Flexoelectricity, describing the polarization response to a gradient of the strain, is a universal property of all insulators that has attracted considerable attention in the past few years.  In spite of its fundamental and practical interest, it has long resisted theoretical attempts at quantifying it with predictive accuracy in realistic materials. In this talk, I will introduce the methodological advances that have recently lifted this limitation in the context of first-principles electronic-structure theory.  I will discuss applications to perovskite-structure SrTiO3, either in the cubic  or ferroelastic tetragonal phase.  I will also emphasize the generality of these newly established theoretical tools, with interesting connections to the physics of orbital magnetism, natural optical activity and magnetoelectric couplings.
 M. Stengel and D. Vanderbilt, in "Flexoelectricity in Solids From Theory to Applications", edited by A. K. Tagantsev and P. V. Yudin (World Scientific Publishing Co., Singapore, 2016).
 Miquel Royo and Massimiliano Stengel, Phys. Rev. X 9, 021050 (2019)
 M. Stengel, Phys. Rev. B 90, 201112(R) (2014)  Andrea Schiaffino and Massimiliano Stengel, Phys. Rev. Lett. 119, 137601 (2018)
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