A First-Principles Approach to Insulators in Finite Electric Fields
  We describe a method for computing the response of an insulator to a static, homogeneous electric field. It consists of iteratively minimizing an electric enthalpy functional expressed in terms of occupied Bloch-like states on a uniform grid of k points. The functional has equivalent local minima below a critical field E_c that depends inversely on the density of k points; the disappearance of the minima at E_c signals the onset of Zener breakdown. We illustrate the procedure by computing the piezoelectric and nonlinear dielectric susceptibility tensors of III-V semiconductors. 
Ivo Souza, Jorge Iniguez, and David Vanderbilt (Department of Physics   and Astronomy, Rutgers University)