Topological Classification of Crystalline Insulators with Point Group Symmetry

We show that in crystalline insulators point group symmetry alone gives rise to a topological classification based on the quantization of electric polarization. Using C3 rotational symmetry as an example, we first prove that the polarization is quantized and can only take three inequivalent values. Therefore, a Z3 topological classification exists. A concrete tight-binding model is derived to demonstrate the Z3 topological phase transition. Using first-principles calculations, we identify graphene on BN substrate as a possible candidate to realize the Z3 topological states. To complete our analysis we extend the classification of band structures to all 17 two-dimensional space groups. This work will contribute to a complete theory of symmetry conserved topological phases and also elucidate topological properties of graphene like systems

Edge Saturation effects on the magnetism and band gaps in multilayer graphene ribbons and flakes

Using a density functional theory based electronic structure method and semi-local density approximation, we study the interplay of geometric confinement, magnetism and external electric fields on the electronic structure and the resulting band gaps of multilayer graphene ribbons whose edges are saturated with molecular hydrogen (H$_2$) or hydroxyl (OH) groups. We discuss the similarities and differences of computed features in comparison with the atomic hydrogen (or H-) saturated ribbons and flakes. For H$_2$ edge-saturation, we find \emph{shifted} labeling of three armchair ribbon classes and magnetic to non-magnetic transition in narrow zigzag ribbons whose critical width changes with the number of layers. Other computed characteristics, such as the existence of a critical gap and external electric field behavior, layer dependent electronic structure, stacking-dependent band gap induction and the length confinement effects remain qualitatively same with those of H-saturated ribbons.Comment: 9 pages, 10 figures, submitte

Comment On >Assessment Of Field-Induced Quantum Confinement In Heterogate Germanium Electron-Hole Bilayer Tunnel Field-Effect Transistor> Appl. Phys. Lett. 105, 082108 (2014)

Not AvailableNRI SWAN programNSF NASCENT ERCMicroelectronics Research CenterElectrical and Computer Engineerin

Effects of edge magnetism and external electric field on energy gaps in multilayer graphene nanoribbons

Using first-principles density-functional theory, we study the electronic structure of multilayer graphene nanoribbons as a function of the ribbon width and the external electric field, applied perpendicular to the ribbon layers. We consider two types of edges (armchair and zigzag), each with two edge alignments (referred to as alpha- and beta-alignments). We show that, as in monolayer and bilayer armchair nanoribbons, multilayer armchair nanoribbons exhibit three classes of energy gaps which decrease with increasing width. Nonmagnetic multilayer zigzag nanoribbons have band structures that are sensitive to the edge alignments and the number of layers, indicating different magnetic properties and resulting energy gaps. We find that energy gaps can be induced in ABC-stacked ribbons with a perpendicular external electric field while in other stacking sequences, the gaps decrease or remain closed as the external electric field increases.Comment: 7 pages, 9 figures, text revised, last version before publicatio