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The topological classification of matter has been extended to include semimetallic phases characterized by the presence of topologically protected band degeneracies. In Weyl semimetals, the foundational gapless topological phase, chiral degeneracies are isolated near the Fermi level and give rise to the Fermi-arc surface states. However, it is now recognized that chiral degeneracies are ubiquitous in the band structures of systems with broken spatial inversion ($\mathcal{P}$) or time-reversal ($\mathcal{T}$) symmetry. This leads to a broadly defined notion of topological metals, which implies the presence of disconnected Fermi surface sheets characterized by non-zero Chern numbers inherited from the enclosed chiral degeneracies. Here, we address the possibility of experimentally observing surface-related signatures of chiral degeneracies in metals. As a representative system we choose bcc iron, a well-studied archetypal ferromagnetic metal with two nontrivial electron pockets. We find that the (110) surface presents arc-like resonances attached to the topologically nontrivial electron pockets. These Fermi-arc resonances are due to two different chiral degeneracies, a type-I elementary Weyl point and a type-II composite (Chern numbers $\pm 2$) Weyl point, located at slightly different energies close to the Fermi level. We further show that these surface resonances can be controlled by changing the orientation of magnetization, eventually being eliminated following a topological phase transition. Our study thus shows that the intricate Fermi-arc features can be observed in materials as simple as ferromagnetic iron, and are possibly very common in polar and magnetic materials broadly speaking. Our study also provides methodological guidelines to identifying Fermi-arc surface states and resonances, establishing their topological origin and designing control protocols., Comment: 12 pages, 9 figures

We theoretically study the electronic structure and spin properties of one-dimensional nanostructures of the prototypical bulk topological insulator Bi$_2$Se$_3$. Realistic models of experimentally observed Bi$_2$Se$_3$ nanowires and nanoribbons are considered using the tight-binding method. At low energies, the band structures are composed of a series of evenly spaced degenerate sub-bands resulting from circumferential confinement of the topological surface states. The direct band gaps due to the non-trivial $\pi$ Berry phase show a clear dependence on the circumference. The spin-momentum locking of the topological surface states results in a pronounced 2$\pi$ spin rotation around the circumference with the degree of spin polarization dependent on the the momentum along the nanostructure. Overall, the band structures and spin textures are more complicated for nanoribbons, which expose two distinct facets. The effects of reduced dimensionality are rationalized with the help of a simple model that considers circumferential quantization of the topological surface states. Furthermore, the surface spin density induced by electric current along the nanostructure shows a pronounced oscillatory dependence on the charge-carrier energy, which can be exploited in spintronics applications., Comment: 10 pages, 9 figures

The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but often challenging problem, with no exhaustive solution at the present time. In this work we compile a series of techniques, some previously known, that allow for a solution to this problem for a large set of the possible band topologies. The method is based on tracking hybrid Wannier charge centers computed for relevant Bloch states, and it works at all levels of materials modeling: continuous k.p models, tight-binding models and ab initio calculations. We apply the method to compute and identify Chern, Z2 and crystalline topological insulators, as well as topological semimetal phases, using real material examples. Moreover, we provide a numerical implementation of this technique (the Z2Pack software package) that is ideally suited for high-throughput screening of materials databases for compounds with non-trivial topologies. We expect that our work will allow researchers to: (a) identify topological materials optimal for experimental probes, (b) classify existing compounds and (c) reveal materials that host novel, not yet described, topological states., Comment: The supplementary files (Z2Pack source and documentation) can be downloaded from http://z2pack.ethz.ch/supplementary.tar.gz

Recent advances in large-scale synthesis of graphene and other 2D materials have underscored the importance of local defects such as dislocations and grain boundaries (GBs), and especially their tendency to alter the electronic properties of the material. Understanding how the polycrystalline morphology affects the electronic properties is crucial for the development of applications such as flexible electronics, energy harvesting devices or sensors. We here report on atomic scale characterization of several GBs and on the structural-dependence of the localized electronic states in their vicinity. Using low temperature scanning tunneling microscopy (STM) and spectroscopy (STS), together with tight binding and ab initio numerical simulations we explore GBs on the surface of graphite and elucidate the interconnection between the local density of states (LDOS) and their atomic structure. We show that the electronic fingerprints of these GBs consist of pronounced resonances which, depending on the relative orientation of the adjacent crystallites, appear either on the electron side of the spectrum or as an electron-hole symmetric doublet close to the charge neutrality point. These two types of spectral features will impact very differently the transport properties allowing, in the asymmetric case to introduce transport anisotropy which could be utilized to design novel growth and fabrication strategies to control device performance.

