viewpoint. The analysis employs an interacting boson model Hamiltonian describing quantum phase transitions between specific quadrupole shapes by…
The behaviour of the critical point between quantum Hall plateaux, as the Zeeman energy is varied, is analysed using modular symmetry of the Hall conductivities following from the law of corresponding states. Flow diagrams for the…
Exotic quantum Hall systems hosting counter-propagating edge states can show seemingly non-universal transport regimes, usually depending on the size of the sample. We experimentally probe transport in a quantum Hall sample engineered to…
We investigate the Hall effect in a quasi one-dimensional system made of weakly coupled Luttinger Liquids at half filling. Using a memory function approach, we compute the Hall coefficient as a function of temperature and frequency in the…
We examine the hydrostatic stress of electrons strongly confined in a quasi-2D quantum well in the presence of a strong perpendicular and weak in-plane magnetic field. This introduces anisotropy into the stress tensor which is inconsistent…
Constricting transport through a one-dimensional quantum point contact in the quantum Hall regime enables gate-tunable selection of the edge modes propagating between voltage probe electrodes. Here we investigate the quantum Hall effect in…
In recent years, there is an increasing interest in transport phenomena that are fundamentally linked to the presence of multiple bands. In this thesis, we develop, discuss, and apply a theory of the electrical conductivity that includes…
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…
We formulate a self-consistent model of the integer quantum Hall effect on an infinite strip, using boundary conditions to investigate the influence of finite-size effects on the Hall conductivity. By exploiting the translation symmetry…
We study the non-Hermitian Hofstadter dynamics of a quantum particle with biased motion on a square lattice in the background of a magnetic field. We show that in quasi-momentum space the energy spectrum is an overlap of infinitely many…
Quantum transport properties in quantum Hall wires in the presence of spatially correlated disordered magnetic fields are investigated numerically. It is found that the correlation drastically changes the transport properties associated…
We investigate spontaneous interlayer phase coherence and the occurrence of the quantum Hall effect in triple-layer electron systems. Our work is based on a simple tight-binding model that greatly facilitates calculations and whose accuracy…