  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.
