The electron-electron scattering does not affect the electrical current in Galilean-invariant systems. We show that, nevertheless, electron-electron collisions may contribute to the electric resistivity of systems with parabolic spectrum provided that they have multiply connected Fermi surfaces, and there is an additional mechanism of scattering. To this end, we calculate the resistivity of a two-dimensional electron gas with two filled transverse subbands in a presence of electron-electron and impurity scattering. Although the collisions between the electrons do not directly affect the current in such systems, they cause a redistribution of the electrons between the Fermi contours, which results in a noticeable change in resistivity for realistic mechanisms of impurity scattering.

Two-dimensional systems with Rashba spin-orbit coupling are not Galilean invariant and therefore electron–electron collisions in them may affect the current. However when taken alone, they cannot ensure a nonzero dc resistivity, so their effects are masked by impurity scattering. Here we calculate the related finite-frequency response and show that the electron–electron scattering in clean Rashba conductors decreases the Drude weight while resulting in a finite dissipative component of the response outside of the Drude peak.

The electron-electron scattering does not affect the electrical current in Galilean-invariant systems. We show that nevertheless electron-electron collisions may contribute to the electric resistivity of systems with parabolic spectrum provided that they have multiply connected Fermi surface and there is an additional mechanism of scattering. To this end, we calculate the resistivity of a two-dimensional electron gas with two filled transverse subbands in a presence of electron-electron and impurity scattering. Though the collisions between the electrons do not directly affect the current in such systems, they cause a redistribution of the electrons between the Fermi contours, which results in a noticeable change of resistivity for realistic mechanisms of impurity scattering.

We calculate the electrical and thermal conductivity of a two-dimensional electron gas with strong spin-orbit coupling in which the scattering is dominated by electron-electron collisions. Despite the apparent absence of Galilean invariance in the system, the two-particle scattering does not affect the electrical conductivity above the band-crossing point where both helicity bands are filled. Below the band-crossing point where one helicity band is empty, switching on the electron-electron scattering leads only to a limited decrease in the electrical conductivity so that its high-temperature value is independent of the scattering intensity. In contrast to this, thermal conductivity is not strongly affected by the spin-orbit coupling and exhibits only a kink as the Fermi level passes through the band-crossing point.

The electrical resistivity of a 2D electron gas that results from two‐particle collisions and strong Rashba spin–orbit coupling is calculated. When combined with impurity scattering, the two‐particle correction to the resistivity is proportional to the square of temperature T if only the lower helicity band is filled, but the term vanishes if the Fermi level is above the Dirac point. If only the electron–electron scattering is present, the resistivity is proportional to below and above the Dirac point, but this term vanishes at the point itself. The results have implications for other systems with doubly‐connected Fermi surfaces.

Electron-electron collisions are known to cause a nonlocal voltage drop in the presence of current flow. The semiphenomenological theory predicts this drop to be opposite to the direction of the current in the ballistic regime. We use a microscopic approach and show that the sign of this drop may be of both signs depending on the temperature and the distance between the source and probe contacts. The change of sign corresponds to the change of the dominant scattering process from head-on collisions to backward scattering of electrons. Our results agree with the experimental data.

This is a detailed derivation of the equation for the voltage noise of a resistively shunted Josephson junction with non-sinusoidal current-phase relation, which was presented in Sov. Phys. JETP {\bf 67}, 579 (1988).

The electron-electron scattering increases the resistance of ballistic many-mode channels whose width is smaller than their length. We show that this increase saturates in the limit of infinitely long channels. Because the mechanisms of angular relaxation of electrons in three and two dimensions are different, the saturation value of the correction to the resistance is temperature-independent in the case of three-dimensional channels and is proportional to the temperature for two-dimensional ones. The spatial behavior of electron distribution in the latter case is described by an unusual characteristic length.

We calculate an AC response of the edge states of a two-dimensional topological insulator, which can exchange electrons with a conducting puddle in the bulk of the insulator. This exchange leads to finite corrections to the response of isolated edge states both at low and high frequencies. By comparing these corrections, one may determine the parameters of the puddle.

