Optical Signatures of Band Flatness and Anisotropic Quantum Geometry in Magic-Angle Twisted Bilayer Graphene

TL;DR

This paper investigates how optical conductivity measurements can reveal band flatness and quantum geometry in magic-angle twisted bilayer graphene, linking optical features to electronic phases and Berry curvature properties.

Contribution

It introduces optical signatures as probes for band flatness, quantum geometry, and topological phases in twisted bilayer graphene, highlighting their dependence on lattice relaxation and symmetry.

Findings

Optical absorption peaks indicate bandwidth and gap sizes relevant for superconductivity and fractional Chern insulators.

Lattice relaxation reduces the optical bound near zero energy, affecting flat band properties.

The imaginary part of optical Hall conductivity reflects Berry curvature distribution and symmetry conditions.

Abstract

We study the degree of band flatness and anisotropic quantum geometry in magic-angle twisted bilayer graphene by varying the twist angle and the lattice relaxation through optical conductivity. We show that the degree of band flatness and its quantum geometry can be revealed through optical absorption and its resulting optical bounds, which are based on the trace condition in quantum geometry. More specifically, the narrow and isolated peak of optical absorption in the low-energy region provides information about the bandwidth between two flat bands. When this value is smaller than the electron interaction, it serves as a critical condition for the emergence of flat band superconductivity. Furthermore, optical absorption also provides the gap value between the flat band and the dispersive band, and when this gap is larger than the electron interaction, it facilitates the realization of fractional Chern insulating phases. We show that the narrow and isolated peak of optical bound near zero energy decreases as lattice relaxation increases. Meanwhile, we demonstrate that the imaginary part of generalized optical Hall conductivity reveals the vanishing of the negative part of Berry curvature, which is enforced by the refined trace-determinant inequality. Accordingly, we show that the total amount of the negative part and component of the Berry curvature approaches zero in the single ideal flat-band case. In contrast, when considering all occupied bands, the total amount of the negative component is slightly different from zero. Finally, we demonstrate that the condition of vanishing of flat band velocities and the emergent chiral symmetry are sufficient for the saturation of the trace condition, which pertains to the isotropic case.