Spinless topological chirality from Umklapp scattering in twisted 3D structures

TL;DR

This paper uncovers how structural chirality in twisted 3D structures of spinless systems induces topological states like Weyl and Dirac semimetals through Umklapp scattering, expanding topological design principles.

Contribution

It demonstrates the emergence of spinless topological chiralities solely from structural patterns in 3D twisted systems, a novel mechanism not previously explored.

Findings

Discovery of a chiral Weyl semimetal phase in twisted structures.

Identification of a higher-order Dirac semimetal with chiral hinge states.

Underlying role of Umklapp scattering and sign-flipped interlayer hopping.

Abstract

Spinless systems exhibit unique topological characteristics compared to spinful ones, stemming from their distinct algebra. Without chiral interactions typically linked to spin, an intriguing yet unexplored interplay between topological and structural chirality may be anticipated. Here we discover spinless topological chiralities solely from structural chiralities that lie in the 3D spatial patterning of structureless units, exemplified using two types of twisted graphite systems. In a 3D screw twisted structure without periodicity in all directions, we find a chiral Weyl semimetal phase where bulk topology and chiral surface states are both determined by the screw direction. And in a 3D periodic structure formed with layer-alternating twist angle signs, a higher-order Dirac semimetal with chiral hinge states is discovered. Underlying these novel topological states is the intervalley Umklapp scattering that captures the chirality of the twisted interfaces, leading effectively to a sign-flipped chiral interlayer hopping, thereby introducing $\pi$-flux Z2 lattice gauge field that alters the symmetry algebra. Our findings point to a new pathway for engineering topological chirality through patterning twisted arrays of featureless units, which can expand the design principles for topological photonics and acoustics.