Higher-than-ballistic conduction of viscous electron flows

Abstract

Strongly interacting electrons can move in a neatly coordinated way, reminiscent of the movement of viscous fluids. Here, we show that in viscous flows, interactions facilitate transport, allowing conductance to exceed the fundamental Landauer's ballistic limit G ball . The effect is particularly striking for the flow through a viscous point contact, a constriction exhibiting the quantum mechanical ballistic transport at T = 0 but governed by electron hydrodynamics at elevated temperatures. We develop a theory of the ballistic-to-viscous crossover using an approach based on quasi-hydrodynamic variables. Conductance is found to obey an additive relation G = G ball + G vis , where the viscous contribution G vis dominates over G ball in the hydrodynamic limit. The superballistic, low-dissipation transport is a generic feature of viscous electronics.electron hydrodynamics | graphene | strongly correlated systems F ree electron flow through constrictions in metals is often regarded as an ultimate high-conduction charge transfer mechanism (1-5). Can conductance ever exceed the ballistic limit value? Here we show that superballistic conduction is possible for strongly interacting systems in which electron movement resembles that of viscous fluids. Electron fluids are predicted to occur in quantum-critical systems and in high-mobility conductors, so long as momentum-conserving electron-electron (ee) scattering dominates over other scattering processes (6-9). Viscous electron flows feature a host of novel transport behaviors (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22). Signatures of such flows have been observed in ultraclean GaAs, graphene, and ultrapure PdCoO2 (23-26).We will see that electrons in a viscous flow can achieve through cooperation what they cannot accomplish individually. As a result, resistance and dissipation of a viscous flow can be markedly smaller than that for the free-fermion transport. As a simplest realization, we discuss viscous point contact (VPC), where correlations act as a "lubricant" facilitating the flow. The reduction in resistance arises due to the streaming effect illustrated in Fig. 1, wherein electron currents bundle up to form streams that bypass the boundaries, where momentum loss occurs. This surprising behavior is in a clear departure from the common view that regards electron interactions as an impediment for transport.A simplest VPC is a 2D constriction pictured in Fig. 1A. The interaction effects dominate in constrictions of width w exceeding the carrier collision mean free path lee (and much greater than the Fermi wavelength λF ). The VPC conductance, evaluated in the absence of impurity scattering, scales as a square of the width w and inversely with the electron viscosity η,where n and e are the carrier density and charge. In the opposite limit, lee w , the ballistic free-fermion model (1, 5) predicts the conductance G ball = 2e 2 /h N , where N ≈ 2w /λF is the number of Landauer's open transmission channels. The conductance G vis grows with width faster than G ball ...

Nonmonotonic magnetoresistance of a two-dimensional viscous electron-hole fluid in a confined geometry

“…In our theory, the Gurzhi resistance exceeds the inviscid Drude resistance. Note, that this is not a contradiction to either the recent observation of super-ballistic flow in graphene 6,53 or the original Gurzhi effect 52 . The reason is that we are considering the electronic fluid in the hydrodynamic regime to begin with and do not compare it with a ballistic (Knudsen-like 54 ) regime where the resistance is determined by the scattering off the system boundaries or large (macroscopic) obstacles.…”

Superballistic flow of viscous electron fluid through graphene constrictions

“…The quantity G ν is calculated for the Stokes flow through a PC in the extreme hydrodynamic regime (that is, for the e-e scattering length l ee w). The additive form of equation (2) is valid 18,19 for all values of l ee /w, even close to the ballistic regime l ee w. This implies that G should increase with T (in the first approximation 15,27 , as ∝1/l ee ∝ T 2 ), which leads to the initial drop in resistance (Fig. 1e).…”

“…To describe the non-metallic behaviour in our PCs, we first invoke the recent theory 18 that predicts that e-e scattering modifies equation (1) as…”

“…To describe both low-T and high-T regimes on an equal footing, we extended the transport model of ref. 18 to account for acousticphonon scattering using an additional term ∝T in the kinetic equation (Supplementary Section 4). The results are plotted in Fig.…”

Diffusion in inhomogeneous media

“…However, motivated by recent experimental progress [3][4][5], there has been considerable theoretical work using hydrodynamics to study thermoelectric transport [2,[6][7][8][9][10][11][12][13][14][15][16][17][18] and it is therefore of interest to see how our general results on diffusion manifest themselves in this particular context. More specifically, we will study this within the context of relativistic hydrodynamics, describing the hydrodynamic limit of a relativistic quantum field theory.…”