Progresses on topological phenomena, time-driven phase transitions, and unconventional superconductivity

In this perspective we discuss three emerging fields of condensed matter physics which in recent years have attracted considerable attention. In particular, we consider the recent challenging topics on time-dependent phase transitions, topological phenomena, and unconventional superconductivity, with the aim to foster the community towards new applications and technological advancements. As for the time-dependent phase transitions, in recent years the experiments have shown light-induced phase transitions and new fields of application are emerging, including material design. Regarding topological materials, new challenges have arisen to detect the Majorana origin of quantized conductance in superconducting hybrid structures, as well as the effect of interaction on edge channels. Finally, concerning superconductivity, non-conventional pairing and correlation effects dominate the physics of a vast class of two-dimensional materials and novel devices were recently conceived. This work offers a comprehensive overview on these topics for promoting new ideas in these fertile fields of research.