AbstractThe few layer transition metal dichalcogenides are two dimensional materials that have an intrinsic gap of the order of ≈2 eV. The reduced screening in two dimensions implies a rich excitonic physics and, as a consequence, many potential applications in the field of opto-electronics. Here we report that a layer perpendicular electric field, by which the gap size in these materials can be efficiently controlled, generates an anomalous inter-layer exciton whose binding energy is independent of the gap size. We show this originates from the rich gap control and screening physics of TMDCs in a bilayer geometry: gating the bilayer acts on one hand to increase intra-layer screening by reducing the gap and, on the other hand, to decrease the inter-layer screening by field induced charge depletion. This constancy of binding energy is both a striking exception to the universal reduction in binding energy with gap size that all materials are believed to follow, as well as evidence of a degree of control over inter-layer excitons not found in their well studied intra-layer counterparts.