Chiral Majorana modes and nodal loops in a periodically driven Kitaev model

The paradigmatic Kitaev model on the honeycomb lattice is known for hosting nondispersive Majorana edge modes. We investigate the system when the couplings are periodically driven in time with a three-step protocol. By analyzing the quasienergy spectra for different edge geometries, we discover a rich interplay of different topological states: nondispersive and chiral Majorana edge modes, corner modes, and nodal loop gap closures. The chiral Majorana 0 and pi modes are induced by the time-reversal symmetry breaking caused by the drive. However, we discover that at a sweet spot of the driving intensity the system experiences frozen dynamics and concomitantly undergoes a topological phase transition to a nodal loop semimetal phase, belonging to its own unique universality class. At the line of frozen dynamics, effective time-reversal and mirror symmetries re-emerge and the corresponding nondispersive Majorana modes are reinstated. Our protocol thus provides a Floquet-engineered route to time-reversal symmetry breaking and tuning for the generation and control of chiral Majorana modes without the need for magnetic fields.