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.

Figure 1

The electric enthalpy $\mathcal{F}$ (solid line) and its components $E_{\mathrm{K}\mathrm{S}}$ (dashed line) and $-\Omega {\mathbf{P}}_{\mathrm{m}\mathrm{a}\mathrm{c}}·\mathcal{E}$ (dotted line), plotted as a function of the parameter $\theta$ that controls the update of a polarized Bloch state in a conjugate-gradients step.