arXiv subjects

Pok Man Chiu

Publications and source records attributed to Pok Man Chiu.

2 recordsLinked to original sources

arXiv2025

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

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.

cond-mat.mes-hall↗

arXiv2025

$Z_2$ topological signature of the optical bound on maximal Berry curvature: Application to two-dimensional time-reversal symmetric insulators

Unlike broken time-reversal symmetric (TRS) systems with a well-defined Chern number, directly measuring the bulk $Z_2$ invariant and Berry curvature (if nonzero) in topological insulators and their higher-order topological families remains an unsolved problem. Here, based on the refined trace-determinant inequality (TDI) involving the trace and determinant of the quantum metric and maximal Berry curvature (MBC), we propose an optical bound on the MBC for two-dimensional TRS insulators. As a result, using experimental data from a series of measurements, where the band-inversion parameter is tuned and the optical conductivity is measured over a certain energy range, one can identify the $Z_2$ topological signature and construct the topological phase diagram by integrating the optical bound over frequency. This is supported by the momentum integration of the refined TDI, $f$-sum rule, and its topological extension, which provide a topological lower bound. To clearly identify the $Z_2$ topological signature, the faster decay of the optical weight in the topologically trivial region is crucial; this faster decay can be controlled by the optical gap and the inverse mass tensor. Crucially, the MBC we introduced enables us to prove the existence of tight topological lower bounds for the optical weight, quantum weight, and the double quantum volume. Based on the tight topological lower bounds, their physical meaning can be interpreted as an upper bound on the number of boundary states. We illustrate our approach using three representative topological models: the Kane-Mele model, mirror-protected insulator, and quadrupole insulator. Our results demonstrate that the MBC can reveal symmetry protected-topology and plays a role analogous to that of the original Berry curvature.

cond-mat.mes-hall↗