Hidden wave function of twisted bilayer graphene: The flat band as a Landau level
Abstract
We study zeroenergy states of the chirally symmetric continuum model (CSCM) of twisted bilayer graphene. The zeroenergy state obeys the Dirac equation on a torus in the external nonAbelian magnetic field. These zeroenergy states could form a flat band—a band where the energy is constant across the Brillouin zone. We prove that the existence of the flat band implies that the wave function of any state from the flat band has a zero and vice versa. We found a hidden flat band of unphysical states in the CSCM that has a pole instead of a zero. Our main result is that in the basis of the flat band and hidden wave functions the flat band could be interpreted as a Landau level in the external magnetic field. From that interpretation we show the existence of extra flat bands in the magnetic field.
 Publication:

Physical Review B
 Pub Date:
 April 2021
 DOI:
 10.1103/PhysRevB.103.155150
 arXiv:
 arXiv:2010.02915
 Bibcode:
 2021PhRvB.103o5150P
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Mathematical Physics
 EPrint:
 4+4 pages, no figures