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Inertial effects play an important role in classical mechanics but have been largely overlooked in quantum mechanics. Nevertheless, the analogy between inertial forces on mass particles and electromagnetic forces on charged particles is not…
The anomalous Hall effect (AHE) has been studied systematically in the low-conductivity ferromagnetic oxide Fe$_{3-x}$Zn$_x$O$_4$ with $x = 0$, 0.1, and 0.5. We used (001), (110), and (111) oriented epitaxial Fe$_{3-x}$Zn$_x$O$_4$ films…
Starting with the Dirac equation for an electron in a constant electromagnetic background on a noncommutative (NC) plane, we obtain a gauge invariant description of the system. Surprisingly, the dynamics of the system is dictated by the…
The fractional quantum Hall effect (FQHE) occurs at certain magnetic field strengths B*(n) in a two-dimensional electron gas of density n at strong magnetic fields perpendicular to the plane of the electron gas. At these magnetic fields…
The quantum geometry has significant consequences in determining transport and optical properties in quantum materials. Here, we use a semiclassical formalism coupled with perturbative corrections unifying the nonlinear anomalous Hall…
Hall effect is detected in organic field-effect transistors, using appropriately shaped rubrene (C42H28) single crystals. It turned out that inverse Hall coefficient, having a positive sign, is close to the amount of electric-field induced…
In a solid, transport of electricity can occur via electrons or via holes. In the normal state no experiment can determine unambiguously whether the elementary mobile carriers have positive or negative charge. This is no longer true in the…
The absorption coefficient for surface acoustic wave $\Gamma$ and variation in the wave velocity $\Delta V/V$ were measured in GaAs/AlGaAs heterostructures; the above quantities are related to interaction of the wave with two-dimensional…
For the two-dimensional ideal electron gas with the Rashba spin-orbit interaction and in the presence of non-magnetic short-ranged potential impurities the spin-Hall conductivity $\sigma_{sH}$ is found by direct microscopic calculation.…
We evaluate the distribution of Hall conductances in magnetic subbands of two-dimensional electron gas with Rashba spin-orbit (SO) coupling placed in a periodic potential and perpendicular magnetic field. In this semiconductor structure the…
We study the role of the Hall current and electron inertia in collisionless magnetic reconnection within the framework of full two-fluid MHD. At spatial scales smaller than the electron inertial length, a topological change of magnetic…
The electronic structure and intrinsic anomalous Hall conductivity of nickel have been calculated based on the generalized gradient approximation (GGA) plus on-site Coulomb interaction (GGA+U) scheme. It is found that the intrinsic…
In QED of two space dimensions, a quantum Hall effect occurs in the absence of any magnetic field. We give a simple and transparent explanation. In solid state physics, the Hall conductivity for non-degenerate ground state is expected to be…
A two-dimensional array of quantum dots in a magnetic field is considered. The electrons in the quantum dots are described as unitary random matrix ensembles. The strength of the magnetic field is such that there is half a flux quantum per…
We study the effects of the interaction between electrons and holes on the conductance G of quasi-one-dimensional graphene systems. We first consider as a benchmark the limit in which all interactions are negligible, recovering the…
We report the observation of nonlinear anomalous Hall effect (NLAHE) in the multilayered organic conductor $\alpha$-(BEDT-TTF)$_2$I$_3$ in the charge order (CO) insulating phase just under the critical pressure for transition into…
Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many--particle configuration space. Electron-magnetic field and electron-electron interactions…
The thermodynamic potential of an ideal nonrelativistic gas of two-dimensional electrons in crossed uniform magnetic and electric fields is constructed. For low temperatures and very weak electric fields, it is shown that the Hall…
We apply homogenization theory to calculate the effective electric conductivity and Hall coefficient tensor of passive three-dimensionally periodic metamaterials subject to a weak external static homogeneous magnetic field. We not only…
We consider a model for a two dimensional electron gas moving on a kagom\'{e} lattice and locally coupled to a chiral magnetic texture. We show that the transverse conductivity $\sigma\_{xy}$ does not vanish even if spin-orbit coupling is…