We use self-consistent calculations to investigate the realization of jelliumlike surfaces at discontinuities in the curvature of two ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterostructure wells. The first well, which has a parabolic center and linearly graded edges, is equivalent to a uniform slab of positive charge. The second, asymmetric well is equivalent to a positive background with an abrupt step in the density. In both structures, dipole layers at the discontinuities in the effective background charge produce steps in the total potential. Such wells provide an ideal laboratory for testing theories of surface response.

• Received 4 May 1992

DOI:https://doi.org/10.1103/PhysRevB.46.4752