This is a service provided by RUcore, Rutgers University Community Repository. https://rucore.libraries.rutgers.edu/rutgers-lib/48688/syndicate/rss/ Copyright 2018, Rutgers, The State University of New Jersey cmmills@libraries.rutgers.edu (RUcore Syndication Service) en-us RUcore Syndication System, v1.0 Wed, 31 Dec 1969 19:00:00 -0500 RUcore, Rutgers University Repository RSS Record Syndication https://rucore.libraries.rutgers.edu/rutgers-lib/48688/ https://doi.org/doi:10.7282/T3G73GQ6 Taherinejad, Maryam Thu, 01 Jan 2015 00:00:00 -0500 The theoretical prediction and experimental observation of topological insulators (TIs) and semiconductors in recent years have opened the floodgates to many interesting physical phenomena and potential technological applications. A major part of this work is devoted to characterization of topological insulators and semiconductors. We argue that various kinds of TIs can be insightfully characterized by an inspection of the charge centers of the hybrid Wannier functions, defined as the orbitals obtained by carrying out a Wannier transform on the Bloch functions in one dimension while leaving them Bloch-like in the other two. From this procedure, one can obtain the Wannier charge centers (WCCs) and plot them in the two-dimensional projected Brillouin zone. We show that these WCC sheets contain the same kind of topological information as is carried in the surface energy bands, with the crucial advantage that the topological properties of the bulk can be deduced from bulk calculations alone. The distinct topological behaviors of these WCC sheets in trivial, Chern, weak, strong, crystalline TIs, and in Weyl semimetal, are first illustrated by calculating them for simple tight-binding models. We then present the results of first-principles calculations of the WCC sheets in the trivial insulator Sb$_2$Se$_3$, the weak TI KHgSb, and the strong TI Bi$_2$Se$_3$, confirming the ability of this approach to distinguish between different topological behaviors in an advantageous way. We also study the adiabatic pumping of the Chern-Simons axion (CSA) coupling along a parametric loop characterized by a non-zero second Chern number $C^{(2)}$ from the viewpoint of the hybrid Wannier representation. We derive a new formula for the CSA coupling, expressing it as an integral involving Berry curvatures and potentials defined on the WCC sheets. We show that a loop characterized by a non-zero $C^{(2)}$ requires a series of sheet-touching events at which $2pi$ quanta of Berry curvature are passed from sheet to sheet, in such a way that $e^2/h$ units of CSA coupling are pumped by a lattice vector by the end of the cycle. We illustrate these behaviors via explicit calculations on a model tight-binding Hamiltonian and discuss their implications. Finally, we study the Bloch-type domain walls in rhombohedral BaTiO$_3$. Ferroelectric domain walls (FDWs) are usually considered to be of Ising type, but there have been suggestions in recent years that Bloch-type FDWs are also possible in some cases, e.g., in the rhombohedral phase of BaTiO$_3$. The mechanically compatible and electrically neutral FDWs in rhombohedral BaTiO$_3$ are of 71$^circ$, 109$^circ$, and 180$^circ$ type. We have investigated these FDWs based both on first-principles calculations and on a Ginzburg-Landau-Devonshire (GLD) model. The results from both approaches confirm the Ising nature of the 71$^circ$ FDW and the Bloch nature of the 180$^circ$ FDW, and predict both Ising-type and Bloch-type FDWs are possible for the 109$^circ$ case. In view of the relatively small rhombohedral strain in BaTiO$_3$, the results can be explained reasonably well by regarding a Bloch FDW as composed of a pair of smaller-angle Ising FDWs, and by comparing the sum of the energies of these constituents with an Ising-type solution. A reduction by 40\% in the parameters describing the gradient term in the GLD model brings it into better agreement with the first-principles results for detailed properties such as the energies and widths of the FDWs.