Index Theorem on Chiral Landau Bands for Topological Fermions

Gauge Field Induced Chiral Zero Mode in Five-Dimensional Yang Monopole Metamaterials

Owing to the chirality of Weyl nodes characterized by the first Chern number, a Weyl system supports one-way chiral zero modes under a magnetic field, which underlies the celebrated chiral anomaly. As a generalization of Weyl nodes from three-dimensional to five-dimensional physical systems, Yang monopoles are topological singularities carrying nonzero second-order Chern numbers c_{2}=±1. Here, we couple a Yang monopole with an external gauge field using an inhomogeneous Yang monopole metamaterial and experimentally demonstrate the existence of a gapless chiral zero mode, where the judiciously designed metallic helical structures and the corresponding effective antisymmetric bianisotropic terms provide the means for controlling gauge fields in a synthetic five-dimensional space. This zeroth mode is found to originate from the coupling between the second Chern singularity and a generalized 4-form gauge field-the wedge product of the magnetic field with itself. This generalization reveals intrinsic connections between physical systems of different dimensions, while a higher-dimensional system exhibits much richer supersymmetric structures in Landau level degeneracy due to the internal degrees of freedom. Our study offers the possibility of controlling electromagnetic waves by leveraging the concept of higher-order and higher-dimensional topological phenomena.

Propagating Chiral Phonons in Three-Dimensional Materials

Chiral phonons were initially proposed and experimentally verified in two-dimensional (2D) systems. Their intriguing effects have generated profound impacts on multiple research fields. However, all chiral phonons reported to date are constrained to be local, in the sense that their group velocities vanish identically. Here, we propose the concept of propagating 3D chiral phonons, which can transport the information on chirality and angular momentum. Guided by the necessary conditions and using first-principles calculations, we demonstrate their existence in WN₂. The chirality, group velocity, and pseudoangular momentum are analyzed. Based on their selective coupling with valley electrons and photons, we propose an experimental setup to detect the unique feature of propagating chiral phonons. Our work endows chiral phonons with a crucial character-the ability to propagate and transport quantized information, which creates a new research direction and opens up the possibility to design novel phononic quantum devices.