Effective Mass in Bilayer Graphene at Low Carrier Densities: the Role of Potential Disorder and Electron-Electron Interaction

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 of order 1 * 10^11 cm^-2. Measurements use temperature-dependent low-field Shubnikov-de Haas (SdH) oscillations are observed in high-mobility hexagonal boron nitride (h-BN) 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 carrier density n = 6 * 10^11 cm^-2 and exhibits a strong suppression of 30% when n reaches 2 * 10^11 cm^-2. Contributions from electron-electron interaction alone, evaluated using several different approximations, cannot explain the experimental trend. Instead, the effect of 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 study reveals an unusual disorder effect unique to two-dimensional semi-metallic systems.