Numerical study of electrostatically-defined quantum dots in bilayer graphene

Abstract

Interacting quantum many-body systems are so challenging to study that even simplified models, such as the Hubbard model, cannot be solved exactly. For this reason, it is interesting to engineer controllable quantum systems, called quantum simulators, that can emulate the behavior of these models. This makes quantum simulators a promising platform for studying the Hubbard model. These can be implemented, for example, using interacting arrays of quantum dots realized in semiconducting materials. The capability to tune the bands in bilayer graphene with patterned gate electrodes provides an innovative platform to study such a model, as it is the first time to explore the Hubbard model with quantum dots in a twodimensional material. Moreover, this platform opens a wide range of possibilities to study the different parameters of the model. In this work, we study theoretically and numerically realistic models of electrostatically defined quantum dots in bilayer graphene. We can calculate the proposed device’s potential and band-gap landscape induced in bilayer graphene by solving the Poisson equation. The result is then fed to a lowenergy model to calculate the bound states of the quantum dots. This allows calculating the parameters of the corresponding Hubbard model, including tunneling amplitudes and on-site interactions. Our results can be directly used to design quantum-simulation devices based on quantum dots that are realized electrostatically in bilayer graphene.