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Capacitively-coupled and inductively-coupled excitons in bilayer MoS$_2$

The interaction of intralayer and interlayer excitons is studied in a two-dimensional semiconductor, homobilayer MoS$_2$. It is shown that the measured optical susceptibility reveals both the magnitude and the sign of the coupling constants. The interlayer exciton interacts capacitively with the intralayer B-exciton (positive coupling constant) consistent with hole tunnelling from one monolayer to the other. Conversely, the interlayer exciton interacts inductively with the intralayer A-exciton (negative coupling constant). First-principles many-body calculations show that this coupling arises via an intravalley exchange-interaction of A- and B-excitons.