In this study, we investigate the conductivity of a two-dimensional (2D) system in HgTe quantum well comprising two types of carriers with linear and quadratic spectra, respectively. The interactions between the two-dimensional Dirac holes and the heavy holes lead to the breakdown of Galilean invariance, resulting in interaction -limited resistivity. Our exploration of the transport properties spans from low temperatures, where both subsystems are fully degenerate, to higher temperatures, where the Dirac holes remain degenerate while the heavy holes follow Boltzmann statistics, creating a partially degenerate regime. Through a developed theory, we successfully predict the behavior of resistivity as rho similar to T2 and rho similar to T3 for the fully degenerate and partially degenerate regimes, respectively, which is in reasonable agreement with experimental observations. Notably, at elevated temperatures, the interaction -limited resistivity surpasses the resistivity caused by impurity scattering by a factor of 5-6. These findings imply that the investigated system serves as a versatile experimental platform for exploring various interaction -limited transport regimes in two component plasma.

The resistivity of two-dimensional (2D) metals generally exhibits insensitivity to electron -electron scattering. However, it is worth noting that Galilean invariance may not hold true in systems characterized by a spectrum containing multiple electronic branches or in scenarios involving electron -hole plasma. In the context of this paper, we focus on 2D electrons confined within a triple quantum well (TQW) based on HgTe. This system displays a coexistence of energy bands featuring both linear and paraboliclike spectra at low energy and, therefore, lacks the Galilean invariance. This paper employs a combined theoretical and experimental approach to investigate the transport properties of this two -component system across various regimes. By manipulating carrier density and temperature, we tune our system from a fully degenerate regime, where resistance follows a temperature -dependent behavior proportional to T 2 to a regime where both types of electrons adhere to Boltzmann statistics. In the nondegenerate regime, electron interactions lead to resistance that is weakly dependent on temperature. Notably, our experimental observations closely align with the theoretical predictions derived in this paper. In this paper, we establish the HgTe-based TQW as a promising platform for exploring different interaction -dominant scenarios for the massless -massive Dirac system.

We investigated magnetotransport in mesoscopic samples containing electrons from three different subbands in GaAs triple wells. At high temperatures, we observed positive magnetoresistance, which we attribute to the imbalance between different types of particles that are sensitive to bulk viscosities. At low temperatures, we found negative magnetoresistance, attributed to shear viscosity. By analyzing the magnetoresistance data, we were able to determine both viscosities. Remarkably, the electronic bulk viscosity was significantly larger than the shear viscosity. Studying multicomponent electron systems in the hydrodynamic regime presents an intriguing opportunity to further explore the physics in systems with high bulk viscosity.

We investigated magnetotransport in mesoscopic samples containing electrons from three different subbands in GaAs triple wells. At high temperatures, we observed positive magnetoresistance, which we attribute to the imbalance between different types of particles that are sensitive to bulk viscosities. At low temperatures, we found negative magnetoresistance, attributed to shear viscosity. By analyzing the magnetoresistance data, we were able to determine both viscosities. Remarkably, the electronic bulk viscosity was significantly larger than the shear viscosity. Studying multicomponent electron systems in the hydrodynamic regime presents an intriguing opportunity to further explore the physics in systems with high bulk viscosity.

Two-dimensional topological insulators are characterized by the bulk gap and one-dimensional helical states running along the edges. The theory predicts the topological protection of the helical transport from coherent backscattering. However, the unexpected deviations of the conductance from the quantized value and localization of the helical modes are generally observed in long samples. Moreover, at millikelvin temperatures significant mesoscopic fluctuations are developed as a function of the electron energy. Here we report the results of an experimental study of the transport in a HgTe quantum well with an inverted energy spectrum that reveal a multifractality of the conductance fluctuations in the helical edge state dominated transport regime. We attribute observed multifractality to mesoscopic fluctuations of the electron wave function or local density of states at the spin quantum Hall transition. We have shown that the mesoscopic two-dimensional topological insulator provides a highly tunable experimental system in which to explore the physics of the Anderson transition between topological states.

In this study, we present our experimental investigation on the magnetotransport properties of a two-dimensional electron system in GaAs quantum wells utilizing a variety of device geometries, including obstacles with thin barriers and periodic width variations. Our primary focus is to explore the impact of these geometries on the electron viscous flow parameters, enabling precise manipulation of hydrodynamic effects under controlled conditions. Through an analysis of the large negative magnetoresistivity and zero field resistivity, we deduce the scattering times for electron-electron and electron-phonon interactions, as well as the effective channel width. Our findings confirm that the system under investigation serves as a tunable experimental platform for investigating hydrodynamic transport regimes at temperatures above 10 K.

