5 SCIENTIFIC HIGHLIGHT OF THE MONTH First-principles calculations of the Berry curvature of Bloch states for charge and spin transport of electrons

Recent progress in wave packet dynamics based on the insight of M. V. Berry pertaining to adiabatic evolution of quantum systems has led to the need that a new property of a Bloch state, the Berry curvature, has to be calculated from first principles. We report here on the response to this challenge by the ab initio community during the past decade. First we give a tutorial introduction of the conceptual developments we mentioned above. Then we describe four methodologies which have been developed for first-principles calculations of the Berry curvature. Finally, in Section 3, to illustrate the significance of the new developments, we report some results of calculations of interesting physical properties like anomalous and spin Hall conductivity.