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We develop a hydrodynamic description of the resistivity and magnetoresistance of an electron liquid in a smooth disorder potential. This approach is valid when the electron-electron scattering length is sufficiently short. In a broad range of temperatures, the dissipation is dominated by heat fluxes in the electron fluid, and the resistivity is inversely proportional to the thermal conductivity, $kappa$. This is in striking contrast with the Stokes flow, in which the resistance is independent of $kappa$ and proportional to the fluid viscosity. We also identify a new hydrodynamic mechanism of spin magnetoresistance.
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We report on angle-dependent measurements of the sheet resistances and Hall coefficients of electron liquids in SmTiO3/SrTiO3/SmTiO3 quantum well structures, which were grown by molecular beam epitaxy on (001) DyScO3. We compare their transport properties with those of similar structures grown on LSAT [(La0.3Sr0.7)(Al0.65Ta0.35)O3]. On DyScO3, planar defects normal to the quantum wells lead to a strong in-plane anisotropy in the transport properties. This allows for quantifying the role of defects in transport. In particular, we investigate differences in the longitudinal and Hall scattering rates, which is a non-Fermi liquid phenomenon known as lifetime separation. The residuals in both the longitudinal resistance and Hall angle were found to depend on the relative orientations of the transport direction to the planar defects. The Hall angle exhibited a robust T2 temperature dependence along all directions, whereas no simple power law could describe the temperature dependence of the longitudinal resistances. Remarkably, the degree of the carrier lifetime separation, as manifested in the distinctly different temperature dependences and diverging residuals near a critical quantum well thickness, was completely insensitive to disorder. The results allow for a clear distinction between disorder-induced contributions to the transport and intrinsic, non-Fermi liquid phenomena, which includes the lifetime separation.
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.
We develop the theory of hydrodynamic electron transport in a long-range disorder potential for conductors in which the underlying electron liquid lacks Galilean invariance. For weak disorder, we express the transport coefficients of the system in terms of the intrinsic kinetic coefficients of the electron liquid and the correlation function of the disorder potential. We apply these results to analyze the doping and temperature dependence of transport coefficients of graphene devices. We show that at charge neutrality, long-range disorder increases the conductivity of the system above the intrinsic value. The enhancement arises from the predominantly vortical hydrodynamic flow caused by local deviations from charge neutrality. Its magnitude is inversely proportional to the shear viscosity of the electron liquid and scales as the square of the disorder correlation radius. This is qualitatively different from the situation away from charge neutrality. In that case, the flow is predominantly potential, and produces negative viscous contributions to the conductivity, which are proportional to the sum of shear and bulk viscosities, and inversely proportional to the square of disorder correlation radius.
We present an overview of the measured transport properties of the two dimensional electron fluids in high mobility semiconductor devices with low electron densities, and of some of the theories that have been proposed to account for them. Many features of the observations are not easily reconciled with a description based on the well understood physics of weakly interacting quasiparticles in a disordered medium. Rather, they reflect new physics associated with strong correlation effects, which warrant further study.
We derive the system of hydrodynamic equations governing the collective motion of massless fermions in graphene. The obtained equations demonstrate the lack of Galilean- and Lorentz invariance, and contain a variety of nonlinear terms due to quasi-relativistic nature of carriers. Using those equations, we show the possibility of soliton formation in electron plasma of gated graphene. The quasi-relativistic effects set an upper limit for soliton amplitude, which marks graphene out of conventional semiconductors. The lack of Galilean and Lorentz invariance of hydrodynamic equations is revealed in spectra of plasma waves in the presence of steady flow, which no longer obey the relations of Doppler shift. The possibility of plasma wave excitation by direct current in graphene channels is also discussed.
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