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The interfaces of quantum Hall insulators with superconductors have emerged as a promising platform to realise interesting physics that may be relevant for topologically protected quantum computing. However, these interfaces can host other…
In high-quality solid-state systems at low temperatures, the hydrodynamic or the ballistic regimes of heat and charge transport are realized in the electron and the phonon systems. In these regimes, the thermal and the electric conductance…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
We investigate an interplay between quantum geometrical effects and surface plasmons through surface plasmonic structures, based on an electron hydrodynamic theory. First we demonstrate that the quantum nonlinear Hall effect can be…
Anisotropic magneto resistances and intrinsic adiabatic transport features are generated on quantum Hall samples based on an (Al,Ga)As/GaAs heterostructure with alloyed Au/Ge/Ni contacts. We succeed to probe the microscopic origin of these…
In this chapter we introduce a microscopic modelling of the surplus electrons on the plasma wall which complements the classical description of the plasma sheath. First we introduce a model for the electron surface layer to study the…
In this work we solve thermo-hydrodynamical equations considering a two dimensional electron system in the integer quantum Hall regime, to calculate the spatial distribution of the local electron temperature. We start from the…
When the chemical potential of an electron system has a discontinuity at a density $n^{*}$, the system is said to be incompressible and a finite energy is required to create mobile charges in the bulk of the system. The quantum Hall effect…
Electroluminescence spectra of a silicon nanostructure with edge channels covered by chains of dipole centers with negative correlation energy are demonstrated. The presence of such chains provides conditions for nondissipative transport of…
A quantum antidot, a submicron depletion region in a two-dimensional electron system, has been actively studied in the past two decades, providing a powerful tool for understanding quantum Hall systems. In a perpendicular magnetic field,…
Heat transport in the quantum Hall regime is investigated using micron-scale heaters and thermometers positioned along the edge of a millimeter-scale two dimensional electron system (2DES). The heaters rely on localized current injection…
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative…
The quantum Hall effect, observed in a two-dimensional electron gas subjected to a perpendicular magnetic field, imposes a 1D-like chiral, downstream, transport of charge carriers along the sample edges. Although this picture remains valid…
A set of stacked two-dimensional electron systems in a perpendicular magnetic field exhibits a three-dimensional version of the quantum Hall effect if interlayer tunneling is not too strong. When such a sample is in a quantum Hall plateau,…
Traditionally, the understanding of quantum transport, coherent and ballistic1, relies on the measurement of macroscopic properties such as the conductance. While powerful when coupled to statistical theories, this approach cannot provide a…
We discuss the development of a sensitive electrometer that utilizes a two-dimensional electron gas (2DEG) in the quantum Hall regime. As a demonstration, we measure the evolution of the Landau levels in a second, nearby 2DEG as the applied…
We review recent theoretical and experimental developments concerning collective spin excitations in two-dimensional electron liquid (2DEL) systems, with particular emphasis on the interplay between many-body and spin-orbit effects, as well…
Nanoelectronic devices embedded in the two-dimensional electron system (2DES) of a GaAs/AlGaAs heterostructure enable a large variety of applications from fundamental research to high speed transistors. Electrical circuits are thereby…
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…
One-dimensional (1D) quasicrystals exhibit physical phenomena associated with the 2D integer quantum Hall effect. Here, we transcend dimensions and show that a previously inaccessible phase of matter --- the 4D integer quantum Hall effect…