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Register a new userViscous magnetoresistance of correlated electron liquids
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We develop a theory of magnetoresistance of two-dimensional electron systems in a smooth disorder potential in the hydrodynamic regime. Our theory applies to two-dimensional semiconductor structures with strongly correlated carriers when the mean free path due to electron-electron collisions is sufficiently short. The dominant contribution to magnetoresistance arises from the modification of the flow pattern by the Lorentz force, rather than the magnetic field dependence of the kinetic coefficients of the electron liquid. The resulting magnetoresistance is positive and quadratic at weak fields. Although the resistivity is governed by both viscosity and thermal conductivity of the electron fluid, the magnetoresistance is controlled by the viscosity only. This enables extraction of viscosity of the electron liquid from magnetotransport measurements.
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We report an universal behaviour of hopping transport in strongly interacting mesoscopic two-dimensional electron systems (2DES). In a certain window of background disorder, the resistivity at low perpendicular magnetic fields follows the expected relation $rho(B_perp) = rho_{rm{B}}exp(alpha B_perp^2)$. The prefactor $rho_{rm{B}}$ decreases exponentially with increasing electron density but saturates to a finite value at higher densities. Strikingly, this value is found to be universal when expressed in terms of absolute resistance and and shows quantisation at $R_{rm{B}}approx h/e^2$ and $R_{rm{B}}approx 1/2$ $ h/e^2$. We suggest a strongly correlated electronic phase as a possible explanation.
At low temperatures, in very clean two-dimensional (2D) samples the electron mean free path for collisions with static defects and phonons becomes greater than the sample width. Under this condition, the electron transport occurs by formation of a viscous flow of an electron fluid. We study the viscous flow of 2D electrons in a magnetic field perpendicular to the 2D layer. We calculate the viscosity coefficients as the functions of magnetic field and temperature. The off-diagonal viscosity coefficient determines the dispersion of the 2D hydrodynamic waves. The decrease of the diagonal viscosity in magnetic field leads to negative magnetoresistance which is temperature- and size dependent. Our analysis demonstrates that the viscous mechanism is responsible for the giant negative magnetoresistance recently observed in the ultra-high-mobility GaAs quantum wells. We conclude that 2D electrons in that structures in moderate magnetic fields should be treated as a viscous fluid.
A hydrodynamic flow of electrons driven by an oscillating electric field is investigated. It is found that a double-peak profile of the electric current can appear. Such a profile originates from the interplay of viscous and inertial properties of the electron fluid as well as the boundary conditions. The nontrivial profile of the current results in a characteristic stray magnetic field where peaks could also occur in one of the field components. Analytical results are supported by numerical calculations in samples of different geometries such as straight channel, nozzle, and cavity and are found to be qualitatively insensitive to a specific form of the oscillating electric field. In addition, it is shown that nozzle and cavity provide an efficient means to locally enhance or reduce the fluid velocity.
We investigate the magnetotransport in large area graphene Hall bars epitaxially grown on silicon carbide. In the intermediate field regime between weak localization and Landau quantization the observed temperature-dependent parabolic magnetoresistivity (MR) is a manifestation of the electron-electron interaction (EEI). We can consistently describe the data with a model for diffusive (magneto)transport that also includes magnetic-field dependent effects originating from ballistic time scales. We find an excellent agreement between the experimentally observed temperature dependence of MR and the theory of EEI in the diffusive regime. We can further assign a temperature-driven crossover to the reduction of the multiplet modes contributing to EEI from 7 to 3 due to intervalley scattering. In addition, we find a temperature independent ballistic contribution to the MR in classically strong magnetic fields.
In this work we consider the hydrodynamic behavior of a coupled electron-phonon fluid, focusing on electronic transport under the conditions of strong phonon drag. This regime occurs when the rate of phonon equilibration due to e.g. umklapp scattering is much slower than the rate of normal electron-phonon collisions. Then phonons and electrons form a coupled out-of-equilibrium state where the total quasi-momentum of the electron-phonon fluid is conserved. A joint flow-velocity emerges as a collective hydrodynamic variable. We derive the equation of motion for this fluid from the underlying microscopic kinetic theory and elucidate its effective viscosity and thermal conductivity. In particular, we derive decay times of arbitrary harmonics of the distribution function and reveal its corresponding super-diffusive relaxation on the Fermi surface. We further consider several applications of this theory to magneto-transport properties in the Hall-bar and Corbino-disk geometries, relevant to experiments. In our analysis we allow for general boundary conditions that cover the crossover from no-slip to no-stress flows. Our approach also covers a crossover from the Stokes to the Ohmic regime under the conditions of the Gurzhi effect. In addition, we consider the frequency dependence of the surface impedance and non-equilibrium noise. For the latter, we notice that in the diffusive regime, a Fokker-Planck approximation, applied to the electron-phonon collision integral in the Eliashberg form, reduces it to a differential operator with Burgers nonlinearity. As a result, the non-equilibrium distribution function has a shock-wave structure in the energy domain. The consequence of this behavior for the Fano factor of the noise is investigated. In conclusion we discuss connections and limitations of our results in the context of recent electron-phonon drag measurements in Dirac and Weyl semimetals.
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