Narrow bands in magnetic field and strong-coupling Hofstadter spectra

We develop an efficient and general method to determine the Hofstadter spectrum of isolated narrow bands. The method works for topological as well as for trivial narrow bands by projecting the zero B-field hybrid Wannier states-which are localized in one direction and Bloch extended in another direction-onto a representation of the magnetic translation group in the Landau gauge. We then apply this method to find the Hofstadter spectrum for the exact single-particle charged excitations in the strong-coupling limit of the magic angle twisted bilayer graphene at the charge neutrality point and at vertical bar v vertical bar = 2 down to low magnetic fields when the flux through the moire unit cell is only similar to 1/25 of the electronic flux quantum, i.e., similar to 1 T at the first magic angle. The resulting spectra provide a means to investigate Landau quantization of the quasiparticles even if their dispersion is interaction induced.

Automated summary

We develop an efficient method to determine the Hofstadter spectrum of isolated narrow bands. The method works for both topological and trivial narrow bands by projecting Wannier states onto a representation of the magnetic translation group. We apply this method to find the Hofstadter spectrum for charged excitations in twisted bilayer graphene and obtain results even at low magnetic fields.