Solvable model of moire superlattice in a magnetic field

Solvable model of moire superlattice in a homogeneous magnetic field is constructed. The system consists of two parallel plane layers with 2D lattices. The lattice at one plane is turned in respect to another one. The dependence of the spectrum of the model Hamiltonian on the magnetic field (i.e. energy-flux diagram) has Hofstadter butterfly type. We compared the energy-flux diagrams for different angles between the orientations of the lattices.