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Field-induced dissociation of excitons in two-dimensional MoS$_{2}$/hBN heterostructures

Atomically thin semi-conductors are characterized by strongly bound excitons which govern the optical properties of the materials below and near the band edge. Efficient conversion of photons into electrical current requires, as a first step, the dissociation of the exciton into free electrons and holes. Here we calculate the dissociation rates of excitons in monolayer MoS$_2$ as a function of an applied in-plane electric field. The dissociation rates are obtained as the inverse lifetime of the resonant states of a two-dimensional Hydrogenic Hamiltonian which describes the exciton within the Mott-Wannier model. The resonances are computed using complex scaling, and the effective masses and screened electron-hole interaction defining the Hydrogenic Hamiltonian are computed from first-principles. For field strengths above 0.1 V/nm the dissociation lifetime is shorter than 1 picosecond, which is shorter than the lifetime of other, competing, decay mechanisms. Interestingly, encapsulation of the \moly layer in just two layers of hBN, enhances the dissociation rate by around one order of magnitude due to the increased screening showing that dielectric engineering is an effective way to control exciton lifetimes in two-dimensional materials.