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arXiv:1312.6890 · Physical Review B

Hydrodynamic Coulomb drag of strongly correlated electron liquids

S. S. Apostolov, Alex Levchenko, Anton V. Andreev

Published Mar 11, 2014• 27 citations
arXivHTMLPDF

Abstract

We develop a theory of Coulomb drag in ultraclean double layers with strongly correlated carriers. In the regime where the equilibration length of the electron liquid is shorter than the interlayer spacing the main contribution to the Coulomb drag arises from hydrodynamic density fluctuations. The latter consist of plasmons driven by fluctuating longitudinal stresses, and diffusive modes caused by temperature fluctuations and thermal expansion of the electron liquid. We express the drag resistivity in terms of the kinetic coefficients of the electron fluid. Our results are nonperturbative in interaction strength and do not assume Fermi-liquid behavior of the electron liquid.

DOI
10.1103/physrevb.89.121104

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We develop a theory of Coulomb drag in ultraclean double layers with strongly correlated carriers. In the regime where the equilibration length of the electron liquid is shorter than the interlayer spacing the main contribution to the Coulomb drag arises from hydrodynamic density fluctuations. The latter consist of plasmons driven by fluctuating longitudinal stresses, and diffusive modes caused by temperature fluctuations and thermal expansion of the electron liquid. We express the drag resistivity in terms of the kinetic coefficients of the electron fluid. Our results are nonperturbative in interaction strength and do not assume Fermi-liquid behavior of the electron liquid.
We study Coulomb drag between an active layer with a clean electron liquid and a passive layer with a pinned electron lattice in the regime of fast intralayer equilibration. Such a two-fluid system offers an experimentally realizable way to disentangle the fast rate of intralayer electron-electron interactions from the much slower rate of momentum transfer between both layers. We identify an intermediate temperature range above the Fermi energy of the electron fluid but below the Debye energy of the electronic crystal where the hydrodynamic drag resistivity is directly proportional to a fast electron-electron scattering rate. The results are compatible with the conjectured scenario for strong electron-electron interactions which poses that a linear temperature dependence of resistivity originates from a ``Planckian'' electron relaxation time ${\ensuremath{\tau}}_{eq}\ensuremath{\sim}\ensuremath{\hbar}/{k}_{B}T$. We compare this to the better known semiclassical case, where the diffusion constant is found to be not proportional to the microscopic timescale.
We develop the theory of hydrodynamic fluctuations for one-dimensional quantum liquids. At low temperatures the relaxation of interacting electrons in a single-channel wire separates into two classes: equilibration, which changes the numbers of right and left movers through backscattering and is exponentially slow, and thermalization, which redistributes energy and momentum at a fixed number of movers at a power-law rate. This separation of time scales gives the electron liquid a two-fluid description analogous to superfluid 4^44He, with the zero mode of the Luttinger liquid as the superfluid component and the gas of thermal excitations as the normal component. Using Onsager reciprocity and the fluctuation-dissipation theorem, we add Langevin fluxes to the two-fluid hydrodynamic equations, including a mutual-friction noise generated by rare backscattering events that has no counterpart in helium. We apply the theory to Coulomb-coupled quantum wires and calculate the dynamic structure factors, which contain a second-sound peak next to the plasmon doublet; the Coulomb drag resistivity, where intrawire equilibration acts as a bottleneck and turns the hydrodynamic drag into an activated temperature dependence; and the near-field heat transfer between the wires. Mode frequencies, spectral weights, linewidths, and the crossover scales of the transport coefficients are expressed through the thermodynamic properties of the liquid and a few dissipative coefficients, providing spectroscopic and transport probes of two-fluid behavior in one-dimensional quantum systems.
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 component that is closely related to Coulomb drag. By using linear-response theory, viscosity, which is 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 two- and three-dimensional metals along with the drag resistivity of double-layer two-dimensional electronic systems. Both the drag resistivity and drag viscosity exhibit a crossover from quadratic-in-TTT behavior at low temperatures to a linear behavior 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.
We consider a hydrodynamic description of transport for generic two-dimensional electron systems that lack Galilean invariance and do not fall into the category of Fermi liquids. We study magnetoresistance and show that it is governed only by the electronic viscosity provided that the wavelength of the underlying disorder potential is large compared to the microscopic equilibration length. We also derive the Coulomb drag transresistance for double-layer non-Fermi-liquid systems in the hydrodynamic regime. As an example, we consider frictional drag between two quantum Hall states with half-filled lowest Landau levels, each described by a Fermi surface of composite fermions coupled to a U(1)U(1)U(1) gauge field. We contrast our results to prior calculations of drag of Chern-Simons composite particles and place our findings in the context of available experimental data.
This thesis focuses on several examples of strongly correlated electronic quantum fluids. In chapter 2 we use a kinetic theory approach to describe the transport properties of bilayer graphene near charge neutrality. After solving the semiclassical Boltzmann equation, we find that the results are well approximated by a hydrodynamic two-fluid model. A fluid of electrons and a fluid of holes interact with each other via Coulomb drag. Chapter 3 looks at quantum Hall edges. We consider a quantum Hall edge coupled to a driven quantum dot and compute the current on the edge downstream from the contact. We show that Coulomb interactions between the dot and the edge renormalize the charge in the current pulses. Chapter 4 focuses on the bilayer quantum Hall system. Two layers of quantum Hall fluid are separated by a variable distance. At large interlayer separation, we have two well-separated composite Fermi liquids and we consider the pairing between the two layers as the interlayer separation is decreased. We propose a new trial state for this paired phase of matter and use exact diagonalization numerics to investigate this proposal.
We address Coulomb drag and near-field heat transfer in a double-layer system of incoherent metals. Each layer is modeled by an array of tunnel-coupled SYK dots with random interlayer interactions. Depending on the strength of intradot interactions and interdot tunneling, this model captures the crossover from the Fermi liquid to a strange metal phase. The absence of quasiparticles in the strange metal leads to temperature-independent drag resistivity, which is in strong contrast with the quadratic temperature dependence in the Fermi liquid regime. We show that all the parameters can be independently measured in near-field heat transfer experiments, performed in Fermi liquid and strange metal regimes.