Mathematical methods in magic moiré materials

When two-dimensional crystals are stacked on top of each other and rotated by a small twist angle, a large-scale moiré pattern is formed which can lead to exotic, strongly correlated effects such as superconductivity.

A better understanding of the mechanisms behind such effects could have far-reaching implications in science and engineering.The most prominent example of such a moiré material is twisted bilayer graphene (TBG), which exhibits a form of superconductivity at special twist angles called magic angles.

In this four-year-project we will develop new mathematical methods to study and understand such phenomena.

First, we will study properties of magic angles (distribution, stability, electronic band structure) in effective one-particle models of TBG.

We will then use this to build a stripped down many-particle model to numerically analyze strongly correlated effects such as superconductivity and Mott insulator states.

We will also construct new mathematical frameworks to study other moiré materials such as twisted semiconductors and multilayers, and physically strained lattice structures.The analysis relies on spectral theory and random perturbations of non-selfadjoint operators, microlocal and semiclassical analysis, and Bloch-Floquet theory.

The questions that we plan to study will require the development of new mathematical tools in these areas. The project will be carried out by the main applicant in cooperation with international experts.