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 π Majorana modes. A time vortex is a point in space around which the phase lag of the Hamiltonian changes by a multiple of 2π. 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 π Majorana modes. We show that a time vortex can be created using Clifford gates, simplifying its realization in near-term quantum simulators.