Force sum rules, stress theorems, and Thomas-Fermi treatment of a 90° jellium edge

A quarter-space jellium or 90° jellium wedge is considered a highly idealized element of real metallic surfaces with ledges or with atomic-scale sharp edges such as those in quantum wires and quantum dots. Using the concept of energy density, an edge energy is defined. Force sum rules are summarized, relating the electric field that arises from the dipole layer along the background discontinuity with density derivatives of the surface energy (of a half-space jellium) and of the sharp edge energy. Within the Thomas-Fermi approximation, the electron density is determined. Besides sharp edges, nonsharp edges with finite curvature are also considered, the latter characterized by the recently introduced curvature energy.