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In a quantum-mechanical system, particle-hole duality implies that instead of studying particles, we can get equivalent information by studying the missing particles, the so-called holes. Using this duality picture for rotating fermion…
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…
Quantum electronic noise, the random current fluctuations generated by electrons crossing a quantum conductor, has been thoroughly studied from the electron point of view. Recent experiments have shown that such noise may have striking…
The topological Hall effect (THE) of electrons in skyrmion crystals is strongly related to the quantum Hall effect (QHE) on lattices. This relation suggests to revisit the QHE because its Hall conductivity can be unconventionally quantized.…
When a graphene layer is stressed, the strain alters the phase an electron accumulates hopping between sites in a way that can be modeled as arising from a pseudo-magnetic vector potential. We examine the case of an oscillating graphene…
Technological advancement towards the quantum era requires secure communication, quantum computation, and ultra-sensitive sensing capabilities. Layered quantum materials (LQMs) have remarkable optoelectronic and quantum properties that can…
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…
We show that acoustic crystalline wave gives rise to an effect similar to that of a gravitational wave to an electron gas. Applying this idea to a two-dimensional electron gas in the fractional quantum Hall regime, this allows for…
In this paper we present a theoretical analysis of the effect of magnetostriction on quantum oscillations of elastic constants in metals under strong magnetic fields. It is shown that at low temperatures a significant softening of some…
Quantum geometry of the electron wave function plays a significant role in the linear and non-linear responses of crystalline materials. Here, we study quantum geometry induced second harmonic generation. We identify non-linear responses…
We predict a novel class of magnetotransport oscillations in ballistic graphene specific for a ring-shape geometry. Using the B\"uttiker-Landauer formalism, we analytically obtain the local Hall and Nernst coefficients in the weak-field…
Symmetry breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the…
Spatially separated bodies in relative motion through vacuum experience a tiny friction force known as quantum friction. This force has so far eluded experimental detection due to its small magnitude and short range. Quantitative details…
We consider quantum wire arrays consisting of GaAs rods embedded in Al$_{x}$Ga$_{1-x}$As and disposed in sites of a square or triangular lattice. The electronic and hole spectra around the conduction band bottom and the valence band top are…
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.…
In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the…
The Hall conductivity of an electron gas on the surface of constant negative curvature (the Lobachevsky plane) in the presence of an orthogonal magnetic field is investigated. It is shown that the effect of the surface curvature is to…
Transport properties of highly mobile 2D electrons are studied in symmetric GaAs quantum wells placed in titled magnetic fields. Quantum positive magnetoresistance (QPMR) is observed in magnetic fields perpendicular to the 2D layer.…
Recent advances in electron microscopy trigger the question whether attosecond electron diffraction can resolve atomic-scale electron dynamics in crystalline materials in space and time. Here we explore the physics of the relevant…
Using the Calogero model as an example, we show that the transport in interacting non-dissipative electronic systems is essentially non-linear. Non-linear effects are due to the curvature of the electronic spectrum near the Fermi energy. As…