Chiral approximation to twisted bilayer graphene: Exact intravalley inversion symmetry, nodal structure, and implications for higher magic angles

Abstract

This paper presents a mathematical and numerical analysis of the flat-band wave functions occurring in the chiral model of twisted bilayer graphene at the “magic” twist angles. We show that the chiral model possesses an exact intravalley inversion symmetry. Writing the flat-band wave function as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are antiquantum Hall wave functions related by the inversion symmetry operation introduced here. We then show numerically that as one moves from the lowest to higher magic angles, the spinor components of the wave function exhibit an increasing number of zeros, resembling the changes in the quantum Hall wave function as the Landau level index is increased. The wave function zeros are characterized by a chirality, with zeros of the same chirality clustering near the center of the moiré unit cell, while opposite chirality zeros are pushed to the boundaries of the unit cell. The enhanced phase winding at higher magic angles suggests an increased circulating current. Physical implications for scanning tunneling spectroscopy, orbital magnetization and interaction effects are discussed.