Mathematics and physics of moiré patterns
Layers of two-dimensional materials stacked with a small twist-angle give rise to periodic beating patterns on a "moiré superlattice" scale much larger than the original lattice. This effective large-scale fundamental domain allows phenomena such as the fractal Hofstadter butterfly to be observed in crystalline materials at experimental magnetic fields. More recently, this new length scale has allowed experimentalists to observe new correlated electronic phases such as superconductivity at a lower electron density than previously accessible and has motivated an intense focus by theorists to develop models for this correlated behavior.
We will present an introduction to some mathematical and computational models for moiré physics. Almost every area of mathematics including partial differential equations, harmonic analysis, functional analysis, dynamical systems, numerical analysis, geometry, topology and number theory has been utilized to gain insight into new phenomena at the moiré scale.