Topological excitations at time vortices in periodically driven systems

Abstract

We consider two-dimensional periodically driven systems of fermions with particle-hole symmetry. Such systems support non-trivial topological phases, including ones that cannot be realized in equilibrium. We show that a space-time defect in the driving Hamiltonian, dubbed a ``time vortex,'' can bind $\ddot{I}€$ Majorana modes. A time vortex is a point in space around which the phase lag of the Hamiltonian changes by a multiple of $2\ddot{I}€$. We demonstrate this behavior on a periodically driven version of Kitaev's honeycomb spin model, where ${\mathbb{Z}}_2$ fluxes and time vortices can realize any combination of $0$ and $\ddot{I}€$ Majorana modes. We show that a time vortex can be created using Clifford gates, simplifying its realization in near-term quantum simulators.

This version matches the published version in npj Quantum Materials. DOI: https://doi.org/10.1038/s41535-025-00745-8