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Non-Abelian Floquet braiding and anomalous Dirac string phase in periodically driven systems

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While a significant fraction of topological materials has been characterized using symmetry requirements, the past two years have witnessed the rise of novel multi-gap dependent topological states, the properties of which go beyond these approaches and are yet to be fully explored. Although already of active interest at equilibrium, 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.


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.


5108 Quantum Physics, 51 Physical Sciences, 5104 Condensed Matter Physics

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Nature Communications

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Nature Portfolio
Royal Society (IES\R1\221060)
Horizon Europe UKRI Underwrite ERC (EP/X025829/1)
EPSRC (EP/W00187X/1)
European Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (893915)
UKRI funding for this open acccess journal grants EP/W00187X/1 and EP/X025829/1 of Dr Robert-Jan Slager, corresponding and first author, of Cambridge. All authors are of Cambridge in fact.
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