Remote free-carrier screening to boost the mobility of Fröhlich-limited two-dimensional semiconductors

Van der Waals heterostructures provide a versatile tool to not only protect or control, but also enhance the properties of a 2D material. We use ab initio calculations and semianalytical models to find strategies which boost the mobility of a current-carrying two-dimensional (2D) semiconductor within a heterostructure. Free-carrier screening from a metallic ``screener'' layer remotely suppresses electron-phonon interactions in the current-carrying layer. This concept is most effective in 2D semiconductors whose scattering is dominated by screenable electron-phonon interactions, and in particular, the Fr\"ohlich coupling to polar-optical phonons. Such materials are common and characterized by overall low mobilities in the small doping limit and much higher ones when the 2D material is doped enough for electron-phonon interactions to be screened by its own free carriers. We use GaSe as a prototype and place it in a heterostructure with doped graphene as the ``screener'' layer and boron nitride as a separator. We develop an approach to determine the electrostatic response of any heterostructure by combining the responses of the individual layers computed within density functional perturbation theory. Remote screening from graphene can suppress the long-wavelength Fr\"ohlich interaction, leading to a consistently high mobility around $500--600\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}$/V s for carrier densities in GaSe from ${10}^{11}$ to ${10}^{13}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. Notably, the low-doping mobility is enhanced by a factor 2.5. This remote free-carrier screening is more efficient than more conventional manipulation of the dielectric environment, and it is most effective when the separator (boron nitride) is thin.