Title: Excitonic response in TMD heterostructures from first-principles: impact of stacking, twisting, and interlayer distance

Abstract: Van der Waals heterostructures of two-dimensional transition metal dichalcogenides provide a unique platform to engineer optoelectronic devices tuning their optical properties via stacking, twisting, or straining. Using ab initio Many-Body Perturbation Theory, we predict the electronic and optical (absorption and photoluminescence spectra) properties of MoS$_2$/WS$_2$ and MoSe$_2$/WSe$_2$ hetero-bilayers with different stacking and twisting. We analyse the valley splitting and optical transitions, and explain the enhancement or quenching of the inter- and intra-layer exciton states. Contrary to established models, that focus on transitions near the high-symmetry point K, our results include all possible transitions across the Brillouin Zone. This result, for a twisted Se-based heterostructures, in an interlayer exciton with significant electron density in both layers and a mixed intralayer exciton distributed over both MoSe$_2$ and WSe$_2$. We propose that it should be possible to produce an inverted order of the excitonic states in some MoSe$_2$/WSe$_2$ heterostructures, where the energy of the intralayer WSe$_2$ exciton is lower than that in MoSe$_2$. We predict the variability of the exciton peak positions ($\sim$100 meV) and the exciton radiative lifetimes, from pico- to nano-seconds, and even micro-seconds in twisted bilayers. The control of exciton energies and lifetimes paves the way towards applications in quantum information technologies and optical sensing.