Structural and topological phase transitions induced by strain in two-dimensional bismuth.

We employ first-principles density-functional calculations to study structural and topological electronic transitions in two-dimensional bismuth layers. Our calculations reveal that a free-standing hexagonal bismuthene phase (the most stable one in the absence of strain) should become thermodinamically unstable against transformation to a putative 'pentaoctite' phase (composed entirely of pentagonal and octagonal rings), under biaxial tensile strain. Moreover, our results indicate that 2D bismuth layers in the pentaoctite phase should undergo a topological electronic phase transition under either a biaxial or uniaxial tensile strain. More specifically, at its equilibrium lattice parameters the pentaoctite lattice is a topologically trivial system with a direct band gap. Strain-induced parity inversion of valence and conduction bands is obtained, and the pentaoctite structure undergoes a transition to a topological-insulator phase at a biaxial tensile strain of 5%. In the case of uniaxial tensile strains, the topological transition happens at a tensile strain of 6% along the armchair direction of the pentaoctite lattice, and at a 5% tensile strain in the zigzag direction. Our study indicates that 2D bismuth layers may prove themselves a rich platform to realize topologically non-trivial 2D materials upon strain engineering.

Bilayers of Ni3C12S12 and Pt3C12S12: graphene-like 2D topological insulators tunable by electric fields.

In the present work we predict, through first-principles calculations, that bilayers of the recently synthesized Ni3 [Formula: see text] [Formula: see text] and Pt3 [Formula: see text] [Formula: see text] layered materials are topological insulators upon electron doping, and that their topological insulator properties can be modulated by the application of electric fields with magnitudes achievable in devices. The electronic structures of both bilayers are characterized by spin-orbit split graphene-like bands, with gap magnitudes that are three orders of magnitude larger than graphene's. In ribbon geometries, chiral edge modes develop at each side with band dispersions similar to that of Kane-Mele graphene model. Surprisingly, the edge states' spin-propagation locking occurs even for very thin ribbons. We also find that the response of the electronic structure of both materials to applied electric fields are similar to both graphene and the Kane-Mele model with a Rashba term. All these findings indicate that these bilayer systems can be considered as large-spin-orbit graphene analogues with a strong sensitivity to applied electric fields.

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

We report ab initio calculations showing that a one-dimensional extended defect generates topologically protected metallic states immersed in the bulk of two-dimensional topological insulators. We find that a narrow extended defect, composed of periodic units consisting of one octagonal and two pentagonal rings (a 558 extended defect), embedded in the hexagonal bulk of a bismuth bilayer, introduces two pairs of one-dimensional counterpropagating helical-Fermion electronic bands with the opposite spin-momentum locking characteristic of the topological metallic states that appear at the edges in two-dimensional topological insulators. Each one of these pairs of helical-Fermion bands is localized, respectively, along each one of the zigzag chains of bismuth atoms at the core of the 558 extended defect, and their hybridization leads to the opening of very small gaps (6 meV or less) in the helical-Fermion dispersions of these defect-related modes. We discuss the connection between the defect-induced metallic modes and the helical-Fermion edge states that occur on bismuth bilayer ribbons.