The recombination dynamics are studied in viscous electron–hole plasma, consisting of electrons and photo-generated heavy and light holes, formed in the high-mobility mesoscopic GaAs channel. It is shown that an increase in the pump power reduces the concentration and mobility of background electrons, which, in turn, slows down their recombination with photogenerated holes. At a critical pump power, the recombination time begins to decrease, which is a consequence of the transition of a viscous electron–hole plasma from the hydrodynamic regime to the Drude diffusive regime. The observed transition occurs when the scattering of electrons with disorder begins to dominate over electron–electron scattering, which leads to the transformation of an inhomogeneous Poiseuille charge flow into a homogeneous diffusion flow. As a result, an optical analogue of the Gurzhi effect has been found.

We study the transport properties of HgTe quantum wells with critical well thickness, where the band gap is closed and the low energy spectrum is described by a single Dirac cone. In this work, we examined both macroscopic and micron-sized (mesoscopic) samples. In micron-sized samples, we observe a magnetic-field-induced quantized resistance (~h/2e) at Landau filling factor ν=0, corresponding to the formation of helical edge states centered at the charge neutrality point (CNP). In macroscopic samples, the resistance near a zero Landau level (LL) reveals strong oscillations, which we attribute to scattering between the edge ν=0 state and bulk ν≠0 hole LL. We provide a model taking an empirical approach to construct a LL diagram based on a reservoir scenario, formed by the heavy holes.

We observe a large negative magnetoresistance and a decrease of resistivity with increasing temperature, known as the Gurzhi effect, in a bilayer electron (BL) system formed by a wide GaAs quantum well. A hydrodynamic model for the single fluid transport parameters in narrow channels is employed and successfully describes our experimental findings. We find that the electron-electron scattering in the bilayer is more intensive in comparison with a single-band well (SW). The hydrodynamic assumption implies a strong dependence on boundary conditions, which can be characterized by slip length, describing the behavior of a liquid near the edge. Our results reveal that slip length in a BL is shorter than in a SW, and that the BL system goes deeper into the hydrodynamic regime. This is in agreement with the model proposed where the slip length is of the order of the electron-electron mean free path.

The thermoelectric response of 80 nm-thick strained HgTe films of a three-dimensional topological insulator (3D TI) has been studied experimentally. An ambipolar thermopower is observed where the Fermi energy moves from conducting to the valence bulk band. The comparison between theory and experiment shows that the thermopower is mostly due to the phonon drag contribution. In the region where the 2D Dirac electrons coexist with bulk hole states, the Seebeck coefficient is modified due to 2D electron–3D hole scattering.

We present a semiclassical approximation for treating the radiation from classical currents. In particular, we present exact quantum states of the quantized electromagnetic field interacting with classical currents. These states are used to calculate a probability of many-photon radiation from the vacuum initial state of the electromagnetic field. In this manner, in the present article, we study characteristics of electromagnetic radiation of a planar undulator. We find the total radiated energy and its spectral-angular distribution. We compare our results with ones obtained in the framework of classical electrodynamics, discussing differences introduced by accurate accounting for the quantum nature of electromagnetic radiation and present results of some numerical calculations that confirm, in particular, the latter discussion. In Appendix we present the calculation of the radiated energy using an alternative parametrization of the trajectory of electrons moving in a planar undulator.

We develop a classical kinetic theory of magnetotransport of 2D electrons in narrow channels with partly diffusive boundary scattering and apply it to the description of magnetoresistance measured in the temperature interval 4.2-30 K in long mesoscopic bars fabricated from high-purity GaAs quantum well structures. Both experiment and theory demonstrate a number of characteristic features in the longitudinal and Hall resistances caused by the size effect in two dimensions owing to the high ballisticity of the transport. In addition to the features described previously, we also reveal a change in the slope of the first derivative of magnetoresistance when the cyclotron orbit diameter equals to half of the channel width. These features are suppressed with increasing temperature as a result of the electronic viscosity due to electron-electron interaction. By comparing theory and experiment, we determine the characteristic time of relaxation of angular distribution of electrons caused by electron-electron scattering.

The electronic analog of the Poiseuille flow is the transport in a narrow channel with disordered edges that scatter electrons in a diffuse way. In the hydrodynamic regime, the resistivity decreases with temperature, referred to as the Gurzhi effect, distinct from conventional Ohmic behaviour. We studied experimentally an electronic analog of the Stokes flow around a disc immersed in a two-dimensional viscous liquid. The circle obstacle results in an additive contribution to resistivity. If specular boundary conditions apply, it is no longer possible to detect Poiseuille type flow and the Gurzhi effect. However, in flow through a channel with a circular obstacle, the resistivity decreases with temperature. By tuning the temperature, we observed the transport signatures of the ballistic and hydrodynamic regimes on the length scale of disc size. Our experimental results confirm theoretical predictions.

