Berry-phase theory of proper piezoelectric response

Recent theoretical advances have established that the electric polarization in an insulating crystal can be viewed as a multivalued quantity that is d etermined by certain Berry phases associated with the occupied Bloch bands. The application of this approach to the computation of piezoelectric coeff icients is not entirely straightforward, since a naive determination of the ("improper") piezoelectric coefficients from finite differences of the pol arization at nearby strain states leads to a dependence upon the choice of "branch" of the polarization. The purpose of the present paper is to clarif y that if one calculates instead the "proper" piezoelectric response, the b ranch dependence is eliminated. From this analysis, a simplified recipe for the direct finite-difference computation of the proper piezoelectric coeff icients emerges naturally. (C) 1999 Elsevier Science Ltd. All rights reserv ed.