I will discuss recent  theoretical work on exciton physics in two-dimensional materials. First, I will focus on the neutral particle-hole pair excitations of correlated “orbital Chern insulators” recently detected in twisted bilayer graphene, whose approximately flat conduction and valence bands have equal and opposite non-zero Chern number. Using a mix of exactly solvable models and microscopic numerical simulations, I will argue that these features can combine to endow the exciton bands with nontrivial Berry curvature [1]. I will then argue, more speculatively, that under certain circumstances this could stabilize a series of “excitonic” fractional quantum Hall states descending from the parent “integer" OCI state [2]. I will then change gears to focus on work motivated by recent experiments on monolayer WTe2. I willl describe the zero-field excitonic insulating phase thought to be present in this system, and clarify the role played by band topology in  the competition between distinct broken-symmetry exciton orders [3]. If there is time, I will also comment on the concomitant observation of quantum oscillations coincident with insulating behaviour when the same system is placed in a transverse magnetic field.

[1] YH Kwan, Y Hu, SH Simon, SP, arXiv: 2003.11560, to appear in PRL.
[2] YH Kwan, Y Hu, SH Simon, SP, arXiv: 2003.11559.
[3] YH Kwan, T Devakul, SL Sondhi, SP, arxiv:2012.5255,  2101.05294.