The role of dimensionality in the decay of surface effects

We computationally investigate the decay of surface effects in one-, two-, and three-dimensional materials using two-band tight-binding models. These general models facilitate a direct comparison between materials of differing dimensionality, which reveals that material dimensionality (not material-specific chemistry/physics) is the primary factor controlling the decay of surface effects. Our results corroborate more sophisticated, material-specific studies, finding that surface effects decay after ∼10, ∼25, and ≳ 100 layers in three-dimensional, two-dimensional, and one-dimensional materials, respectively. Physically, higher-dimensional materials screen surface effects more efficiently, as theoretically described by integration over each layer's Brillouin zone. Finally, we discuss several implications of these results.