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In this paper, we develop a unified theory for describing Hall effect in various electronic systems based on a pure electron picture (without the hole concept). We argue that the Hall effect is the magnetic field induced symmetry breaking…
In the Hall effect, a voltage drop develops perpendicularly to the current flow in the presence of a magnetic field, leading to a transverse Hall resistance. Recent developments with quantum simulators have unveiled strongly correlated and…
We numerically investigate the interplay of disorder and electron-electron interactions in the integer quantum Hall effect. In particular, we focus on the behaviour of the electronic compressibility as a function of magnetic field and…
A decade of intense research on two-dimensional (2D) atomic crystals has revealed that their properties can differ greatly from those of the parent compound. These differences are governed by changes in the band structure due to quantum…
We report on the scaling behavior of V-doped (Bi,Sb)$_2$Te$_3$ samples in the quantum anomalous Hall regime for samples of various thickness. While previous quantum anomalous Hall measurements showed the same scaling as expected from a…
Exotic electronic states are realized in novel quantum materials. This field is revolutionized by the topological classification of materials. Such compounds necessarily host unique states on their boundaries. Scanning tunneling microscopy…
We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…
The control of the electronic properties of materials via the vacuum fields of cavity electromagnetic resonators is one of the emerging frontiers of condensed matter physics. We show here that the enhancement of vacuum field fluctuations in…
The use of low-dimensional structures such as quantum wells, wires or dots in the absorbing regions of solar cells strongly affects the spectral response of the latter, the spectral properties being drastically modified by quantum…
In this Chapter, we give a brief review of the state of the art of theoretical and experimental studies of synthetic magnetic fields and quantum Hall effects in ultracold atomic gases. We focus on integer, spin, and fractional Hall effects,…
We have studied magnetotransport of a degenerate two-dimensional electron gas in a Hall sample in the Knudsen regime, when the mean free paths of electrons with respect to their collisions with each other and with impurities are much larger…
Measurement techniques based upon the Hall effect are invaluable tools in condensed matter physics. When an electric current flows perpendicular to a magnetic field, a Hall voltage develops in the direction transverse to both the current…
We propose a realistic scheme to detect the 4D quantum Hall effect using ultracold atoms. Based on contemporary technology, motion along a synthetic fourth dimension can be accomplished through controlled transitions between internal states…
Recent theoretical results on magnetotransport of electrons in a 2D system in the range of moderately strong transverse magnetic fields are reviewed. The phenomena discussed include: quasiclassical memory effects in systems with various…
An important route of engineering topological states and excitations is to combine superconductors (SC) with the quantum Hall (QH) effect, and over the past decade, significant progress has been made in this direction. While typical…
The quantum Hall effect occuring in two-dimensional electron gases was first explained by Laughlin, who envisioned a thought experiment that laid the groundwork for our understanding of topological quantum matter. His proposal is based on a…
This paper presents an overview of scanning-gate microscopy applied to the imaging of electron transport through buried semiconductor nanostructures. After a brief description of the technique and of its possible artifacts, we give a…
Graphene enables precise carrier-density control via gating, making it an ideal platform for studying electronic interactions. However, sample inhomogeneities often limit access to the low-density regimes where these interactions dominate.…
The skin effect, which is unique to non-Hermitian systems, can generate an extensive number of eigenstates localized near the boundary in an open geometry. Here we propose that in 2D and 3D other quantities besides charge density are…
Quantum Hall edge states have some characteristic features that can prove useful to measure and control solid state qubits. For example, their high voltage to current ratio and their dissipationless nature can be exploited to manufacture…