Polarization-Based Calculation of the Dielectric Tensor of Polar Crystals

The modern quantum theory of polarization in dielectrics has been formulated only in recent years [1]. This development has opened a new era in the first principles theory of ferroelectricity and pyroelectricity [2]. The new theory has been used successfully to calculate, in a well defined and computationally efficient way, the macroscopic polarization changes induced by perturbations other than an electric field. Examples of such perturbations are, e.g., lattice vibrations [2], ferroelectric distortions [2], and piezoelectric deformations [3,4], whereby the quantities being calculated are typically dynamical Born charges, spontaneous polarization, and piezoelectric constants. So far, no direct attempt has been made towards the goal of determining the dielectric tensor (which of course quantifies the response to an external electric field) using polarization theory. In this Letter we present a novel method for calculating the static dielectric tensor of a crystal based on concepts from polarization theory; in particular, the method rests entirely on the evaluation of the dielectric polarization in zero field via the geometric quantum phase approach [1]. The method works in any polar material, i.e., any material having infrared-active zone-center modes. As an application, we provide, to our knowledge, the first determination of the dielectric constants ́k along the (0001) axis for the wurtzite III-V nitride compounds AlN, GaN, and InN. The current method of choice for dielectric response calculations is density functional perturbation theory (DFPT) [5], a general and powerful approach to response properties. The method presented here, besides its different foundations, is less general but considerably simpler to implement than DFPT, and it may become a useful alternative. The static dielectric tensor.—The calculation of the dielectric tensor is highly nontrivial, because it entails the determination of the electronic, as well as vibrational and elastic-piezoelectric, responses to an external electrostatic field. The elements of the dielectric tensor are ́ij ­ dij 1 4p dPi dEj , (1)