Characterization of topological insulators and semiconductors
Creators: name: Taherinejad, Maryam
Publisher: name: No Publisher Supplied
Year: 2015

description: 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.