On higher-order quantum stress

Abstract

In this paper, we present a novel theory of the higher-order quantum stress and its formulations in the framework of density functional theory. Specifically, we have systematically derived the third-order quantum stress expression based on the higher-order Cauchy–Born rule in combination with the higher-order strain gradient theory. The higher-order quantum stress formulation provides a theoretical foundation for first-principle calculation of stress couples at atomistic scale, which may help us understand possible quantum strain gradient effects, and related ferroelectric and flexoelectric effects at small scales.