Theory of semi-conducting moiré materials

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The stacking of atomically thin 2D crystals into multilayers has introduced to the condensed matter community an essentially new system: the small angle moire lattice. Moire systems beyond graphene, the prototype of such materials, are, spurred by developments in fabrication techniques, now beginning to be investigated. The remarkable physics of the graphene moire leads to hopes that the general moire material, especially when created from 2d semiconductors, may present a system both fundamental scientific interest, as well as being of potentially wide technological application. However, the structural complexity of small angle moires created from 2d semiconductors such as transition metal dichalcogenides, has, to date, prevented exploration these systems.We thus aim to provide an understanding of the basic electronic structure of small angle semi-conducting moire: (i) the development and application of continuum theories that will allow the small angle limit to be explored, (ii) the nature of the gap edge and the role of moire driven localization in the small angle limit, and (iii) the possibility of “moire designing” the gap edge of few layer semiconductors. Subsequent to the accumulation of this expertise we then plan to investigate the key optical properties of such systems. In particular the optical absorption spectrum will be calculated both with a parameter free "bootstrap" approach, and the interplay of single particle and excitonic localization on the moire investigated.