Significant progress in field of Weak Topological Insulators and Composite Weyl Semimetals was achieved by school of Physics, Beijing Institute of Technology
2016年05月31日
Abstract While strong topological insulators (STIs) were experimentally realized soon after they were theoretically predicted, a weak topological insulator (WTI) has yet to be unambiguously confirmed. A major obstacle is the lack of distinct natural cleavage surfaces to test the surface selective hallmark of a WTI. With a new scheme, we discover that β−Bi4X4 (X=Br,I are natural WTIs. Most distinctly, their side surfaces (e.g., the {100} surfaces) are insulating with a band gap of ∼200 meV, while their top and bottom surfaces are metallic with topological surface states. We further demonstrate that a moderate uniaxial strain can readily drive these WTIs into STIs or Weyl semimetals. More interestingly, we predict a composite Weyl semimetal, which hosts both Weyl nodes and nodal rings. Our work not only identifies the first family of natural WTIs, but also provides a new route to designing novel topological phases.
Figure 1 The crystal structure of a conventional cell of β−Bi4X4 (X=Br,I. (b) The corresponding first BZ with high-symmetry points labeled. (c) The calculated phonon spectrum of β−Bi4I4, which confirms its dynamical stability.
Figure 2 (a),(b) The bulk band structures for β−Bi4I4 and β−Bi4Br4 without and with SOC, respectively. (c),(d) The calculated band structures for the (001) surfaces of β−Bi4I4 and β−Bi4Br4. (e),(f) The calculated band structures for the (100) surfaces of β−Bi4I4 and β−Bi4Br4. The insets in (c) and (d) show the constant energy contours at E=0.1 and 0.15 eV, respectively.
Figure 3 The topological phase diagrams vs the uniaxial strain along the a axis are depicted in (a) for β−Bi4I4 and in (b) for β−Bi4Br4. The topological indices (Z2) are given in the form of (ν0;ν1ν2ν3). The WSM phase is marked by the number of pairs of Weyl nodes. The direct band gaps at the L and M points are also plotted.
Figure 4 (a) Schematic phase diagram of a NI, STI, WSM, WTI, and the novel phase CWSM. The two curves depict the direct gaps near the relevant L and M points. (b) Existence of two open Fermi arcs at the (001) surface of the calculated CWSM. (c) Coexistence of two open Fermi arcs and one closed Fermi circle at the (100) surface of the same CWSM. In (b) and (c), the dimensions have been magnified for clarity.
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