Related papers: Quantum Hall transitions: An exact theory based on…
We investigate, analytically and numerically, the effects of disorder on the density of states and on the localization properties of the relativistic two dimensional fermions in the lowest Landau level. Employing a supersymmetric technique,…
I elaborate on the earlier suggestion that the model describing the plateaux transition in Integer Quantum Hall effect scales to a particular point on the line of critical points of a theory with a higher symmetry
Disorder and electron-electron interaction play essential roles in the physics of electron systems in condensed matter. In two-dimensional, quantum Hall systems, extensive studies of disorder-induced localization have led to the emergence…
We consider models for the plateau transition in the integer quantum Hall effect. Starting from the network model, we construct a mapping to the Dirac Hamiltonian in two dimensions. In the general case, the Dirac Hamiltonian has randomness…
The integer quantum Hall transition (IQHT) is one of the most mysterious members of the family of Anderson transitions. Since the 1980s, the scaling behavior near the IQHT has been vigorously studied in experiments and numerical…
A mapping is developed between the quantum Hall plateau transition and two-dimensional self-interacting lattice polymers. This mapping is exact in the classical percolation limit of the plateau transition, and diffusive behavior at the…
The localization behavior of noninteracting two-dimensional electrons in a random potential and strong magnetic field is of fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of power-law…
We study the possible phase transitions between (2+1)-dimensional abelian Chern-Simons theories. We show that they may be described by non-unitary rational conformal field theories with c_eff = 1. As an example we choose the fractional…
We present a novel approach to the localization-delocalization transition in the integer quantum Hall effect. The Hamiltonian projected onto the lowest Landau level can be written in terms of the projected density operators alone. This and…
The quantum Hall effect in graphene p-n junctions is studied numerically with emphasis on the effect of disorder at the interface of two adjacent regions. Conductance plateaus are found to be attached to the intensity of the disorder, and…
The low-lying excitations of a quantum Hall state on a disk geometry are edge excitations. Their dynamics is governed by a conformal field theory on the cylinder defined by the disk boundary and the time variable. We give a simple and…
In this paper we propose a new $S$-matrix approach to numerical simulations of network models and apply it to random networks that we proposed in a previous work 10.1103/PhysRevB.95.125414. Random networks are modifications of the…
We study the critical behavior near the integer quantum Hall plateau transition by focusing on the multifractal (MF) exponents $X_q$ describing the scaling of the disorder-average moments of the point contact conductance $T$ between two…
We construct an effective conformal field theory by using a procedure which induces twisted boundary conditions for the fundamental scalar fields. That allows to describe a quantum Hall fluid at Jain hierarchical filling, nu=m/(2pm+1), in…
We investigate numerically whether the chiral symmetry is the sole factor dominating the criticality of the quantum Hall transitions in disordered graphene. When the disorder respects the chiral symmetry, the plateau-to-plateau transition…
The past few years have produced major advances in our understanding of the quantum Hall effects---quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
A theory of integer quantum Hall effect(QHE) in realistic systems based on von Neumann lattice is presented. We show that the momentum representation is quite useful and that the quantum Hall regime(QHR), which is defined by the propagator…
Many robust physical phenomena in quantum physics are based on topological invariants arising due to intriguing geometrical properties of quantum states. Prime examples are the integer and fractional quantum Hall effects that demonstrate…
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…