Related papers: Scaling Theory of the Integer Quantum Hall Effect
We show that the plateau transitions in the quantum Hall effect is the same as the dimerization transition of a half-filled, one dimensional, $U(2n)$ Hubbard model at $n=0$. We address the properties of the latter by a combination of…
The quantum Hall effect was originally observed in a two-dimensional electron gas forming Landau levels when exposed to a strong perpendicular magnetic field and was later generalized to Chern insulators without net magnetization. Here,…
Delocalization problem for a two-dimensional non-interacting electron system is studied under a random magnetic field. With the presence of a random magnetic field, the Hall conductance carried by each eigenstate can become nonzero and…
We present a new theoretical approach for the integer quantum Hall effect, which is able to describe the inter-plateau transitions as well as the transition to the Hall insulator. We find two regimes (metallic and insulator like) of the top…
Comment on ``Scaling in Plateau-Plateau Transition: A Direct Connection of Quantum Hall Systems with Anderson Localization Model'' [Wanli Li et al., Phys.Rev.Lett. 102, 216801 (2009)]
We investigate the emerging consequences of an applied strong in-plane electric field on a macroscopically large graphene sheet subjected to a perpendicular magnetic field, by determining in exact analytical form various many-body…
We present a simple classification of the different liquid and solid phases of quantum Hall systems in the limit where the Coulomb interaction between the electrons is significant, i.e. away from integral filling factors. This…
The effect of inter-Landau-band mixing on electron localization in an integer quantum Hall system is studied. We find that mixing of localized states with {\it opposite chirality} tends to delocalize the states. This delocalization effect…
Two-dimensional electron gas in the integer quantum Hall regime is investigated numerically by studying the dynamics of an electron hopping on a square lattice subject to a perpendicular magnetic field and random on-site energy with white…
We examine the effect of disorder on the electromagnetic response of quantum Hall stripes using an effective elastic theory to describe their low-energy dynamics, and replicas and the Gaussian variational method to handle disorder effects.…
Within the mature field of Anderson transitions, the critical properties of the integer quantum Hall transition still pose a significant challenge. Numerical studies of the transition suffer from strong corrections to scaling for most…
The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective…
We study the phase structure and Hall conductance quantization in weakly coupled multi-layer electron systems in the integer quantum Hall regime. We derive an effective field theory and perform a two-loop renormalization group calculation.…
The scaling theory of critical phenomena has been successfully extended for classical first order transitions even though the correlation length does not diverge in these transitions. In this paper we apply the scaling ideas to quantum…
We argue that the finite temperature dynamics of the integer quantum Hall system is governed by two independent length scales. The consistent scaling description of the transition makes crucial use of two temperature critical exponents,…
We investigate integer and fractional quantum Hall states in quantum point contacts (QPCs) of different geometries, defined in AlGaAs/GaAs heterostructures employing different doping and screening techniques. We find that, even in the…
We study both the continuous model and the discrete model of the integer quantum Hall effect on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper [CHMM]. Here we model impurities, that is we…
Recently, a zero Hall conductance plateau with random domains is experimentally observed in quantum anomalous Hall (QAH) effect. We study the effects of random domains on the zero Hall plateau in QAH insulators. We find the structure…
We present here a model of carrier distribution and transport in semiconductor alloys accounting for quantum localization effects in disordered materials. This model is based on the recent development of a mathematical theory of quantum…
We study a delocalization transition for non-interacting quasiparticles moving in two dimensions, which belongs to a new symmetry class. This symmetry class can be realised in a dirty, gapless superconductor in which time reversal symmetry…