Extended Hubbard model describing small multi-dot arrays in bilayer graphene

TL;DR

This paper develops a Hubbard model for quantum dots in bilayer graphene, analyzing their spin and valley properties, and derives an effective Heisenberg model to describe their interactions under various conditions.

Contribution

It introduces a parametrized Hubbard model for bilayer graphene quantum dots and explores their tunable spin and valley multiplets, including an effective Heisenberg model for large valley splittings.

Findings

Demonstrated tunability of spin and valley multiplets via electrostatic and magnetic controls.

Mapped energy gaps for different dot sizes and separations.

Derived an effective Heisenberg model for half-filled, large valley splitting regimes.

Abstract

We set up and parametrize a Hubbard model for interacting quantum dots in bilayer graphene and study double dots as the smallest multi-dot system. We demonstrate the tunability of the spin and valley multiplets, Hubbard parameters, and effective exchange interaction by electrostatic gate potentials and the magnetic field. Considering both the long- and short-range Coulomb interaction, we map out the various spin and valley multiplets and calculate their energy gaps for different dot sizes and inter-dot separations. For half-filling and large valley splittings, we derive and parametrize an effective Heisenberg model for the quantum dot spins.