We have investigated current-current correlations in a cross-shaped conductor made of graphene. The mean free path of charge carriers is on the order of the ribbon width which leads to a hybrid conductor where there is diffusive transport in the device arms while the central connection region displays near ballistic transport. Our data on auto and cross correlations deviate from the predictions of Landauer-B ü ttiker theory, and agreement can be obtained only by taking into account contributions from non-thermal electron distributions at the inlets to the semiballistic center, in which the partition noise becomes strongly modified. The experimental results display distinct Hanbury – Brown and Twiss (HBT) exchange correlations, the strength of which is boosted by the non-equilibrium occupation-number fluctuations internal to this hybrid conductor. Our work demonstrates that variation in electron coherence along atomically-thin, two-dimensional conductors has significant implications on their noise and cross correlation properties.

We investigate a possibility of pair electron-electron e-e collisions in a ballistic wire with spin-orbit coupling and only one populated mode. Unlike in a spin-degenerate system, a combination of spin-splitting in momentum space with a momentum-dependent spin-precession opens up a finite phase space for pair e-e collisions around three distinct positions of the wire's chemical potential. For a short wire, we calculate corresponding resonant contributions to the conductance, which have different power-law temperature dependencies, and, in some cases, vanish if the wire's transverse confinement potential is symmetric. Our results may explain the recently observed feature at the lower conductance plateau in InAs wires.

We calculate current (shot) noise in a metallic diffusive conductor generated by spin imbalance in the absence of a net electric current. This situation is modeled in an idealized three-terminal setup with two biased ferromagnetic leads (F-leads) and one normal lead (N-lead). Parallel magnetization of the F-leads gives rise to spin-imbalance and finite shot noise at the N-lead. Finite spin relaxation results in an increase in the shot noise, which depends on the ratio of the length of the conductor (L) and the spin relaxation length (l(s)). For L >> l(s) the shot noise increases by a factor of two and coincides with the case of the antiparallel magnetization of the F-leads.

We consider the relaxation of a uniform current in a planar 2D conductor with account taken of electromagnetic retardation effects. If the 2D conductivity is larger than the speed of light, the straightforward solution for an infinite plane gives a negative relaxation rate. However if one starts from a conducting cylinder of finite radius and then increases it to infinity, the relaxation rate just tends to zero while remaining positive. We suggest that recent unusual plasmon-dispersion curves obtained by V. A. Volkov and A. A. Zabolotnykh [arXiv:1605.00430] result from the incorrect finite-to-infinite transition.

Recent results on the effect of electron–electron collisions on the electric properties of contacts to a twodimensional electron gas with a direct conductivity in the absence of scattering by impurities and boundaries have been reviewed. A correction to the conductance of such contacts owing to the electron–electron scattering can be either positive or negative depending on the contact geometry. The magnitude of this correction strongly depends on the magnetic field.

We calculate the resistance and shot noise in the edge states of a 2D topological insulator that result from the exchange of electrons between these states and conducting puddles in the bulk of the insulator. The two limiting cases where the energy relaxation is either absent or very strong are considered. A finite time of spin relaxation in the puddles is introduced phenomenologically. Depending on this time and on the strength of coupling between the edge states and the puddles, the ratio of the shot noise to the Possonian one ranges from 0 to 1/3, which is in an agreement with the available experimental data.

We have investigated current-current correlations in a cross-shaped conductor made of graphene ribbons. We measured auto and cross correlations and compared them with the theoretical predictions for ideal diffusive conductors. Our data deviate from these predictions and agreement can be obtained only by adding contributions from occupation-number noise in the central region connecting the arms of the cross. Furthermore, we have determined Hanbury – Brown and Twiss (HBT) exchange correlations in this system. Contrary to expectations for a cross-shaped diffusive system, we find finite HBT exchange effects due to the occupation-number noise at the crossing. The strength of these HBT exchange correlations is found to vary with gate voltage, and very a distinct HBT effect with large fluctuations is observed near the Dirac point.

We present a simple quantum-mechanical derivation of correlation function of Langevin sources in the semiclassical Boltzmann–Langevin equation. The specific case of electron–phonon scattering is considered. It is shown that the assumption of weak scattering leads to the Poisson nature of the scattering fluxes.