Mechanical stress is arguably the simplest type of external field that can be applied to a crystalline solid. What happens to the electronic wavefunctions in the course of a deformation, however, is nowhere simple; on the contrary, interesting functionalities can emerge that are nowadays under the spotlight of researchers and engineers alike. An example of such functionalities is flexoelectricity, which describes the electrical polarization response to the gradient of a strain (Figure).
During the last five years or so, we have made tremendous advances towards the development of a “modern” theory of flexoelectricity, and only very recently we have reached the stage where first-principles calculations for realistic materials can be performed with relative ease. Achieving this goal forced us to rethink the methodological bases of density-functional theory from their very root: strain gradients break translational symmetry and this is a major obstacle for the established approaches. Here, we address this issue by representing the Schrödinger equation in the curvilinear “co-moving” frame of the deformed crystal; the main advantage is that the perturbation no longer changes the boundary conditions of the Hamiltonian, and can be more easily dealt with.
Apart from the methodological advances, which have already been used in public code implementations, our work also unveils some peculiar and unsuspected aspects of flexoelectricity, e.g. its relationship to the theory of orbital magnetism. These results are an important milestone towards a fundamental understanding of phenomena where an electrical polarization results from a spatially inhomogeneous configuration of the crystal.
Massimiliano Stengel1,2 and David Vanderbilt3
1Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Spain
2ICREA–Institució Catalana de Recerca i Estudis Avançats, Spain
3Department of Physics and Astronomy, Rutgers University, USA
Quantum theory of mechanical deformations
Physical Review B 98, 125133 (2018)
Schematic illustration of the flexural deformation of a slab. Thick arrows indicate the Cartesian axes; thick gray curves indicate the slab surfaces.