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In this paper we develop a new discrete method for calculating the dielectrictensor and Born effective charge tensor in finite electric field by usingBerry's phase and the gauge invariance. We present a new method to overcomenon-periodicity of the potential in finite electric field due to the gaugeinvariance, and construct the dielectric tensor and Born effective chargetensor that satisfy translational symmetry in finite electric field. In orderto demonstrate the correctness of this method, we also perform calculations forthe semiconductors AlAs and GaAs under the finite electric field to comparewith the preceding method and the experiment.

New discrete method for investigating the response properties in finite electric field