Electronic-structure methods for twisted moiré layers

When single layers of 2D materials are stacked on top of one another with a small twist in orientation, the resulting structure often involves incommensurate moire patterns. In these patterns, the loss of angstrom-scale periodicity poses a significant theoretical challenge, and the new moire length scale leads to emergent physical phenomena. The range of physics arising from twisted bilayers has led to significant advances that are shaping into a new field, twistronics. At the moire scale, the large number of atoms in these systems can make their accurate simulation daunting, necessitating the development of efficient multiscale methods. In this Review, we summarize and compare such modelling methods — focusing in particular on density functional theory, tight-binding Hamiltonians and continuum models — and provide examples spanning a broad range of materials and geometries. When single layers of 2D materials are stacked on top of one another with a small twist, the resulting moire pattern introduces new electronic properties. This Review surveys and compares the modelling techniques used in this emerging field of twistronics.