The Stark effect on excitons in a bilayer system

The Stark effect on excitons in a bilayer system is investigated theoretically within the framework of the effective-mass approximation. The calculations indicate that the energy of the excitons decreases as the value of the in-plane electric field $F$ increases at a fixed value of the distance $d$ between the layers. However, the energy of the excitons increases with $d$ at a fixed value of $F$⁠. In particular, it increases linearly at small values of $d$ but increases as $1∕d$ at large values. Therefore, it can be concluded that excitons in a bilayer system have a small binding energy equal to the absolute value of the excitonic energy at large $d$ or small $F$⁠. In addition, the radiative lifetime of heavy-hole excitons in this system is calculated and is found to be short at small values of both $F$ and $d$⁠. The radiative lifetime of heavy-hole excitons in a bilayer system can be increased by two orders by an in-plane electric field of $2kV∕cm$ when $d$ is twice the excitonic Rydberg.