Hydrodynamic charge and heat transport on inhomogeneous curved spaces

Abstract

We develop the theory of hydrodynamic charge and heat transport in strongly interacting quasi-relativistic systems on manifolds with inhomogeneous spatial curvature. In solid-state physics, this is analogous to strain disorder in the underlying lattice. In the hydrodynamic limit, we find that the thermal and electrical conductivities are dominated by viscous effects, and that the thermal conductivity is most sensitive to this disorder. We compare the effects of inhomogeneity in the spatial metric to inhomogeneity in the chemical potential, and discuss the extent to which our hydrodynamic theory is relevant for experimentally realizable condensed matter systems, including suspended graphene at the Dirac point.Comment: 15+8 pages, 4+1 figures; v2: added references, published versio

Hydrodynamics of electrons in graphene

“…Our starting point is to generalize (82), in the stationary limit, to study the response of an inhomogeneous fluid, in a background electric field or temperature gradient. For simplicity we assume that the disorder couples to the chemical potential, as in [99]; the case with inhomogeneous strain disorder is described in [181,182]. We also focus only on time-independent solutions.…”

Diffusion in inhomogeneous media

“…As well as generalizing the work of [14] to include a conserved Uð1Þ charge (as also studied in [18]), we will also be able to use the formalism to illustrate the results of the previous section. In particular, associated with the heat current and the Uð1Þ current we construct two diffusion modes with dispersion relations satisfying the generalized Einstein relation (2.44).…”

“…Note added.-While writing up this work, Ref. [18] appeared which also generalizes [14] to include a conserved Uð1Þ charge and independently derived the hydrodynamic Eqs. (3.23), for the special case of no time dependence and for curved manifolds with a unit norm timelike Killing vector (i.e.…”

“…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.…”

“…This is particularly interesting since it corresponds to allowing for spatially dependent chemical potential or, equivalently, spatially dependent charge density. One can anticipate that our results will be useful for understanding thermoelectric transport in real systems, such as charged puddles, with or without strain, in graphene [24][25][26][27] as also discussed in [18].…”