Non-local hydrodynamic transport and collective excitations in Dirac fluids

Abstract

We study the response of a Dirac fluid to electric fields and thermal gradients at finite wavenumbers and frequencies in the hydrodynamic regime. We find that non-local transport in the hydrodynamic regime is governed by infinite set of kinetic modes that describe non-collinear scattering events in different angular harmonic channels. The scattering rates of these modes τ −1 m increase as |m|, where m labels the angular harmonics. In an earlier publication, we pointed out that this dependence leads to anomalous, Lévy-flight-like phase space diffusion [1]. Here, we show how this surprisingly simple, non-analytic dependence allows us to obtain exact expressions for the non-local heat and charge conductivities. The peculiar dependence of the scattering rates on m also leads to a non-trivial structure of collective excitations: Besides the well known plasmon, second sound and diffusive modes, we find non-degenerate damped modes corresponding to excitations of higher angular harmonics. We use these results to investigate the transport of a Dirac fluid through Poiseuille-type geometries of different widths, and to study the response to surface acoustic waves in graphene-piezoelectric devices.

Hydrodynamic collective modes in graphene

“…where τ −1 ij are the scattering rates that can be obtained by solving the kinetic equation within the three-mode approximation 15,16,25,44 . The zeros in the matrix (10e) are the manifestation of energy and momentum conservation, which is also responsible for the vanishing dissipative correction to the energy current in the absence of the magnetic field 16 .…”

“…6 we present the results of a numerical calculation of the real part of the dispersion for the two values of the carrier density, n = 10 12 cm −2 and n = 10 11 cm −2 . The equation (25) was solved using the typical values of the effective coupling constant 12,63 α g = 0.23, disorder scattering time 12 τ −1 dis = 1 THz, kinematic viscosity 3,46 ν = 0.2 m 2 /s, and temperature T = 300 K. The result is qualitatively similar to that shown in Fig. 1, therefore we postpone the discussion until after we have considered the two limiting cases where the dispersion can be obtained analytically, see Eq.…”

“…In graphene, hydrodynamic collective modes have been considered by many authors 2,15,[19][20][21][22][23][24][25][26] . All of them agree that at charge neutrality, the ideal electronic fluid (i.e., neglecting all dissipative processes) allows for a soundlike collective mode (which has been referred to as either the "cosmic sound" 20 or the "second sound" 25 ) with the dispersion relation…”

“…In particular, the underlying gradient expansion is valid at length scales much larger than the typical length scale ee describing the energy-and momentum-conserving interaction (responsible for equilibration of the system). At smaller length scales, one can study more traditional collective excitations in interacting many-electron systems, including plasmons 15,21,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] , which behavior is well established both theoretically and experimentally.…”

“…In this paper we provide a consistent, unified calculation of the dispersion relations of the hydrodynamic collective modes in graphene. While the true hydrodynamics is universal (as long as no symmetries are broken), graphene is somewhat unique in the sense that there are two length scales associated with electron-electron interaction that are parametrically different in the weak coupling limit 2,25,43,44 . This allows us to extend the linearized hydrodynamic theory 15,43,45 to the length scales smaller that ee (going beyond the small-momentum expansion of Ref.…”