Related papers: The Quantum Hall Effect and Inter-edge State Tunne…
Two laterally adjacent quantum Hall systems separated by an extended barrier of a thickness on the order of the magnetic length possess a complex Landau band structure in the vicinity of the line junction. The energy dispersion is obtained…
The quantum anomalous Hall effect in magnetic topological insulators has been recognized as a promising platform for applications in quantum metrology. The primary reason for this is the electronic conductance quantization at zero external…
We study the effect of backward scatterings in the tunneling at a point contact between the edges of a second level hierarchical fractional quantum Hall states. A universal scaling dimension of the tunneling conductance is obtained only…
The spectrum and the eigenstates of a finite 2D tight-binding electronic system, with Dirichlet boundary conditions, in magnetic field and external linear potential are studied. The eigenstates show an equipotential character and may cross…
Despite the success of Landau-level theory and edge-state transport formalisms, a direct microscopic link between bulk quantization and the observed hierarchy of quantum Hall plateaus has not been established. In particular, no unified…
The low-temperature magnetoresistance of parabolic quantum wells displays pronounced minima between integer filling factors. Concomitantly the Hall effect exhibits overshoots and plateau-like features next to well-defined ordinary quantum…
We investigate how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. The Hall effect, measured by contacting those channels, remains…
Low frequency AC-measurements are commonly used to determine the voltage and currents through mesoscopic devices. We calculate the effect of the alternating Hall voltage on the recorded time-averaged voltage in the presence of a top-gate…
We consider spin-polarized electrons in a single Landau level on a cylinder as the circumference of the cylinder goes to infinity. This gives a model of interacting electrons on a circle where the momenta of the particles are restricted and…
Two-terminal conductance quantization in the context of quantum Hall (QH) physics is intimately related to the current carried by a discrete number of chiral edge modes. Upon pinching off a QH bar, one may engineer setups where some modes…
We report on the stability of the quantum Hall plateau in wide Hall bars made from a chemically gated graphene film grown on SiC. The $\nu=2$ quantized plateau appears from fields $B \simeq 5$ T and persists up to $B \simeq 80$ T. At high…
Tunneling of electrons into a two-dimensional electron system is known to exhibit an anomaly at low bias, in which the tunneling conductance vanishes due to a many-body interaction effect. Recent experiments have measured this anomaly…
A scanning probe technique was used to obtain a high-resolution map of the random electrostatic potential inside the quantum Hall liquid. A sharp metal tip, scanned above a semiconductor surface, sensed charges in an embedded…
Using a new MBE growth technique, we fabricate a two-dimensional electron system which is bent around an atomically sharp 90 degree corner. In the quantum Hall regime under tilted magnetic fields, we can measure equilibration between both…
We developed the theory of elastic electron tunneling through a potential barrier driven by a strong high-frequency electromagnetic field. It is demonstrated that the driven barrier can be considered as a stationary two-barrier potential…
These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The…
We report tunneling phenomena in double In$_{0.53}$Ga$_{0.47}$As quantum-well structures that are at odds with the conventional parallel-momentum-conserving picture of tunneling between two-dimensional systems. We found that the tunneling…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
Edge states reflect the key physical properties yet are difficult to probe individually, particularly when several states are present at an edge. We present momentum resolved tunneling spectroscopy between a quantum well and a quantum wire…
We consider the influence of an external periodic potential on the fractional quantum Hall effect of two-dimensional interacting electron systems. For many electrons on a torus, we find that the splitting of incompressible ground state…