Moiré Patterns in Two-Dimensional Materials
According to Wikipedia a moiré pattern (/mwɑːrˈeɪ/; French: [mwaˈʁe]) is a large scale interference pattern that is produced when an opaque regular pattern with transparent gaps is overlaid on another similar pattern with a different pitch or orientation. Moiré patterns are ubiquitous in two-dimensional van der Waals materials in which the regular patterns are formed by two-dimensional crystals, differences in pitch are established by differences in lattice constants and differences in orientation, which can be controlled experimentally. The electronic properties of two-dimensional semiconductor, gapless semiconductor, and semimetal systems in which moiré patterns have been established have continuum model Hamiltonians with the periodicity of the moiré pattern. I will discuss some examples [2,3,4] of new physics that can be explored using van der Waals material moiré patterns, comment on the recent discovery  of superconductivity in magic angle twisted bilayer graphene, and speculate on interesting future directions.
 Moire bands in twisted double-layer graphene, R. Bistritzer and A.H. MacDonald, PNAS 108, 12233 (2011).
 Fractional Hofstadter States in Graphene on Hexagonal Boron Nitride, Ashley M. DaSilva, Jeil Jung, and A.H. MacDonald, Phys. Rev. Lett. 117, 036802 (2016).
 Topological Exciton Bands in Moiré Heterojunctions, Fengcheng Wu, Timothy Lovorn, and A.H. MacDonald, Phys. Rev. Lett. 118, 14701 (2017).
 Theory of phonon-mediated superconductivity in twisted bilayer graphene, Fengcheng Wu, A.H. MacDonald, and I. Martin, Phys. Rev. Lett. 121, 257001 (2018).
 Magic-angle graphene superlattices: a new platform for unconventional superconductivity, Y. Cao et al. Nature (2018).