Stark effect of doped two-dimensional transition metal dichalcogenides

The bandgap of two-dimensional (2D) semiconductors can be efficiently tuned by a gate electric field, which is the so-called the Stark effect. We report that doping, which is essential in realistic devices, will substantially change the Stark effect of few-layer transition metal dichalcogenides in unexpected ways. Particularly, in bilayer structures, because of the competition between strong quantum confinement and the intrinsic screening length, electron and hole dopings exhibit surprisingly different Stark effects: doped electrons actively screen the external field and result in a nonlinear Stark effect; however, doped holes do not effectively screen the external field, causing a linear Stark effect that is the same as that of undoped materials. Our further analysis shows that this unusual doping effect is not limited within transition metal dichalcogenides but general for 2D structures. Therefore, doping plays a much more crucial role in functional 2D devices, and this unusual Stark effect also provides a new degree of freedom to tune bandgaps and optical properties of 2D materials.