Novel correlated quantum materials: phenomena and theory
The exploration of novel materials exhibiting non-generic quantum effects continues to deliver many surprises. Recently, for example, two-dimensional moiré quantum materials have taken center stage - most prominently twisted bilayer graphene. Among the most exciting traits of moiré quantum materials is the observed emergence of strongly-correlated states, including Mott insulators, superconductivity, and more. In general, the stacking of two-dimensional materials offers an unprecedented level of targeted access to the manipulation of electronic properties merely via gate doping or tuning of the twist angle. Therefore, they enable the controlled engineering of unconventional quantum states of matter, which not only opens new perspectives on fundamental aspects of strongly-correlated systems, but also constitutes a very promising route towards the functionalization of novel materials.
In this lecture series, I will provide an introduction to the physics and recent developments of moiré quantum materials and outline the challenges that have to be met in the theoretical descriptions of their complex many-body physics. We will then explore how quantum field theoretical methods, such as the renormalization group, provide a versatile toolkit to approach many universal and non-universal aspects of strongly-correlated moiré heterostructures, including the description of competing correlations, Fermi-surface instabilities, quantum critical behavior, and the possible emergence of Chern insulators and topological superconductivity.