Flexoelectricity via coordinate transformations

Flexoelectricity describes the electric polarization that is linearly induced by a strain gradient, and is being intensely investigated as a tantalizing new route to converting mechanical stimulation into electrical signals and vice versa [1]. While several breakthough experiments have been reported in the past few years, progress on the theoretical front has been comparatively slow, especially in the context of first-principles electronic-structure theory. The main difficulty with calculating the flexoelectric response of a material is the inherent breakdown of translational periodicity that a strain gradient entails, which at first sight questions the very applicability of traditional plane-wave pseudopotential methods. In this talk I will show how these obstacles can be overcome by combining density-functional perturbation theory with generalized coordinate transformations [2,3], gaining access to the full microscopic response (in terms of electronic charge density, polarization and atomic displacements) of a crystal or nanostructure to an arbitrary deformation field. As a practical demonstration, I will present results on the full flexoelectric response of a SrTiO$_3$ film, including atomic relaxations and surface effects. \\[4pt] [1] P. Zubko, G. Catalan, and A. K. Tagantsev, Annu. Rev. Mater. Res. {\bf 43}, 387-421 (2013).\\[0pt] [2] M. Stengel, Phys. Rev. B, in press. (arXiv:1306.4240).\\[0pt] [3] M. Stengel, Nature Communications {\bf 4}, 2693 (2013).