Flexoelectricity from density-functional perturbation theory

Abstract

We derive the complete flexoelectric tensor, including electronic and lattice-mediated effects, of an arbitrary insulator in terms of the microscopic linear response of the crystal to atomic displacements. The basic ingredient, which can be readily calculated from first principles in the framework of density-functional perturbation theory, is the quantum-mechanical probability current response to a long-wavelength acoustic phonon. Its second-order Taylor expansion in the wavevector q around the Gamma (q=0) point in the Brillouin zone naturally yields the flexoelectric tensor. At order one in q we recover Martin's theory of piezoelectricity [R. M. Martin, Phys. Rev. B 5, 1607 (1972)], thus providing an alternative derivation thereof. To put our derivations on firm theoretical grounds, we perform a thorough analysis of the nonanalytic behavior of the dynamical matrix and other response functions in a vicinity of Gamma. Based on this analysis, we find that there is an ambiguity in the specification of the "zero macroscopic field" condition in the flexoelectric case; such arbitrariness can be related to an analytic band-structure term, in close analogy to the theory of deformation potentials. As a byproduct, we derive a rigorous generalization of the Cochran-Cowley formula [W. Cochran and R. A. Cowley, J. Phys. Chem. Solids 23, 447 (1962)] to higher orders in q. This can be of great utility in building reliable atomistic models of electromechanical phenomena, as well as for improving the accuracy of the calculation of phonon dispersion curves. Finally, we discuss the physical interpretation of the various contributions to the flexoelectric response, either in the static or dynamic regime.

26 pages, 2 figures. The newly added Section VI deals with the nonanalytic properties of the electronic response functions, and generalizes the lattice-dynamical theory of Pick, Cohen and Martin (Ref. 32) to higher orders in q

References in corpus (4)

• Strain gradient induced polarization in SrTiO3 single crystals
• First-principles theory and calculation of flexoelectricity
• Quantum Flexoelectricity in Low Dimensional Systems
• Towards a bulk theory of flexoelectricity

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