Related papers: Hall conductivity as a topological invariant
Two-dimensional systems with honeycomb lattice are known to be a paradigmatic platform to explore the various types of Hall effects, owing to that the interplay of lattice geometry, spin-orbit coupling and magnetism can give rise to very…
In this letter we study the Hall conductivity in holographic models where translational invariance is broken by a lattice. We show that generic holographic theories will display a different temperature dependence in the Hall angle as to the…
I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic…
Here, we elaborate on and develop the geometrical approach introduced in K. Le Hur, Physics Reports 1104 1-42 (2025) between the magnetic monopole created from a radial field, quantum physics and topological lattice models through quantum…
Motivated by recent experimental attempts to detect the Hofstadter butterfly, we numerically calculate the Hall conductivity in a modulated two-dimensional electron system with disorder in the quantum Hall regime. We identify the critical…
Symmetry is a cornerstone of condensed matter physics, fundamentally shaping the behavior of electronic systems and inducing the emergence of novel phenomena. The Hall effect, a key concept in this field, demonstrates how symmetry breaking,…
The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall…
We analysis the quantum Hall effect exhibited by a system of particles moving in a higher dimensional space. This can be done by considering particles on the Bergman ball {\bb{B}_{\rho}^d} of radius \rho in the presence of an external…
By restricting the motion of high-mobility 2D electron gas to a network of channels with smooth confinement, we were able to trace, both classically and quantum-mechanically, the interplay of backscattering, and of the bending action of a…
In a two-dimensional electron gas, the quantized Hall conductance can be induced by a strong magnetic field, known as the quantum Hall effect, and it can also result from the strong exchange coupling of magnetic ions, dubbed as the "quantum…
A field-theoretic formulation of a planar Hall-electron system with edges is presented and some fundamental aspects of the integer quantum Hall effect are studied with emphasis on clarifying general symmetry-based consequences of…
The well-known Hall effect describes the transverse deflection of charged particles (electrons or holes) in an electric-current carrying conductor under the influence of perpendicular magnetic fields, as a result of the Lorentz force.…
We study Berry curvature driven and Zeeman magnetic field dependent electric current responses of two-dimensional electron system with spin-orbit coupling. New non-dissipative component of the electric current occurring in the applied…
To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many…
We discuss quantum Hall effects in a gapped insulator on a periodic two-dimensional lattice. We derive a universal relation among the the quantized Hall conductivity, and charge and flux densities per physical unit cell. This follows from…
The electronic properties of quasi two-dimensional multicomponent systems are investigated in the presence of a perpendicular magnetic field. The effects of the presence of a few valence band holes on the properties of quantum Hall systems…
A theory of the static electron polarizability of crystals whose energy spectrum is modified by quantizing magnetic fields is presented. It is argued that The polarizability is strongly affected by non-dissipative Hall currents induced by…
We report on theoretical and experimental investigations of the integer quantized Hall effect in narrow channels at various mobilities. The Hall bars are defined electrostatically in two-dimensional electron systems by biasing metal gates…
We consider electrons in uniform external magnetic and electric fields which move on a plane whose coordinates are noncommuting. Spectrum and eigenfunctions of the related Hamiltonian are obtained. We derive the electric current whose…
The intrinsic anomalous Hall effect is one of the most exciting manifestations of the geometric properties of the electronic wave-function. Here, we predict that the electronic wave-function's geometric nature also gives rise to a purely…