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We compute the electronic component of the thermal conductivity (TC) and thethermoelectric power (TEP) of monolayer graphene, within the hydrodynamicregime, taking into account the slow rate of carrier population imbalancerelaxation. Interband electron-hole generation and recombination processes areinefficient due to the non-decaying nature of the relativistic energy spectrum.As a result, a population imbalance of the conduction and valence bands isgenerically induced upon the application of a thermal gradient. We show thatthe thermoelectric response of a graphene monolayer depends upon the ratio ofthe sample length to an intrinsic length scale l_Q, set by the imbalancerelaxation rate. At the same time, we incorporate the crucial influence of themetallic contacts required for the thermopower measurement (under open circuitboundary conditions), since carrier exchange with the contacts also relaxes theimbalance. These effects are especially pronounced for clean graphene, wherethe thermoelectric transport is limited exclusively by intercarrier collisions.For specimens shorter than l_Q, the population imbalance extends throughout thesample; the TC and TEP asymptote toward their zero imbalance relaxation limits.In the opposite limit of a graphene slab longer than l_Q, at non-zero dopingthe TC and TEP approach intrinsic values characteristic of the infiniteimbalance relaxation limit. Samples of intermediate (long) length in the doped(undoped) case are predicted to exhibit an inhomogeneous temperature profile,whilst the TC and TEP grow linearly with the system size. In all cases exceptfor the shortest devices, we develop a picture of bulk electron and hole numbercurrents that flow between thermally conductive leads, where steady-staterecombination and generation processes relax the accumulating imbalance.

Slow imbalance relaxation and thermoelectric transport in graphene