Enhancement of phonon-drag thermopower in bilayer graphene

Abstract

Phonon-drag thermopower ${S}^{\text{g}}$ is theoretically studied in a bilayer graphene (BLG). Two-dimensional (2D) electrons with chiral property, finite effective mass, and parabolic dispersion are assumed to interact with the 2D acoustic phonons having a linear dispersion via deformation-potential coupling. A comparison is made with the very recent experimental results of Nam et al. [arXiv:1005.4739 (unpublished)] for $30\ensuremath{\le}T\ensuremath{\le}70\text{ }\text{K}$. Numerically ${S}^{\text{g}}$ is studied as a function of temperature $T$, electron concentration ${n}_{\text{s}}$, and phonon mean-free path. ${T}^{3}$ behavior of ${S}^{\text{g}}$ at very low $T$ changes gradually to sublinear at higher $T$ and the effect of chiral property of the electrons is seen explicitly. We suggest the possibility of significant enhancement of ${S}^{\text{g}}$ at lower carrier concentrations by increasing the linear dimension of the sample and reducing its edge roughness. We find that ${S}^{\text{g}}$ in BLG is enhanced by a factor of 7 compared with the magnitude of ${S}^{\text{g}}$ in monolayer graphene, for ${n}_{\text{s}}=0.5\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }{\text{cm}}^{\ensuremath{-}2}$ in the Bloch-Gr\uneisen (BG) regime. In BG regime ${S}^{\text{g}}\ensuremath{\sim}{T}^{3}$, a manifestation of 2D phonons with linear dispersion and ${S}^{\text{g}}\ensuremath{\sim}{n}_{\text{s}}^{\ensuremath{-}3/2}$, a characteristic of 2D electrons with parabolic dispersion. A comparison is also made with the results in conventional and ideal 2D systems. ${S}^{\text{g}}$ is found to be very significant in comparison with the diffusion thermopower ${S}^{\text{d}}$ and the latter is shown to be $\ensuremath{\sim}T$, ${n}_{\text{s}}^{\ensuremath{-}1}$ at low $T$ and high ${n}_{\text{s}}$. Herring's law, ${S}^{\text{g}}{\ensuremath{\mu}}_{\text{p}}\ensuremath{\sim}{T}^{\ensuremath{-}1}$, relating phonon-limited mobility ${\ensuremath{\mu}}_{\text{p}}$ to ${S}^{\text{g}}$, is found to be valid in BLG.