Abstract

During the last two decades first-principles methods, particularly Density Functional Theory (DFT), have become an indispensable tool in the study of solid-state systems. However, interpreting or predicting the results of experiments requires, in many cases, to go beyond the length and/or time scales allowed by current computational power. Based on the idea that not all electrons play a relevant role in the determination of the physical magnitudes under scrutiny, a systematically improvable approximation to DFT is presented. The resulting method, related to self-consistent tight-binding DFT , can be used to perform simulations in systems with tens of thousands of atoms at an accuracy that is comparable with DFT and able to deal with metals and magnetic systems. Several applications of second-principles will be shown, particularly their use to determine the structure of ferroelectric domain walls in PbTiO$_3$/SrTiO$_3$ superlattices under different strain conditions, revealing the appearance of chirality and topological properties. Some initial transport simulations on toy models will also be presented.