Thermopower of Graphene under Strong Electron–Hole Scattering

Abstract

We study the evolution of thermoelectric coefficients of monolayer graphene at the crossover between drift- diffusive and hydrodynamic transport regimes. The crossover is governed by the dimensionless strength of \(e{-} h\) interaction \(r\)-ratio of inter-carrier collision frequency and scattering rate with external agents, impurities and phonons. We find an anomalous growth of the Seebeck coefficient \(S\) in a narrow vicinity of the charge neutrality point: the maximum of density-dependent \(S\) scales as \({{r}^{{1/2}}}\). This scaling is explained by strong suppression of electric current via electron–hole scattering when both carrier concentrations are comparable, and insensitivity of carrier thermal transport to this scattering. For the same reason, the electronic thermal conductivity \(\varkappa \) is first maximized at charge neutrality, and also reaches large values at high carrier density due to the partial restoration of the Wiedemann–Franz law in the monopolar limit. Between these large values, the density-dependent thermal conductivity reaches a minimum. To evaluate \(S\) and \(\varkappa \) at arbitrary collision frequencies, we develop an exactly solvable kinetic model with inter-carrier collision integrals in the generalized relaxation time approximation. We find that operation of graphene-based thermoelectric photodetectors based on \(p{-} n\) junctions is favored by the transition to the hydrodynamic regime, which is characterized by large thermopower and suppressed hot carrier cooling via heat diffusion to the contacts.