Local doping of monolayer WSe$_2$ on piezoelectric GaInP$_2$ and GaN substrates

Non-contact local doping of monolayer WSe$_2$ transferred to piezoelectric epitaxial structures based on InP/GaInP$_2$ and GaN, having surface potential variations with an amplitude of $\sim$0.1 V and a size of $\sim$0.2–1 $\mu$m is shown. Using scanning probe microscopy surface potential measurements, as well as optical reflectance, photoluminescence, and Raman spectroscopy measurements we observed variations in charged exciton (trion) emission/reflectance and Raman intensity due to variations in the surface potential of WSe$_2$ monolayers, indicating local doping at $n\sim$10$^{12}$ cm$^{-2}$. Our results can be used to create Wigner quantum dots in transition metal dichalcogenides, which is promising for the development of fault-tolerant topological quantum computing at room temperature and without a magnetic field.