Effective mass of electrons and holes in bilayer graphene: Electron-hole asymmetry and electron-electron interaction

Abstract

Precision measurements of the effective mass ${m}^{*}$ in high-quality bilayer graphene using the temperature dependence of the Shubnikov--de Haas oscillations are reported. In the density range $0.7\ifmmode\times\else\texttimes\fi{}{10}^{12}$ $<$ $n$ $<$ $4.1\ifmmode\times\else\texttimes\fi{}{10}^{12}$ cm${}^{\ensuremath{-}2}$, both the hole mass ${m}_{\mathrm{h}}^{*}$ and the electron mass ${m}_{\mathrm{e}}^{*}$ increase with increasing density, demonstrating the hyperbolic nature of the bands. The hole mass ${m}_{\mathrm{h}}^{*}$ is approximately 20--30% larger than the electron mass ${m}_{\mathrm{e}}^{*}$. Tight-binding calculations provide a good description of the electron-hole asymmetry and yield an accurate measure of the interlayer hopping parameter ${v}_{4}=0.063$. Both ${m}_{\mathrm{h}}^{*}$ and ${m}_{\mathrm{e}}^{*}$ are suppressed compared with single-particle values, suggesting renormalization of the band structure of bilayer graphene induced by electron-electron interaction.