Long-wavelength density-functional perturbation theory

Density-functional perturbation theory (DFPT) is nowadays the method of choice for the accurate computation of linear and non-linear response properties of materials from first principles. A notable advantage of DFPT over alternative approaches is the possibility of treating incommensurate lattice distortions with an arbitrary wavevector, q, at comparable computational cost as the lattice-periodic case.
In this talk, I will show that q can be formally treated as a perturbation parameter, and used in conjunction with established results of perturbation theory (e.g. the "2n+1" theorem) to perform a long-wave expansion of an arbitrary response function in powers of the wavevector components. This provides a powerful, general framework to accessing the physical response to the spatial gradient of an arbitrary external field (electric, magnetic, strain or atomic displacement), with a computational cost that is comparable to that of a standard linear-response calculation. As applications of the method, I will discuss the flexoelectric tensor (the polarization response to a gradient of the strain field) and on the "dynamical quadrupoles" (a higher-order multipolar generalization of the Born effective charge tensor).