The interaction of electrons with a flux of ballistic phonons leads to excitation of many angular harmonics of an electron distribution function. We show that this property dramatically modifies the magnetothermoelectric phenomena in two-dimensional electron systems with boundaries. By considering classical magnetotransport of electrons in a narrow channel with partly diffusive boundary scattering, we show that the phonon flux excites a pattern of current stripes with alternating directions of propagation along the channel. The Nernst voltage due to phonon drag appears already in the classical transport regime and can be comparable with the Seebeck voltage, while the latter acquires a dependence on the magnetic field. The temperature dependence of these voltages shows an unusual behavior determined by relaxation of higher-order harmonics of the distribution function via electron-electron scattering. Our experimental studies of mesoscopic samples based on high-quality GaAs quantum wells confirm the main properties of the thermoelectric response suggested by the theory.

The thermoelectric response of HgTe quantum wells in the state of two-dimensional topological insulator (2D TI) has been studied experimentally. Ambipolar thermopower, typical for an electron–hole system, has been observed across the charge neutrality point, where the carrier type changes from electrons to holes according to the resistance measurements. The hole-type thermopower is much stronger than the electron-type one. The thermopower linearly increases with temperature. We present a theoretical model which accounts for both the edge and bulk contributions to the electrical conductivity and thermoelectric effect in a 2D TI, including the effects of edge to bulk leakage. The model, contrary to previous theoretical studies, demonstrates that the 2D TI is not expected to show anomalies of thermopower near the band conductivity threshold, which is consistent with our experimental results. Based on the experimental data and theoretical analysis, we conclude that the observed thermopower is mostly of the bulk origin, while the resistance is determined by both the edge and bulk transport.

We have measured the differential resistance in a two-dimensional topological insulator (2DTI) in a HgTe quantum well, as a function of the applied dc current. The transport near the charge neutrality point is characterized by a pair of counter propagating gapless edge modes. In the presence of an electric field, the energy is transported by counter propagating channels in the opposite direction. We test a hot carrier effect model and demonstrate that the energy transfer complies with the Wiedemann Franz law near the charge neutrality point in the edge transport regime.

We have measured the differential resistance in a two-dimensional topological insulator (2DTI) in a HgTe quantum well, as a function of the applied dc current. The transport near the charge neutrality point is characterized by a pair of counter propagating gapless edge modes. In the presence of an electric field, the energy is transported by counter propagating channels in the opposite direction. We test a hot carrier effect model and demonstrate that the energy transfer complies with the Wiedemann Franz law near the charge neutrality point in the edge transport regime.

In this paper, we consider two examples of an entanglement in two-qubit systems and an example of entanglement in quantum field theory (QFT). In the beginning, we study the entanglement of two spin states by a magnetic field. A nonzero entanglement appears for interacting spins. When the coupling between the spins is constant, we study the entanglement by several types of time-dependent magnetic fields. In the case of a constant difference between [Formula: see text] components of magnetic fields acting on each spin, we find several time-dependent coupling functions [Formula: see text] that also allow us to analyze analytically and numerically the entanglement measure. Considering two photons moving in an electron medium, we demonstrate that they can be entangled in a controlled way by applying an external magnetic field. The magnetic field affecting electrons of the medium affects photons and, thus, causes an entanglement of the photon beams. The third example is related to the effect of production of electron–positron pairs from the vacuum by a strong external electric field. Here, we have used a general nonperturbative expression for the density operator of the system under consideration. Applying a reduction procedure to this density operator, we construct mixed states of electron and positron subsystems. Calculating the von Neumann entropy of such states, we obtain the loss of information due to the reduction and, at the same time, the entanglement measure of electron and positron subsystems. This entanglement can be considered as an example of an entanglement in QFT.

Hall viscosity is a nondissipative response function describing momentum transport in two-dimensional (2D) systems with broken time-reversal symmetry. In the classical regime, Hall viscosity contributes to the viscous flow of 2D electrons in the presence of a magnetic field. We observe a pronounced, negative Hall resistivity at low magnetic field in a mesoscopic size, two-dimensional electron system, which is attributed to Hall viscosity in the inhomogeneous charge flow. Experimental results supported by a theoretical analysis confirm that the conditions for observation of Hall viscosity are correlated with predictions.