Quadratic Band Touching and Nontrivial Winding Reveal Generalized Angular Momentum Conservation

TL;DR

This paper uncovers a generalized angular momentum conservation law in two-dimensional lattices with quadratic band touchings, linking topology and pseudospin to angular-momentum dynamics, and experimentally demonstrates this in a photonic Kagome lattice.

Contribution

It introduces a generalized total angular momentum that remains conserved at quadratic band-touching points, extending the understanding of angular momentum in topological lattice systems.

Findings

Conventional angular momentum is not conserved near QBTPs.

GTAM is conserved and determined by the topological winding number.

Experimental validation using a photonic Kagome lattice.

Abstract

Angular momentum conservation stands as one of the most fundamental and robust laws of physics. In discrete lattices, however, its realization can deviate markedly from the continuous case, especially in the presence of nontrivial momentum-space band touchings. Here, we investigate angular momentum conservation associated with quadratic band-touching points (QBTPs) in two-dimensional lattices. We show that, unlike in graphene lattices hosting linear band-touching points (LBTPs), the conventional angular momentum is no longer conserved near QBTPs. Instead, we identify a generalized total angular momentum (GTAM) that remains conserved for both LBTPs and QBTPs, inherently determined by the topological winding number at the band-touching point (BTP). Using a photonic Kagome lattice, we experimentally demonstrate GTAM conservation through pseudospin-orbital angular momentum conversion. Furthermore, we show that this conservation principle extends to a broad class of discrete lattices with arbitrary pseudospin textures and higher-order winding numbers. These results reveal a fundamental link between pseudospin, angular momentum, and topology, establishing a unified framework for angular-momentum dynamics in discrete systems.