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There is a close analogy between the response of a quantum Hall liquid (QHL) to a small change in the electron density and the response of a superconductor to an externally applied magnetic flux - an analogy which is made concrete in the…
We give a universal description of the mesoscopic effects occurring in fractional quantum Hall disks due to the Aharonov-Bohm flux threading the system. The analysis is based on the exact treatment of the flux within the conformal field…
We model the quantum Hall effect in heterostructures made of two gapped graphene stripes with different gaps, $\Delta_1$ and $\Delta_2$. We consider two main situations, $\Delta_1=0,\Delta_2\neq0$ and $\Delta_1=-\Delta_2$. They are…
The quantum anomalous Hall (QAH) effect holds fundamental importance in topological physics and technological promise for electronics. It is generally believed that the QAH effect can only be realized in insulators. In this Letter, we…
We derive quantum field theory Ward identities based on linear area preserving and conformal transformations in 2+1 dimensions. The identities relate Hall viscosities, Hall conductivities and the angular momentum. They apply both for…
The predictive power of mean-field theory is emphasized by comparing theory with simulations under controlled conditions. The recently developed test-field method is used to extract turbulent transport coefficients both in kinematic as well…
We show that the study of conductivity nonlinearity gives a possibility to determine the condition when the diffusion conductivity changes to the hopping one with increasing disorder. It is experimentally shown that the conductivity of…
This report reviews recent progress in computing Kubo formulas for general interacting Hamiltonians. The aim is to calculate electric and thermal magneto-conductivities in strong scattering regimes where Boltzmann equation and Hall…
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…
We present a detailed theory of transport through line junctions formed by counterpropagating single-branch fractional-quantum-Hall edge channels having different filling factors. Intriguing transport properties are exhibited when strong…
The electronic transport of a noninteracting quantum ring side-coupled to a quantum wire is studied via a single-band tunneling tight-binding Hamiltonian. We found that the system develops an oscillating band with antiresonances and…
The topological valley Hall effect was predicted as a consequence of the bulk topology of electronic systems. Now it has been observed in photonic crystals, showing that both topology and valley are innate to classical as well as quantum…
At very large tilt of the magnetic (B) field with respect to the plane of a two-dimensional electron system the transport in the integer quantum Hall regime at $\nu$ = 4, 6, and 8 becomes strongly anisotropic. At these filling factors the…
We analyse numerically the linear stability of the fully developed liquid metal flow in a square duct with insulating side walls and thin electrically conducting horizontal walls with the wall conductance ratio $c=0.01\cdots 1$ subject to a…
We present experimental results on the quantized Hall insulator in two dimensions. This insulator, with vanishing conductivities, is characterized by the quantization (within experimental accuracy) of the Hall resistance in units of the…
In the present thesis, we study the heat flow in mesoscopic one-dimensional transport systems. Using the analysis of full counting statistics, we calculate the cumulant generating function of the particle and heat flows and prove its…
Near the superconducting phase transition, fluctuations significantly modify the electronic transport properties. Here we study the fluctuation corrections to the Hall conductivity in disordered films, extending previous derivations to a…
The quantum Hall effect realizes a quantized Hall resistance $R_{xy} = h/(\nu e^2)$ whereas the longitudinal resistance vanishes. The quantized value consists of the fundamental physical quantities, the elementary charge $e$ and the Planck…
We investigate the possibility of observing the anomalous Hall effect (AHE) in two dimensional paramagnetic systems. We apply the semiclassical equations of motion to carriers in the conduction and valence bands of wurtzite and zincblende…
We have introduced a controllable nano-scale incursion into a potential barrier imposed across a two-dimensional electron gas, and report on the phenomena that we observe as the incursion develops. In the quantum Hall regime, the…