The Electronic Structure of Coupled Semiconductor Quantum Dots Arranged as a Graphene Hexagonal Lattice under a Magnetic Field

We study the electronic spectrum of coupled quantum dots (QDs) arranged as a graphene hexagonal lattice in the presence of an external perpendicular magnetic field. In our tight-binding model, the effect of the magnetic field is included in both the Peierls phase of the Hamiltonian and the tight-binding basis Wannier function. The energy of the system is analyzed when the magnetic flux through the lattice unit cell is a rational fraction of the quantum flux. The calculated spectrum has recursive properties, similar to those of the classical Hofstadter butterfly. However, unlike the ideal Hofstadter butterfly structure, our result is asymmetric since the impacts of the specific material and the magnetic field on the wavefunctions are included, making the results more realistic.