$WSe_2$ as transparent top gate for near-field experiments

Independent control of carrier density and out-of-plane displacement field is essential for accessing novel phenomena in two-dimensional material heterostructures. While this is achieved with independent top and bottom metallic gate electrodes in transport experiments, it remains a challenge for near-field optical studies as the top electrode interferes with the optical path. Here, we systematically characterize the requirements for a material to be used as top-gate electrode, and demonstrate experimentally that few-layer WSe_2 can be used as a transparent, ambipolar top gate electrode in infrared near-field microscopy. We perform nano-imaging of plasmons in a bilayer graphene heterostructure and tune the plasmon wavelength using a trilayer WSe_2 gate, achieving a density modulation amplitude exceeding 2 10^{12} cm^{-2}. Moreover, the observed ambipolar gate-voltage response allows to extract the energy gap of WSe_2 yielding a value of 1.05 eV. Our results will provide an additional tuning knob to cryogenic near-field experiments on emerging phenomena in two-dimensional materials and moir\'e material heterostructures.