We investigate the effect of electron-electron interaction on the temperature dependence of the Hall coefficient of 2D electron gas at arbitrary relation between the temperature T and the elastic mean-free time τ . At small temperature T τ ≪h we reproduce the known relation between the logarithmic temperature dependences of the Hall coefficient and of the longitudinal conductivity. At higher temperatures, this relation is violated quite rapidly; correction to the Hall coefficient becomes ∝ 1/T whereas the longitudinal conductivity becomes linear in temperature.
We develop a hydrodynamic description of transport properties in graphene-based systems, which we derive from the quantum kinetic equation. In the interaction-dominated regime, the collinear scattering singularity in the collision integral leads to fast unidirectional thermalization and allows us to describe the system in terms of three macroscopic currents carrying electric charge, energy, and quasiparticle imbalance. Within this "three-mode" approximation, we evaluate transport coefficients in monolayer graphene as well as in double-layer graphene-based structures. The resulting classical magnetoresistance is strongly sensitive to the interplay between the sample geometry and leading relaxation processes. In small, mesoscopic samples, the macroscopic currents are inhomogeneous, which leads to a linear magnetoresistance in classically strong fields. Applying our theory to double-layer graphene-based systems, we provide a microscopic foundation for a phenomenological description of giant magnetodrag at charge neutrality and find the magnetodrag and Hall drag in doped graphene.
U. BRISKOT et al. PHYSICAL REVIEW B 92, 115426 (2015) and therefore is not a conserved quantity. However, it is conserved in the collinear scattering processes and hence the corresponding relaxation rate does not contain the logarithmic enhancement. Finally, the imbalance current j I is proportional to the sign of the quasiparticle energy and to the velocity. Similarly to the electric current, it does not experience logarithmically enhanced relaxation. The imbalance current is related to the quasiparticle number or imbalance density [10] n I = n + + n − , where n + and n − are the particle numbers in the upper (conduction) and lower (valence) bands. Neglecting the Auger processes, quasiparticle recombination due to, e.g., electron-phonon interaction, and three-particle collisions due to weak coupling, one finds that n + and n − are conserved independently. In this case, which will be considered in the rest of the paper, not only the total charge density n = n + − n − , but also the quasiparticle density n I is conserved.At times longer than τ g , physical observables can be described within the macroscopic (or hydrodynamic) approach. The existence of the three slow-relaxing modes in graphene implies a peculiar two-step thermalization.Short-time electron-electron scattering (at time scales up to τ g ) establishes the so-called "unidirectional thermalization" [24]: the collinear scattering singularity implies that the electron-electron interaction is more effective along the same direction. Within linear response [18], one can express the nonequilibrium distribution function in terms of the three macroscopic currents j , j E , and j I . The currents can then be found from the macroscopic equations. The currents j and j I are not conserved and can be relaxed by the electron-electron interaction. Close to charge neutrality, the corresponding relaxation rates can be estimated as [6,40] g . These rates enter the macroscopic equations as frictionlike terms. The macroscopic linear-response theory has the same form on time scales shorter or longer than τ ee .Beyond linear response, the scattering processes characterized by the time scale τ ee play an important role in thermalizing quasiparticles moving in different directions and thus lead to establishing the local equilibrium. This is the starting point for derivation of the nonlinear hydrodynamics, which is valid at time scales much longer than τ ee . In view of conservation of the particle number, energy, and momentum, as well as independent conservation of the number of particles in the two bands in graphene, we may write the local equilibrium distribution function as [12,14] where ε λ,k = λv g k denotes the energies of the electronic states with the momentum k in the band λ = ±, μ λ (r) the local chemical potential, the local temperature is encoded in β(r) = 1/T (r), and u(r) is the hydrodynamic velocity field which we define in the following (this field should not be confused with quasiparticle velocities v). The distribution function (1) follows from the sta...
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