Topological Exciton Bands in Moir\'e Heterojunctions*

Moir\'e patterns are common in Van der Waals heterostructures and can be used to apply periodic potentials to elementary excitations. We will show that the optical absorption spectrum of transition metal dichalcogenide bilayers is profoundly altered by long period moir\'e patterns that introduce twist-angle dependent satellite excitonic peaks.\footnote{F. Wu, T. Lovorn, and A. H. MacDonald, arXiv: 1610.03855.} Topological exciton bands with non-zero Chern numbers that support chiral excitonic edge states can be engineered by combining three ingredients: i) the valley Berry phase induced by electron-hole exchange interactions, ii) the moir\'e potential, and iii) the valley Zeeman field. We will also show that the moir\'e pattern can enable the optical probe of intra-Landau level excitations in the fractional quantum Hall regime.\footnote{F. Wu and A. H. MacDonald, arXiv: 1611.00776.}