Non-Abelian Floquet braiding and anomalous Dirac string phase in periodically driven systems
jats:titleAbstract</jats:title>jats:pWhile a significant fraction of topological materials has been characterized using symmetry requirementsjats:sup1–4</jats:sup>, the past two years have witnessed the rise of novel multi-gap dependent topological statesjats:sup5–9</jats:sup>, the properties of which go beyond these approaches and are yet to be fully explored. Although already of active interest at equilibriumjats:sup10–15</jats:sup>, we show that the combination of out-of-equilibrium processes and multi-gap topological insights galvanize a new direction within topological phases of matter. We show that periodic driving can induce anomalous multi-gap topological properties that have no static counterpart. In particular, we identify Floquet-induced non-Abelian braiding, which in turn leads to a phase characterized by an anomalous Euler class, being the prime example of a multi-gap topological invariant. Most strikingly, we also retrieve the first example of an ‘anomalous Dirac string phase’. This gapped out-of-equilibrium phase features an unconventional Dirac string configuration that physically manifests itself via anomalous edge states on the boundary. Our results not only provide a stepping stone for the exploration of intrinsically dynamical and experimentally viable multi-gap topological phases, but also demonstrate periodic driving as a powerful way to observe these non-Abelian braiding processes notably in quantum simulators.</jats:p>
Acknowledgements: R.J.S. acknowledges funding from a New Investigator Award, EPSRC grant EP/W00187X/1, EPSRC-ERC underwrite grant EP/X025829/1, and a Royal Society exchange grant IES/R1/221060, as well as Trinity College, Cambridge. A.B. was funded by a Marie-Curie fellowship, grant no. 101025315. F.N.Ü. acknowledges funding from the Royal Society under a Newton International Fellowship, the Marie Skłodowska-Curie program of the European Commission Grant No. 893915, Trinity College Cambridge, and thanks Aspen Center for Physics for their hospitality where this work was partially funded by a grant from the Sloan Foundation.