| Density-functional theory (DFT) has provided a powerful tool for studying solid-state physics problems accurately from a first-principles approach. The applications of DFT have undergone rapid development in recent decades in a broad area in condensed-matter physics. In my thesis work, I am focusing on the study of the problems that are related to the ground-state properties of insulating solids in the framework of DFT.; First, using the methods of density-functional perturbation theory, it is possible to compute the first derivatives of the electronic wavefunctions with respect to atomic-displacement, electric-field, and strain perturbations; and from these, tensors of second energy derivatives including both 'diagonal responses' and 'off-diagonal' ones. We developed a systematic approach for computing all of these quantities in a unified fashion, and for combining the information thus obtained to compute such properties as clamped-strain vs. free-stress dielectric tensors, elastic constants under different electrical boundary conditions, and piezoelectric coupling factors.; Next, using first-principles density-functional methods, we investigate PbTiO3 superlattices in which the polarization alternates from up to down along the growth direction, and in which the large polarization charges at the 180° head-to-head and tail-to-tail domain walls are compensated by heterovalent substitution. We show that it is theoretically possible to construct insulating superlattice structures of this kind, and investigate their novel properties.; In the third part, I will present our work in which we have extended a method that maps out the energy as a function of polarization E (P) in insulating solids by including the strain relaxation. I will show by examples that in ferroelectric materials, the strain relaxation is crucial for the real application of the E(P) mapping method.; The maximally localized Wannier function (WF) method of Marzari and Vanderbilt (Phys. Rev. B 56, 12847 (1997)) generates WFs and WF centers directly related to electronic polarization. In the last part, in superlattices made of perovskites, we defined a new concept of "layer polarization" (LP) based on the charges and locations of both WF centers and ionic centers in different layers in the direction normal to the plane. It is shown by examples that LP is a powerful tool for analyzing local properties associated with interfaces, structural distortions, etc. |
