Doping driven metal-insulator transition in disordered graphene

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 the 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 $〈\text{sign}〉$ 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 metal-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 compare our results with experimental data and conclude that, in actual graphene materials, the localization effect induced by doping plays a dominant role, resulting in an insulating phase.