Qiang Gao, The University of Texas at Austin

"Exotic Phases in Condensed Matter Systems: Space-time Crystals and Moiŕe Superlattices"

Abstract: As suggested by the title, I will divide my defense talk into two parts.

The first part will be on the Space-time crystals (Floquet-Bloch systems) which have emerged as a novel and intriguing concept in quantum mechanics, uniquely distinguished by their periodicities in both space and time. I will first introduce the notion of spacetime crystals and investigate the simplest possible case in (1+1)D. Within specific experimental setups, like that of a monoatomic crystal driven by coherent sound waves, these space-time periodic structures have shown a remarkable ability to convert energy quanta of sound waves into potential energy of DC electric fields. This energy conversion process is deeply tied to the intricate topologies of quasi-energy bands. Furthermore, detailed studies on DC current generation in periodically driven Bloch systems have unveiled two distinct types of currents: the intrinsic currents, which are in harmony with the system's quasi-equilibrium state, and the extrinsic currents, which emerge from shifts between different equilibrium states. These insights not only deepen our understanding of space-time crystal dynamics but also pave the way for potential applications in energy and quantum technologies. Finally, I will provide a semiclassical point of view for the electronic dynamics and responses which offers a systematic treatment of the Floquet-Bloch systems under slowly varying perturbations in space and time.

The topics of the second part will be changed to moiré physics that has been intensively investigated for the past five years. Instead of directly studying the physics in twisted bilayer or multilayer systems, I will introduce a new graphene-based platform that has shown the same physical significance as in the twisted bilayer graphene: periodically strained monolayer graphene. I will start with the single particle picture and argue both analytically and numerically that the system under specific condition can host almost ideal Chern flat bands. This innovative setup mimics the dynamics of twisted moiré structures without a twist, offering a promising platform for exploring strong correlating physics such as quantum anomalous Hall states, and fractional Chern insulator phases.