Abstract
We present results of a microscopic tight-binding modeling of BiSe three-dimensional topological insulator using a sp Slater–Koster Hamiltonian, with parameters calculated from density functional theory. Based on the calculated atomic- and orbital-projections of the wavefunctions associated with valence- and conduction-band states at the center of the Brillouin zone, we propose a real-space description of band inversion for both bulk and a slab of finite thickness. A systematic analysis of the key features of the surface states, in particular the spatial distribution and the spin-character of the surface states wavefunction, is carried out for slabs of different thickness, ranging from one to tens of quintuple layers. We obtain an estimate of the slab thickness at which the energy gap induced by interaction between the top and bottom surface states becomes negligible, based on the present available numerical precision. We anticipate that this finding will be relevant for all microscopic calculations addressing the effect of external perturbations on the surface states near the Dirac point. The modifications in the helical spin-texture of the Dirac-cone surface states, in the form of in-plane and out-of-plane spin projections, are calculated as a function of the slab thickness. These calculations are important for the interpretation of ongoing experiments, which probe the spin-polarization of the surface states in topological insulator thin films.
Highlights
IntroductionTopological insulator[1,2] (TI) materials host on their boundaries a novel type of topological states of quantum matter, which, unlike the quantum Hall state, exist without the breaking of time-reversal symmetry.[3,4] Theoretical prediction and subsequent experimental demonstration of these topological states in both two-5,6 (2D) and three-dimensional[7,8,9,10,11,12,13,14,15,16,17] (3D) systems have given rise to what is one of the most rapidly developing fields in condensed matter physics
Several studies have recently appeared in the literature, in which TB descriptions with different level of complexity have been introduced, ranging from models built on a simplified lattice structure[37] or a restricted orbital basis set inferred from symmetry arguments[38,39] to fully microscopic models, with parameters extracted from density functional theory (DFT).[28,40,41,42]
We have employed the sp[3] tight-binding model, with parameters extracted from ab initio calculations, to model the electronic structure of bulk and (111) surface of Bi2Se3 3D TI
Summary
Topological insulator[1,2] (TI) materials host on their boundaries a novel type of topological states of quantum matter, which, unlike the quantum Hall state, exist without the breaking of time-reversal symmetry.[3,4] Theoretical prediction and subsequent experimental demonstration of these topological states in both two-5,6 (2D) and three-dimensional[7,8,9,10,11,12,13,14,15,16,17] (3D) systems have given rise to what is one of the most rapidly developing fields in condensed matter physics. More accurate ab initio methods often lack the conceptual transparency and flexibility of the model Hamiltonian approaches, which have been of fundamental importance for driving progress in this research field.[3,4] Microscopic tight-binding (TB) models, which have already proved successful in quantitative description of electronic and magnetic properties of semiconductors,[35,36] may provide a convenient platform to address similar issues in TIs. Several studies have recently appeared in the literature, in which TB descriptions with different level of complexity have been introduced, ranging from models built on a simplified lattice structure[37] or a restricted orbital basis set inferred from symmetry arguments[38,39] to fully microscopic models, with parameters extracted from density functional theory (DFT).[28,40,41,42] To date, the latter class of models is still the least represented among the model Hamiltonian approaches to TIs
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