Multi-gap topology and non-Abelian braiding of phonons from first principles

TL;DR

This paper reveals that phonons in certain materials can exhibit non-Abelian braiding behavior, which can be controlled via external stimuli, offering a new platform for topological quantum computation.

Contribution

It introduces a first-principles framework to analyze phonon topological configurations and demonstrates non-Abelian braiding in Al$_2$O$_3$ through band inversions.

Findings

Phonons can carry non-Abelian frame charges at band crossings.

Electrostatic doping induces phonon band inversions and non-Abelian braiding.

A general topological invariant called Euler class is used to analyze phonon topology.

Abstract

Non-Abelian states of matter, in which the final state depends on the order of the interchanges of two quasiparticles, can encode information immune from environmental noise with the potential to provide a robust platform for topological quantum computation. We demonstrate that phonons can carry non-Abelian frame charges at the band crossing points of their frequency spectrum, and that external stimuli can drive their braiding. We present a general framework to understand the topological configurations of phonons from first principles calculations using a topological invariant called Euler class, and provide a complete analysis of phonon braiding by combining different topological configurations. Taking a well-known dielectric material, Al$_2$O$_3$, as a representative example, we demonstrate that electrostatic doping gives rise to phonon band inversions that can induce redistribution of the frame charges, leading to non-Abelian braiding of phonons. Our work provides a new quasiparticle platform for realizable non-Abelian braiding in reciprocal space, and expands the toolset for studying braiding processes.