Anomalous and normal dislocation modes in Floquet topological insulators

Electronic bands featuring nontrivial bulk topological invariant manifest through robust gapless modes at the boundaries, e.g., edges and surfaces. As such this bulk-boundary correspondence is also operative in driven quantum materials. For example, a suitable periodic drive can convert a trivial insulator into a Floquet topological insulator (FTI) that accommodates nondissipative dynamic gapless modes at the interfaces with vacuum. Here we theoretically demonstrate that dislocations, ubiquitous lattice defects in crystals, can probe FTIs as well as unconventional π-trivial insulator in the bulk of driven quantum systems by supporting normal and anomalous modes, localized near the defect core. Respectively, normal and anomalous dislocation modes reside at the Floquet zone center and boundaries. We exemplify these outcomes specifically for two-dimensional (2D) Floquet Chern insulator and px + ipy superconductor, where the dislocation modes are respectively constituted by charged and neutral Majorana fermions. Our findings should be, therefore, instrumental in probing Floquet topological phases in the state-of-the-art experiments in driven quantum crystals, cold atomic setups, and photonic and phononic metamaterials through bulk topological lattice defects.

What is the Environment of Quantum Systems?

Henry and Eve try to outrace each other, so as to get first to the unique quantum crystals deposited in an underground mine. In his descent into the mine, Henry resorts to coherent transfer. When he tries to return the same way, he gets stuck halfway up, because his entanglement to Eve’s sensors decoheres him. This scenario represents any environment where the interaction of each constituent with the quantum system is weak. Yet, together these many constituents and the system become completely entangled, causing environment-induced decoherence. This consensual narrative on decoherence conceals conceptual hurdles. Where does one draw the line between the system and the environment? How can the unitarity of QM be reconciled, whereby our past and future are interchangeable, with the irreversible evolution of quantum systems under decoherence, culminating in death? The appendix to this chapter describes coherent oscillations in a quantum system and their decay by decoherence.