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The interaction between an electric field and the electric charges in amaterial is described by electrostatic screening, which in metallic systems iscommonly thought to be confined within a distance of the order of theThomas-Fermi length. The validity of this picture, which holds for surfacecharges up to $\sim 10^{13}\,\mathrm{cm^{-2}}$, has been recently questioned byseveral experimental results when dealing with larger surface charges, such asthose routinely achieved via the ionic gating technique. Whether these resultscan be accounted for in a purely electrostatic picture is still debated. Inthis work, we tackle this issue by calculating the spatial dependence of thecharge carrier density in thin slabs of niobium nitride via an ab initiodensity functional theory approach in the field-effect transistorconfiguration. We find that perturbations induced by surface charges $\lesssim10^{14}\,\mathrm{cm^{-2}}$ are mainly screened within the first layer, whilethose induced by larger surface charges $\sim 10^{15}\,\mathrm{cm^{-2}}$ canpenetrate over multiple atomic layers, in reasonable agreement with theavailable experimental data. Furthermore, we show that a significantcontribution to the screening of large fields is associated not only to theaccumulation layer of the induced charge carriers at the surface, but also tothe polarization of the pre-existing charge density of the undoped system.

Anomalous screening of an electrostatic field at the surface of niobium nitride