Topological excitations at time vortices in periodically driven systems

TL;DR

This paper explores how time vortices in two-dimensional periodically driven fermionic systems with particle-hole symmetry can host Majorana modes, revealing new topological phases beyond equilibrium possibilities.

Contribution

It introduces the concept of time vortices in driven systems and demonstrates their ability to bind Majorana modes, with a practical method for creating them using Clifford gates.

Findings

Time vortices can bind $$ Majorana modes.

A driven Kitaev model exhibits various Majorana configurations.

Clifford gates enable creation of time vortices in quantum simulators.

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