Topological edge states at Floquet quantum criticality

Abstract

Topologically protected edge states exactly at topological phase boundaries challenge the conventional belief that topological states must be associated with a bulk energy gap. Because periodically driven (Floquet) systems host unusually intricate topological phase boundaries, topological edge states can be prolific at such Floquet quantum criticality. Working on a class of chiral-symmetric, Floquet-driven Majorana fermion chains, we analytically and computationally show that the precise boundaries between different Floquet topological gapped phases can accommodate topological edge modes, including the so-called Majorana $\pi$ modes. We also identify a general bulk-edge correspondence formula to predict and understand the emergence of topological edge modes at Floquet quantum criticality. Of direct interest to quantum simulation experiments, our results break new grounds for studies of nonequilibrium topological phases of matter undergoing topological phase transitions.

To make the manuscript clearer, we have reorganized the paper structure and rewritten some parts. 8 pages with supplemental materials, 6 figures

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• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Self-trapping and skin solitons in two-dimensional non-Hermitian lattices
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Impact of Boundary Conditions on the Double-Kicked Quantum Rotor
• Breakdown of the symmetry constraint in a Floquet topological insulator
• Topologically nontrivial multicritical points
• Zero and Nonzero Energy Majorana Modes in an Extended Kitaev Chain
• Anomalous Dynamical Scaling at Topological Quantum Criticality
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems