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Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically…
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…
It is demonstrated that all observed fractions at moderate Landau level fillings in the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
Formulation of quantum Hall dynamics using von Neumann lattice of guiding center coordinates is presented. A topological invariant expression of the Hall conductance is given and a new mean field theory of the fractional Hall effect based…
Kubo formula gives a linear response of a quantum system to external fields, which are classical and weak with respect to the energy of the system. In this work, we take the quantum nature of the external field into account, and define a…
Computer modelling of the integer quantum Hall effect based on self-consistent Hartee-Fock calculations has now reached an astonishing level of maturity. Spatially-resolved studies of the electron density at near macroscopic system sizes of…
The status of the ac quantum Hall effect is reviewed with emphasis on the theoretical development in recent years. In particular, the numerical approaches for the calculation of the frequency dependent Hall and longitudinal conductivities…
We demonstrate how integer quantization of Hall conductance arises from the large-scale geometry of the sample. Specifically, the Hall conductance is a higher-trace pairing of the Fermi projection with a coarse cohomology class coming from…
The surface states of topological insulators, which behave as charged massless Dirac fermions, are studied in the presence of a quantizing uniform magnetic field. Using the method of D.H. Lee[1], analytical formula satisfied by the energy…
We derive the effective field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be…
Topological states of matter are characterized by topological invariant, which are physical quantities whose values are quantized and do not depend on details of the measured system. Of these, the easiest to probe in experiments is the…
The Hall and longitudinal conductivities of a recently studied holographic model of a quantum Hall ferromagnet are computed using the Karch-O'Bannon technique. In addition, the low temperature entropy of the model is determined. The…
In this work we obtain the Landau levels and the Hall conductivity at zero temperature of a two-dimensional electron gas on a conical surface. We investigate the integer quantum Hall effect considering two different approaches. The first…
It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
We discuss the relationship between the quantum Hall conductance and a fractal energy band structure, Hofstadter's butterfly, on a square lattice under a magnetic field. At first, we calculate the Hall conductance of Hofstadter's butterfly…
We examine the quantization of the motion of two charged vortices in a Ginzburg--Landau theory for the fractional quantum Hall effect recently proposed by the first two authors. The system has two second-class constraints which can be…
We demonstrate experimentally that the transitions between adjacent integer quantum Hall (QH) states are equivalent to a QH-to-insulator transition occurring in the top Landau level, in the presence of an inert background of the other…
It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
The Quantum Hall Effect for free electrons in external periodic field is discussed without using the linear response approximation. We find that the Hall conductivity is related in a simple way to Floquet energies (associated to the…
With the recent observation of graphene-like Landau levels at the surface of topological insulators, the possibility of fractional quantum Hall effect, which is a fundamental signature of strong correlations, has become of interest. Some…