Periodically driving a quantum system may lead to new non-equilibrium topological phenomena, not attainable in time-independent systems.
Two-dimensional systems of a few layers of graphene, twisted relative to each other or stacked in special ways, display a wide variety of fascinating physical phenomena, originating from the enhancement of electron-electron interactions.
In a broad class of materials, electron correlations and quantum mechanics conspire to give rich and fascinating behaviors, defying the central paradigms of condensed matter physics and giving rise to unconventional superconductivity.
Many seemingly distinct phenomena in condensed matter physics can be understood by a common framework of an underlying topological structure in the ground-state wavefunction. Examples include the quantum Hall effect, topological insulators and superconductors. In the last decades, and with greater intensity in the last few years, such exotic states have been discovered - or engineered - in the lab. The main challenges for theory are to design physical setups that can realize such topological states and to predict their properties.