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 ${\mathcal{E}}_{\mathrm{c}}$ that depends inversely on the density of $k$ points; the disappearance of the minima at ${\mathcal{E}}_{\mathrm{c}}$ signals the onset of Zener breakdown. We illustrate the procedure by computing the piezoelectric and nonlinear dielectric susceptibility tensors of III-V semiconductors.