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We present a perturbative treatment of the response properties of insulatingcrystals under a dc bias field, and use this to study the effects of such biasfields on the Born effective charge tensor and dielectric tensor of insulators.We start out by expanding a variational field-dependent total-energy functionalwith respect to the electric field within the framework of density-functionalperturbation theory. The second-order term in the expansion of the total energyis then minimized with respect to the first-order wave functions, from whichthe Born effective charge tensor and dielectric tensor are easily computed. Wedemonstrate an implementation of the method and perform illustrativecalculations for the III-V semiconductors AlAs and GaAs under finite biasfield

First-principles perturbative computation of dielectric and Born charge tensors in finite electric fields