  We derive a dielectric-dependent hybrid functional which accurately describes
the electronic properties of heterogeneous interfaces and surfaces, as well as
those of three- and two-dimensional bulk solids. The functional, which does not
contain any adjustable parameter, is a generalization of self-consistent hybrid
functionals introduced for homogeneous solids, where the screened Coulomb
interaction is defined using a spatially varying, local dielectric function.
The latter is determined self-consistently using density functional
calculations in finite electric fields. We present results for the band gaps
and dielectric constants of 3D and 2D bulk materials, and band offsets for
interfaces, showing an accuracy comparable to that of GW calculations.
