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In this work we predict a family of noncentrosymmetric two-dimensional (2D) Weyl semimetals composed by porous Ge and SiGe structures. These systems are energetically stable graphenylene-like structures with a buckling, spontaneously breaking the inversion symmetry. The nontrivial topological phase for these 2D systems occurs just below the Fermi level, resulting in nonvanishing Berry curvature around the Weyl nodes. The emerged Weyl semimetals are protected by $C_3$ symmetry, presenting one-dimensional edge Fermi-arcs connecting Weyl points with opposite chiralities. Our findings complete the family of Weyl in condensed-matter physics, by predicting the first noncentrosymmetric class of 2D Weyl semimetals.

We have investigated magnetic interactions between transition metal ions in bismuthene topological insulator with protected edge states. We find that these topological states have a crucial role on the magnetic interactions in 2D topological insulators. Using first-principles and model Hamiltonian we make a comparative study of transition metal doped bulk and nanoribbon bismuthene. While direct overlap between the transition metal prevails in gapped bulk bismuthene, at the borders of nanoribbons a long-range magnetism is present. The exchange interactions are well described by a RKKY-like Hamiltonian mediated by topological states. Our results show a dominance of antiferromagnetism promoted by the topological states, preserving the spin-locked Dirac crossing states due to a global time-reversal symmetry preservation. This extended magnetic interactions mediated by massless electrons can increase the spin diffusion length being promising for fast dissipationless spintronic devices., Comment: 6 pages, 4 figures

We study the properties of flat-bands that appear in a heterostructure composed of strands of different widths of graphene armchair nanoribbons. One of the flat-bands is reminiscent of the one that appears in pristine armchair nanoribbons and has its origin in a quantum mechanical destructive interference effect, dubbed `Wannier orbital states' by Lin et al. in Phys. Rev. B 79, 035405 (2009). The additional flat-bands found in these heterostructures, some reasonably closer to the Fermi level, seem to be generated by a similar interference process. After doing a thorough tight-binding analysis of the band structures of the different kinds of heterostructures, focusing in the properties of the flat-bands, we use Density Functional Theory to study the possibility of magnetic ground states when placing, through doping, the Fermi energy close to the different flat-bands. Our DFT results confirmed the expectation that these heterostructures, after being appropriately hole-doped, develop a ferromagnetic ground state that seems to require, as in the case of pristine armchair nanoribbons, the presence of a dispersive band crossing the flat-band. In addition, we found a remarkable agreement between the tight-binding and DFT results for the charge density distribution of the so-called Wannier orbital states., Comment: 13 pages, 18 figures

We perform first-principles calculations of electronic and dielectric properties of bismuthene functionalized with small ligands using first-principle calculations. We show that all functionalized structures have topological insulating (TI) behavior with a sizeable gap by calculating the Z$_2$ topological invariant. Furthermore the adsorption of all groups induce a quasi-planar structure to the initially pristine bismuthene structure. Finally we show that the dielectric properties show a large anisotropy with two main in plane absorption peaks.

Whereas SnTe is a inverted band gap topological crystalline insulator, the topological phase of the alloy Sn_{1-x}In_xTe, a topological superconductor candidate, has not been clearly studied so far. Our calculations show that the Sn_{1-x}In_xTe band gap reduces by increasing the In content, becoming a metal for x>0.1. However, the band inversion at the fcc L point for both gapped and gapless phases has been maintained. Furthermore, the computed topological invariant shows a non-trivial phase with a mirror Chern number n_M = -2 for In concentrations of x=0.03125, x=0.125, and x=0.25. We also identify pairs of topologically protected states on the (001) surface of Sn_{1-x}In_xTe with +/- i mirror eigenvalues. The character of these topological states is affected by In dopant. As the In content x increases, the Dirac crossing point moves further away from the L point, and the Fermi velocity of the topological states increases significantly. Our results demonstrate a non-trivial topological phase for the superconductor Sn_{1-x}In_xTe, and provide a detailed description of the topological state properties.

We have performed a systematic investigation of the formation of topologically protected boundary states (TPBS) in topological/normal insulators (TI/NI) heterostructures. Using a recently developed scheme to construct {\it ab-initio} tight-binding Hamiltonian matrices from density functional theory (DFT) calculations, we studied systems of realistic size with high accuracy and control over the relevant parameters such as TI and NI band alignment, NI gap and spin-orbit coupling strength. Our findings point to the existence of an NI critical thickness for the emergence of TPBS and to the importance of the band alignment between the TI and NI for the appearance of the TPBS. We chose Bi$_{2}$Se$_{3}$ as a prototypical case where the topological/normal insulator behavior is modeled by regions with/without spin-orbit coupling. Finally, we validate our approach comparing our model with fully relativistic DFT calculations for TI/NI heterostructures of Bi$_{2}$Se$_{3}$/Sb$_{2}$Se$_{3}$.

By stacking PbTe layers there is a non-monotonic topological phase transition as a function of the number of monolayers. Based on first principles calculations we find that the proper stacked crystal symmetry determines the topological nature of the slab. While a single PbTe monolayer has a nontrivial phase, pressure can induce topological phase transition in bulk PbTe. Between these two limits, where finite size effects are inherent, we verified that, by applying an external pressure, odd stacking layers can be tuned easily to a topological phase, while even stacking keeps a larger band gap, avoiding band inversion. The quite distinct behavior for odd/even layer is due to the symmetry of the finite stacking. Odd layers preserve the bulk symmorphic symmetry with strong surface hybridization, while even layers belong to a nonsymmorphic group symmetry. Nonsymmorphism induces extra degeneracy reducing the hybridization, thus protecting band inversion, postponing topological phase transitions.

States of matter with nontrivial topology have been classified by their bulk symmetry properties. However, by cutting the topological insulator into ribbons, the symmetry of the system is reduced. By constructing effective Hamiltonians containing the proper symmetry of the ribbon, we find that the nature of topological states is dependent on the reduced symmetry of the ribbon and the appropriate boundary conditions. We apply our model to the recently discovered two-dimensional topological crystalline insulators composed by IV-VI monolayers, where we verify that the edge terminations play a major role on the Dirac crossings. Particularly, we find that some bulk cuts lead to nonsymmorphic ribbons, even though the bulk material is symmorphic. The nonsymmorphism yields a new topological protection, where the Dirac cone is preserved for arbitrary ribbon width. The effective Hamiltonians are in good agreement with ab initio calculations., Comment: 9 pages, 4 figures

Based upon first-principles methods, we investigate the magnetic anisotropy and the spin-texture of Co adatoms embedded in the topmost Se network of the topological insulator Bi$_2$Se$_3$ surface. We find the formation of energetically stable magnetic moment perpendicular to the surface plane, S$_z$. Our results for the pristine Bi$_2$Se$_3$ surface indicate the presence of helical spin-texture not only in the massless surface Dirac states, but also surface states resonant within the valence band present spin-texture. On the other hand, upon the presence of Co adatoms we find that the out-of-plane surface magnetism represents the dominant spin state (S$_z$), while the planar spin components, S$_x$ and S$_y$, are almost suppressed.