Effects of Electric Polarization in Hybridized Materials

[Abstract]:
In this dissertation, consequences of the treatment of electronic polarization of condensed matter systems beyond some common approximations are investigated. Striking behavior and phenomena which fail to be captured by conventional methods are directly predicted through the relaxation of these approximations. First, the influence of complex electronic wavefunctions instead of plane wave states in Lindhard charge susceptibility is shown to be responsible for the lack of longitudinal Peierls instabilities in alkali chains contrary to hydrogen chains. Specifically, the even-odd interatomic hybridization between s and p orbitals is demonstrated to be the main cause of the suppression of this instability. Then, the same even-odd s-p hybridization is shown to drive purely charge-based topological phases for elemental alkali and alkaline earth systems, both in 1D chains and in 2D hexagonal lattices. The topological edge states hosted by such phases correspond to effective end charges leading to measurable net electric polarization. Contrary to topological behavior originating from spin-orbit coupling-induced band inversion favoring heavier elements, this mechanism is demonstrated to encourage topology for light elements. 
Next, the charge-based topology of the Ti4Mn chains inside of quasi-1D material Ti4MnBi2 is investigated. By default, this material is shown to possess two degenerate and orthogonal subspaces that each correspond to two independent two-band strong topological systems with exactly exclusive topological conditions. When mixing is allowed between the two subspaces, the resulting four-band system is still topological but exhibits a richer phase diagram containing distinct topological phases. 
Finally, the screened Coulomb interaction between two doped holes in cuprate superconductors is calculated through a real space approach foregoing the uniformly polarizable medium approximation. This leads to the discovery of a pronounced local repulsion minimum at a distance of one lattice constant, providing an explanation for the short coherence lengths of unconventional superconductors. Due to anisotropic Cu-O bond polarizability, the repulsion minimum only occurs along Cu-O bond directions, a result consistent with the d-wave gap symmetry of the cuprates. Furthermore, the suppression of long-range screening in low-dimension systems is demonstrated to stem from the three-dimensional nature of the Coulomb interaction.