2D nanoscale systems have become the subject of intense research efforts, starting with the discovery and potential applications of graphene over fifteen years ago, followed more recently by the discovery of 2D structures with semiconducting or insulating character. During the past few years, materials scientists have sought to combine these layers in interesting ways to develop smaller and improved devices than traditional materials for optical and electronic applications.

Major mathematical challenges arise from the fact that although each single layer 2D material is periodic, the combined stacked layers are incommensurate (not periodic) because either the ratio of the lattice constants of each layer are irrational or because one layer is rotated on another. The incommensurate structure makes it impossible to apply the standard tools for periodic structures that utilize the Fourier-Bloch-Floquet transform.

The electric conductivity of atomically thick materials such as graphene and black phosphorous yields an effective complex permittivity with a negative real part in the far- and mid-infrared spectrum. This feature allows for the propagation of slowly decaying electromagnetic waves, called surface plasmons-polaritons (SPPs) that are confined near the material interface with wavelengths much shorter than the wavelength of the free-space radiation. These SPPs are promising ingredients in the design of ultrafast photonic circuits

Recent research in the mathematics community has made great progress towards the development of rigorous foundations and efficient and accurate methods to compute the electronic, optical, and mechanical properties of incommensurate 2D heterostructures, defects, edge states, and surface plasmonics. This workshop will bring together mathematicians and scientists to review recent progress and to chart new directions.