Slow imbalance relaxation and thermoelectric transport in graphene

By M. Foster, I. Aleiner. 2008

155 citations recorded by the source corpus.

We compute the electronic component $(\ensuremath{\kappa})$ of the thermal conductivity and the thermoelectric power $(\ensuremath{\alpha})$ of monolayer graphene within the hydrodynamic regime, taking into account the slow rate of carrier population imbalance relaxation. Interband electron-hole generation and recombination processes are inefficient due to the nondecaying nature of the relativistic energy spectrum. As a result, a population imbalance of the conduction and valence bands [i.e., a nonequilibrium state with ${\ensuremath{\mu}}_{e}+{\ensuremath{\mu}}_{h}\ensuremath{\ne}0$, where ${\ensuremath{\mu}}_{e}$ $({\ensuremath{\mu}}_{h})$ denotes the electron (hole) chemical potential] is generically induced upon the application of a thermal gradient. We show that the thermoelectric response of a graphene monolayer depends upon the ratio of the sample length to an intrinsic length scale ${l}_{Q}$ set by the imbalance relaxation rate. At the same time, we incorporate the crucial influence of the metallic contacts required for the thermopower measurement (under open circuit boundary conditions) since carrier exchange with the contacts also relaxes the imbalance. These effects are especially pronounced for clean graphene, where the thermoelectric transport is limited exclusively by intercarrier collisions. For specimens shorter than ${l}_{Q}$, the population imbalance extends throughout the sample; $\ensuremath{\kappa}$ and $\ensuremath{\alpha}$ asymptote toward their zero imbalance relaxation limits. In the opposite limit of a graphene slab longer than ${l}_{Q}$, at nonzero doping $\ensuremath{\kappa}$ and $\ensuremath{\alpha}$ approach intrinsic values characteristic of the infinite imbalance relaxation limit. Samples of intermediate (long) length in the doped (undoped) case are predicted to exhibit an inhomogeneous temperature profile, while $\ensuremath{\kappa}$ and $\ensuremath{\alpha}$ grow linearly with the system size. In all cases except for the shortest devices, we develop a picture of bulk electron and hole number currents that flow between thermally conductive leads, where steady-state recombination and generation processes relax the accumulating imbalance. Our analysis incorporates, in addition, the effects of (weak) quenched disorder.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/148daeed709c4491695128faa18ed273c293221b

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Citations in the corpus

Holographic Quantum Matter (2016, background): “Other work has examined the influence of long relaxation times between the electron and hole subsystems [266; 662].”
Electronic transport in two-dimensional graphene (2010, background): “More details along this idea can be found in the literature (Foster and Aleiner, 2008, 2009; Fritz et al., 2008; Kashuba, 2008; Müller et al., 2008).”
Application of graphene and graphene‐based materials in clean energy‐related devices (2009, background): “optical properties [9], mechanical properties [10], thermoelectrical transport properties [11], etc.”
Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene (2015, methodology): “A number of exotic properties have been predicted including nearly perfect (inviscid) flow [18] and a diverging thermal conductivity resulting in the breakdown of the Wiedemann-Franz law [5, 6].”
Graphene mode-locked ultrafast laser. (2009, background): “required to move an electron from conduction to valence band.(35,36) Interband relaxation by phonon emis-”
Transport in inhomogeneous quantum critical fluids and in the Dirac fluid in graphene (2015, background): “Furthermore, it has been shown [25] that strongly interacting quantum critical fluids have a somewhat different hydrodynamic description than the canonical Fermi liquids described above, and this can lead to very different hydrodynamic properties, including in transport [25, 19, 20, 26, 27, 28, 29],”