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Register a new userDrag viscosity of metals and its connection to Coulomb drag
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Recent years have seen a surge of interest in studies of hydrodynamic transport in electronic systems. We investigate the electron viscosity of metals and find a new component that is closely related to Coulomb drag. Using the linear response theory, viscosity, a transport coefficient for momentum, can be extracted from the retarded correlation function of the momentum flux, i.e., the stress tensor. There exists a previously overlooked contribution to the shear viscosity from the interacting part of the stress tensor which accounts for the momentum flow induced by interactions. This contribution, which we dub drag viscosity, is caused by the frictional drag force due to long-range interactions. It is therefore linked to Coulomb drag which also originates from the interaction induced drag force. Starting from the Kubo formula and using the Keldysh technique, we compute the drag viscosity of 2D and 3D metals along with the drag resistivity of double-layer 2D electronic systems. Both the drag resistivity and drag viscosity exhibit a crossover from quadratic-in-T behavior at low temperatures to a linear one at higher temperatures. Although the drag viscosity appears relatively small compared with the normal Drude component for the clean metals, it may dominate hydrodynamic transport in some systems, which are discussed in the conclusion.
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Coulomb drag is a process whereby the repulsive interactions between electrons in spatially separated conductors enable a current flowing in one of the conductors to induce a voltage drop in the other. If the second conductor is part of a closed circuit, a net current will flow in that circuit. The drag current is typically much smaller than the drive current owing to the heavy screening of the Coulomb interaction. There are, however, rare situations in which strong electronic correlations exist between the two conductors. For example, bilayer two-dimensional electron systems can support an exciton condensate consisting of electrons in one layer tightly bound to holes in the other. One thus expects perfect drag; a transport current of electrons driven through one layer is accompanied by an equal one of holes in the other. (The electrical currents are therefore opposite in sign.) Here we demonstrate just this effect, taking care to ensure that the electron-hole pairs dominate the transport and that tunneling of charge between the layers is negligible.
Using a novel structure, consisting of two, independently contacted graphene single layers separated by an ultra-thin dielectric, we experimentally measure the Coulomb drag of massless fermions in graphene. At temperatures higher than 50 K, the Coulomb drag follows a temperature and carrier density dependence consistent with the Fermi liquid regime. As the temperature is reduced, the Coulomb drag exhibits giant fluctuations with an increasing amplitude, thanks to the interplay between coherent transport in the graphene layer and interaction between the two layers.
The presence of pronounced electronic correlations in one-dimensional systems strongly enhances Coulomb coupling and is expected to result in distinctive features in the Coulomb drag between them that are absent in the drag between two-dimensional systems. We review recent Fermi and Luttinger liquid theories of Coulomb drag between ballistic one-dimensional electron systems, and give a brief summary of the experimental work reported so far on one-dimensional drag. Both the Fermi liquid (FL) and the Luttinger liquid (LL) theory predict a maximum of the drag resistance R_D when the one-dimensional subbands of the two quantum wires are aligned and the Fermi wave vector k_F is small, and also an exponential decay of R_D with increasing inter-wire separation, both features confirmed by experimental observations. A crucial difference between the two theoretical models emerges in the temperature dependence of the drag effect. Whereas the FL theory predicts a linear temperature dependence, the LL theory promises a rich and varied dependence on temperature depending on the relative magnitudes of the energy and length scales of the systems. At higher temperatures, the drag should show a power-law dependence on temperature, $R_D ~ T^x$, experimentally confirmed in a narrow temperature range, where x is determined by the Luttinger liquid parameters. The spin degree of freedom plays an important role in the LL theory in predicting the features of the drag effect and is crucial for the interpretation of experimental results.
We report Coulomb drag measurements between vertically-integrated quantum wires separated by a barrier only 15 nm wide. The temperature dependence of the drag resistance is measured in the true one-dimensional (1D) regime where both wires have less than one 1D subband occupied. As a function of temperature, an upturn in the drag resistance is observed in three distinct devices at a temperature $T^* sim 1.6$ K. This crossover in Coulomb drag behaviour is consistent with Tomonaga-Luttinger liquid models for the 1D-1D drag between quantum wires.
We find that the temperature dependence of the drag resistivity ($rho_{D}$) between two dilute two-dimensional hole systems exhibits an unusual dependence upon spin polarization. Near the apparent metal-insulator transition, the temperature dependence of the drag, given by $T^{alpha}$, weakens with the application of a parallel magnetic field ($B_{||}$), with $alpha$ saturating at half its zero field value for $B_{||} > B^{*}$, where $B^{*}$ is the polarization field. Furthermore, we find that $alpha$ is roughly 2 at the parallel field induced metal-insulator transition, and that the temperature dependence of $rho_{D}/T^{2}$ at different $B_{||}$ looks strikingly similar to that found in the single layer resistivity. In contrast, at higher densities, far from the zero field transition, the temperature dependence of the drag is roughly independent of spin polarization, with $alpha$ remaining close to 2, as expected from a simple Fermi liquid picture.
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