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This paper presents a mathematical and numerical analysis of the flatbandwavefunctions occurring in the chiral model of twisted bilayer graphene at the"magic" twist angles. We show that the chiral model possesses an exactintra-valley inversion symmetry. Writing the flatband wavefunction as a productof a lowest Landau level quantum Hall state and a spinor, we show that thecomponents of the spinor are anti-quantum Hall wavefunctions related by theinversion symmetry operation introduced here. We then show numerically that asone moves from the lowest to higher magic angles, the spinor components of thewavefunction exhibit an increasing number of zeros, resembling the changes inthe quantum Hall wavefunction as the Landau level index is increased. Thewavefunction zeros are characterized by a chirality, with zeros of the samechirality clustering near the center of the moire unit cell, while oppositechirality zeros are pushed to the boundaries of the unit cell. The enhancedphase winding at higher magic angles suggests an increased circulating current.Physical implications for scanning tunneling spectroscopy, orbitalmagnetization and interaction effects are discussed.

Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles