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arXiv:1706.03775 · Physical review. B./Physical review. B

Hydrodynamic flows of non-Fermi liquids: Magnetotransport and bilayer drag

Aavishkar A. Patel, Richard A. Davison, Alex Levchenko

Published Nov 9, 2017• 21 citations
arXivHTMLPDF

Abstract

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 $U(1)$ 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.

DOI
10.1103/physrevb.96.205417

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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.
The hydrodynamic regime of electron transport has been recently realized in conductors with ultralow densities of defects. Although relaxation processes in two-dimensional (2D) fluids have been studied in many theoretical works, the viscosity of the realistic Fermi gas of 2D electrons having a quadratic energy spectrum and interacting by Coulomb's law has not been reliably determined either in theory or in experiment. Here, we construct a theory of viscosity and thermal conductivity in such a system. We compare the calculated viscosity of the 2D electron Fermi gas and the previously known viscosity of a 2D Fermi liquid with available experimental data extracted from the hydrodynamic negative magnetoresistance of the best-quality GaAs quantum wells. Based on this comparison, we argue that measurements of the temperature dependence of the viscosity can allow us to trace the transition between an electron Fermi liquid and a Fermi gas.
Modern quantum materials host a wide range of electronic phases in which transport properties are governed by strong interactions and collective effects. This thesis investigates charge, heat, and momentum transport in interacting electronic systems across different theoretical frameworks, ranging from Fermi liquid theory to strongly coupled strange metals.The first part of the thesis focuses on two-dimensional Fermi liquids at finite temperature, where rapid electron-electron scattering can give rise to hydrodynamic behavior. A kinetic-theory framework allowing an exact treatment of quasiparticle distribution functions beyond the asymptotic low-temperature regime is used to compute the full spectrum of collective modes, providing a detailed characterization of long-lived odd-parity excitations and the intermediate transport regime between ballistic and hydrodynamic flow. The same framework is employed to determine the shear viscosity of interacting electron liquids beyond conventional perturbative limits.The second part of the thesis concerns strongly interacting quantum systems where the quasiparticle picture breaks down.Holographic duality is used to study transport and thermoelectric response in quantum critical systems subject to periodic potentials, providing a controlled framework for momentum relaxation and magnetotransport in non-Fermi liquids. The thesis further develops holographic models of collective charge dynamics in systems with dynamical electromagnetism, including bulk plasmons and surface plasmon polaritons, and explores connections between Fermi surface physics and holographic gauge-field dynamics.
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 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.
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 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.