Evan Telford with Harsh Mathur
The Relativistic Hofstadter Problem
Hofstadter studied electrons in a strong magnetic field perturbed by a weak periodic potential on a square lattice. He found that the energy levels plotted as a function of the magnetic field formed a beautiful pattern with a recursive structure now Hofstadter butterfly. Subsequently it was realized that this system would show an anomalous quantum Hall effect. This effect has recently been experimentally verified in moire superlattices consisting of bilayer graphene coupled with hexagonal boron nitride. Electrons in graphene obey the Dirac equation and the periodic potential in the experimental system had a triangular symmetry. Therefore we propose to restudy the Hofstadter problem for relativistic electrons in a triangular periodic potential in order to make quantitative contact with the experiments.