Topologically Protected Metallic States Induced by a One-Dimensional Extended Defect in the Bulk of a 2D Topological Insulator

Abstract

We report ab initio calculations showing that a single one-dimensional extended defect can originate topologically-protected metallic states in the bulk of two-dimensional topological insulators. We find that a narrow extended defect composed of periodic units consisting of one octogonal and two pentagonal rings embedded in the hexagonal bulk of a bismuth bilayer introduces two pairs of one-dimensional Dirac-fermion states with opposite spin-momentum locking. Although both Dirac pairs are localized along the extended-defect core, their interactions are screened due to the trivial topological nature of the extended defect. studies due to the coexistence of an insulating bulk band structure with a non-trivial topology that, when interfaced with a topologically trivial insulator such as the vacuum, gives rise to time-reversal-protected metallic surface states, with Dirac-fermion dispersions spanning the bulk band gap in the one-dimensional (1D) edges in twodimensional (2D) TIs. Existence of the edge states is a requirement imposed by the different topologies of the band structures across the interface. In these edge states, the spin quantization axis and the momentum direction are locked-in, implying that the metallic edge states are protected from backscattering, rendering their electronic conductance robust against the presence of disorder. Robust conduction and spin polarization may allow the manipulation of edge modes of TIs in many applications such as spintronics [7] and quantum computation [4,5].While topological-insulating band structures are also found in three-dimensional (3D) systems, manipulation of the metallic surface modes in 3D TIs is commonly hampered by the difficulty in tuning the Fermi level to achieve sufficiently low (ideally null) levels of bulk carriers, and the metallic surface carriers are significantly outnumbered by bulk carriers in most 3D TI samples [8,9]. Hence, 2D TIs can be advantageous in transport applications, because the 2D bulk is fully exposed to chemical manipulation and, besides, the bulk Fermi level can also be tuned by proper gating. When an insulating bulk is achieved, electrons can conduct only along the edge in these structures. From this, many efforts have been made to find candidate 2D TI systems.

Tunable Type-I and Type-II Dirac Fermions in Graphene with Nitrogen Line Defects

“…The originations of the two types of Dirac fermions are explained by tight-binding models. All the Dirac fermions exist in the "bulk" rather than the line defects, which is different from the cases that defects induce Dirac fermions [43,44].…”

Self-organized pseudo-graphene on grain boundaries in topological band insulators

“…This rapidly expanding list includes Bi x Sb 1−x with band inversions at the L-points [44], the topological Kondo insulator SmB 6 with band inversions at three X points [45,46] and the recently discovered bismuth iodide compounds that feature a transitionally active phase with band inversions at the Y points [47]. Topological semimetals are expected also on GBs in the topological crystalline Sn-based compounds [48][49][50], that feature band inversions at the L points as long as the protecting symmetry is respected [13,24], as well as in Bismuth bilayers with a band inversion at the M point, where a GB state has been identified in a recent ab initio study [51].Grain boundaries provide a natural setting for arrays of localized topological solitons to hybridize in any crystalline materials. The emergent extended states depend on the topology and the symmetry class of the parent state.…”

New Pentaoctite Phase of Group‐V Nanostructures

“…The flattening of the band structure is due to the different hybridization within the octagon-pentagon rings, as discussed in refs. [13,14].…”

“…[44] In group-V materials, hexagonal and pentaoctite bismuth monolayers have been predicted to be a 2D topological insulator (TI). [13,14,[45][46][47][48][49] To investigate whether the pentaoctite structures behave like topological insulators, we have calculated the Z 2 invariant according to the study by Kane. [43] On the contrary of pentaoctite Bi, our investigated hexagonal and pentaoctite structures are not topological insulators.…”