Moire butterflies in twisted bilayer graphene

The Hofstadter butterfly spectral patterns of lattice electrons in an external magnetic field yield some of the most beguiling images in physics. Here we explore the magnetoelectronic spectra of systems with moire spatial patterns, concentrating on the case of twisted bilayer graphene. Because long-period spatial patterns are accurately formed at small twist angles, fractal butterfly spectra and associated magnetotransport and magnetomechanical anomalies emerge at accessible magnetic field strengths.