Effective mass in bilayer graphene at low carrier densities: The role of potential disorder and electron-electron interaction

Abstract

In a two-dimensional electron gas, the electron-electron interaction generally becomes stronger at lower carrier densities and renormalizes the Fermi-liquid parameters, such as the effective mass of carriers. We combine experiment and theory to study the effective masses of electrons and holes ${m}_{e}^{*}$ and ${m}_{h}^{*}$ in bilayer graphene in the low carrier density regime on the order of $1\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{11}\phantom{\rule{0.28em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$. Measurements use temperature-dependent low-field Shubnikov--de Haas oscillations observed in high-mobility hexagonal boron nitride supported samples. We find that while ${m}_{e}^{*}$ follows a tight-binding description in the whole density range, ${m}_{h}^{*}$ starts to drop rapidly below the tight-binding description at a carrier density of $n=\phantom{\rule{0.16em}{0ex}}6\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{11}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ and exhibits a strong suppression of 30% when $n$ reaches $2\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{11}\phantom{\rule{0.28em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$. Contributions from the electron-electron interaction alone, evaluated using several different approximations, cannot explain the experimental trend. Instead, the effect of the potential fluctuation and the resulting electron-hole puddles play a crucial role. Calculations including both the electron-electron interaction and disorder effects explain the experimental data qualitatively and quantitatively. This Rapid Communication reveals an unusual disorder effect unique to two-dimensional semimetallic systems.