  Controlling the metal-insulator transition in graphene-based material is a
crucial topic as it directly impacts its potential applications. Inspired by
recent experiments, we study the effects of doping and bond disorder on
metal-insulator transition in graphene within the Hubbard model on a honeycomb
lattice. By using the determinant quantum Monte Carlo method, we first conduct
tests on the value of <sign> under various parameters, such as electron
density, on-site interactions, temperature, and lattice size, so as to select
the appropriate parameters to alleviate the impact of the sign problem. Given
the knowledge that bond disorder can lead to a mental-insulator transition, our
study has revealed, after ruling out the influence of size effects, that the
critical strength of disorder increases as the electron density decreases while
decreasing as the on-site interactions increase. Furthermore, we compared our
results with experimental data and concluded that, in actual graphene
materials, the localization effect induced by doping plays a dominant role,
resulting in an insulating phase.
