Related papers: Quantum Hall Effect on the Hyperbolic Plane
Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed…
The theory of the intrinsic Hall effect, both linear and nonlinear, is rooted in a geometry which is defined in the Bloch-vector parameter space; the formal expressions are mostly derived from semiclassical concepts. When disorder and…
The quantum Hall effect (QHE) is a topologically protected phenomenon which has been observed in various systems. In experiments, the size of Hall bar device to realize the QHE is generally much larger than the phase coherence length, in…
The study of quantum Hall effect (QHE) is a foundation of topological physics, inspiring extensive explorations of its high-dimensional generalizations. Notably, the four dimensional (4D) QHE has been experimentally realized in synthetic…
When a two-dimensional electron gas is exposed to a perpendicular magnetic field and an in-plane electric field, its conductance becomes quantized in the transverse in-plane direction: this is known as the quantum Hall (QH) effect. This…
The quantum Hall conductivity in the presence of constant magnetic field may be represented as the topological TKNN invariant. Recently the generalization of this expression has been proposed for the non - uniform magnetic field. \rev{The…
In recent years, there is an increasing interest in transport phenomena that are fundamentally linked to the presence of multiple bands. In this thesis, we develop, discuss, and apply a theory of the electrical conductivity that includes…
We study Faraday rotation in the quantum relativistic limit. Starting from the photon self-energy in the presence of a constant magnetic field the rotation of the polarization vector of a plane electromagnetic wave which travel along the…
We study the Hall effect in topologically trivial isolated flat-band systems (i.e., flat bands are separated from other bands and have zero Chern number) for a weak magnetic field. In a naive semiclassical picture, the Hall conductivity…
We study the quantum anomalous thermal Hall effect in a topological superconductor which possesses an integer bulk topological number, and supports Majorana excitations on the surface. To realize the quantum thermal Hall effect, a finite…
It is well known that noncommutative geometry naturally emerges in the quantum Hall states due to the presence of strong and constant magnetic fields. Here, we discuss the underlying noncommutative geometry of quantum Hall fluids in which…
The semi-classical study of the integer Quantum Hall conductivity is investigated for electrons in a bi-periodic potential $V(x,y)$. The Hall conductivity is due to the tunnelling effect and we concentrate our study to potentials having…
Most of the experiments on the quantum Hall effect (QHE) were made at approximately the same height above sea level. A future international comparison will determine whether the gravitational field $\mathbf{g}(x)$ influences the QHE. In the…
Using recently developed tools from space-adiabatic perturbation theory, in particular the construction of a non-equilibrium almost stationary state, we give a new proof that the Kubo formula for the Hall conductivity remains valid beyond…
A semiclassical constrained Hamiltonian system which was established to study dynamical systems of matrix valued non-Abelian gauge fields is employed to formulate spin Hall effect in noncommuting coordinates at the first order in the…
The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators - topologically non-trivial states of two-dimensional matter with broken…
Starting from the Kubo formula, we expand the Hall conductivity using a cumulant approach which converges quickly at high temperatures (k_BT > energy differences of initial and final scattering states) and can be extended to low…
Studies of the 3D quantum Hall effect (QHE) have primarily emphasized transport features that mimic the well-established 2D QHE. In this work, we show that qualitatively new features arise when an in-plane magnetic field is applied to a 3D…
We present a microscopic theory to give a physical picture of the formation of quantum anomalous Hall (QAH) effect in graphene due to a joint effect of Rashba spin-orbit coupling $\lambda_R$ and exchange field $M$. Based on a continuum…
Real-space separations of counter-moving states to opposite surfaces or edges are associated with different types of Hall effects, such as the quantum-, spin-, or the anomalous Hall effect. Some systems provide the possibility to separate a…