Screening in reduced dimensions has strong consequences on the electronic properties in van der Waals semiconductors, impacting the quasiparticle band gap and exciton binding energy. Screening in these materials is typically treated isotropically, yet black phosphorus exhibits in-plane electronic anisotropy seen in its effective mass, carrier mobility, excitonic wavefunctions, and plasmonic dispersion. Here, we use the adsorption of individual potassium atoms on the surface of black phosphorus to vary the near-surface doping over a wide range, while simultaneously probing the dielectric screening via the ordering of the adsorbed atoms. Using scanning tunneling microscopy, we visualize the role of strongly anisotropic screening which leads to the formation of potassium chains with a well-defined orientation and spacing. We quantify the mean interaction potential utilizing statistical methods and find that the dimensionality and anisotropy of the screening is consistent with the presence of a band-bending induced confinement potential near the surface. We corroborate the observed behavior with coverage-dependent studies of the electronic structure with angle-resolved photoemission.
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