Weyl points in ball-and-spring mechanical systems

TL;DR

This paper demonstrates how simple ball-and-spring mechanical systems can replicate the eigenfrequency degeneracies of electronic band structures, including Weyl points and quadratic degeneracies, serving as accessible models for topological physics.

Contribution

It introduces classical mechanical analogs of Weyl points and complex degeneracy patterns, extending the understanding of topological phenomena in a tangible, experimental setting.

Findings

Identified mechanical degeneracy patterns mimicking Weyl points

Discovered chirality flip effects in mechanical systems

Observed quadratic degeneracy points in simple setups

Abstract

Degeneracy points of parameter-dependent Hermitian matrices play a fundamental role in quantum physics, as illustrated by the concept of Berry phase in quantum dynamics, the Weyl semimetals in condensed-matter physics, and the robust ground-state degeneracies in topologically ordered quantum systems. Here, we construct simple ball-and-spring mechanical systems, whose eigenfrequency degeneracies mimic the behaviour of degeneracy points of electronic band structures. These classical-mechanical arrangements can be viewed as de-quantized versions of Weyl Josephson circuits, i.e., superconducting nanostructures proposed recently to mimic band structure effects of Weyl semimetals. In the mechanical setups we study, we identify degeneracy patterns beyond simple Weyl points, including the chirality flip effect and a quadratic degeneracy point. Our theoretical work is a step toward simple and illustrative table-top experiments exploring topological and differential geometrical aspects of physics.