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

TL;DR

This paper analyzes the flatband wavefunctions in twisted bilayer graphene at magic angles, revealing an exact intra-valley inversion symmetry and how the wavefunction structure evolves with higher magic angles, impacting physical properties.

Contribution

It introduces an exact intra-valley inversion symmetry in the chiral model and characterizes the evolution of wavefunction zeros and phase winding at higher magic angles.

Findings

Wavefunction components are related by intra-valley inversion symmetry.

Zeros of wavefunctions increase and cluster near the center at higher angles.

Enhanced phase winding suggests increased circulating currents.

Abstract

This paper presents a mathematical and numerical analysis of the flatband wavefunctions occurring in the chiral model of twisted bilayer graphene at the "magic" twist angles. We show that the chiral model possesses an exact intra-valley inversion symmetry. Writing the flatband wavefunction as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are anti-quantum Hall wavefunctions 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 wavefunction exhibit an increasing number of zeros, resembling the changes in the quantum Hall wavefunction as the Landau level index is increased. The wavefunction zeros are characterized by a chirality, with zeros of the same chirality clustering near the center of the moire 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.