Recent progress in the field of topological states of matter(1,2) has largely been initiated by the discovery of bismuth and antimony chalcogenide bulk topological insulators (TIs)(3-6), followed by closely related ternary compounds(7-16) and predictions of several weak TIs(17-19). However, both the conceptual richness of Z$_2$ classification of TIs as well as their structural and compositional diversity are far from being fully exploited. Here, a new Z$_2$ topological insulator is theoretically predicted and experimentally confirmed in the $\beta$-phase of quasi-one-dimensional bismuth iodide Bi$_4$I$_4$. The electronic structure of $\beta$-Bi$_4$I$_4$, characterized by Z$_2$ invariants (1;110), is in proximity of both the weak TI phase (0;001) and the trivial insulator phase (0;000). Our angle-resolved photoemission spectroscopy measurements on the (001) surface reveal a highly anisotropic band-crossing feature located at the point of the surface Brillouin zone and showing no dispersion with the photon energy, thus being fully consistent with the theoretical prediction.

Nanoelectromechanical systems (NEMS) constitute a class of devices lying at the interface between fundamental research and technological applications. Integrating novel materials such as graphene into NEMS allows studying their mechanical and electromechanical characteristics at the nanoscale and addressing fundamental questions such as electron-phonon interaction and bandgap engineering. In this work, we integrate single and bilayer graphene into NEMS and probe the interplay between their mechanical and electrical properties. We show that the deflection of monolayer graphene nanoribbons results in a linear increase in their electrical resistance. Surprisingly, we observe oscillations in the electromechanical response of bilayer graphene. The proposed theoretical model suggests that these oscillations arise from quantum mechanical interference taking place due to the lateral displacement of graphene layers with respect to each other. Our work shows that bilayer graphene conceals unexpectedly rich and novel physics with promising potential in NEMS-based applications., Comment: First three authors contributed equally

Hydrogen adatoms and other species covalently bound to graphene act as resonant scattering centers affecting the electronic transport properties and inducing Anderson localization. We show that attractive interactions between adatoms on graphene and their diffusion mobility strongly modify the spatial distribution, thus fully eliminating isolated adatoms and increasing the population of larger size adatom aggregates. Our scaling analysis shows that such aggregation of adatoms increases conductance by up to several orders of magnitude and results in significant extension of the Anderson localization length in the strong localization regime. We introduce a simple definition of the effective adatom concentration $x^\star$ , which describes the transport properties of both random and correlated distributions of hydrogen adatoms on graphene across a broad range of concentrations., Comment: Main text: 5 pages, 5 figures. Supplementary material: 7 pages, 5 figures

Kane and Mele predicted that in presence of spin-orbit interaction graphene realizes the quantum spin Hall state. However, exceptionally weak intrinsic spin-orbit splitting in graphene ($\approx 10^{-5}$ eV) inhibits experimental observation of this topological insulating phase. To circumvent this problem, we propose a novel approach towards controlling spin-orbit interactions in graphene by means of covalent functionalization of graphene edges with functional groups containing heavy elements. Proof-of-concept first-principles calculations show that very strong spin-orbit coupling can be induced in realistic models of narrow graphene nanoribbons with tellurium-terminated edges. We demonstrate that electronic bands with strong Rashba splitting as well as the quantum spin Hall state spanning broad energy ranges can be realized in such systems. Our work thus opens up new horizons towards engineering topological electronic phases in nanostructures based on graphene and other materials by means of locally introduced spin-orbit interactions., Comment: 5 pages, 3 figures

We investigate the dependence of band dispersion of the quantum spin Hall effect (QSHE) edge states in the Kane-Mele model on crystallographic orientation of the edges. Band structures of the one-dimensional honeycomb lattice ribbons show the presence of the QSHE edge states at all orientations of the edges given sufficiently strong spin-orbit interactions. We find that the Fermi velocities of the QSHE edge-state bands increase monotonically when the edge orientation changes from zigzag (chirality angle $\theta = 0^\circ$) to armchair ($\theta = 30^\circ$). We propose a simple analytical model to explain the numerical results., Comment: to appear in Phys. Status Solidi RRL, Focus Issue on Topological Insulators

We study here, both experimentally and theoretically, the anisotropy of magnetoresistance in atomic contacts. Our measurements on iron break junctions reveal an abrupt and hysteretic switch between two conductance levels when a large applied field is continuously rotated. We show that this behaviour stems from the coexistence of two metastable electronic states which result from the anisotropy of electronic interactions responsible for the enhancement of orbital magnetization. In both states giant orbital moments appear on the low coordinated central atom in a realistic contact geometry. However they differ by their orientation, parallel or perpendicular, with respect to the axis of the contact. Our explanation is totally at variance with the usual model based on the band structure of a monatomic linear chain, which we argue cannot be applied to 3d ferromagnetic metals.

We present a theoretical study of spin polarized transport in Fe atomic contacts using a self-consistent tight-binding Hamiltonian in a non-orthogonal $s$, $p$ and $d$ basis set, the spin-polarization being obtained from a non-collinear Stoner-like model and the transmission probability from the Fisher-Lee formula. The behaviour of an infinite perfect Fe wire is compared with that of an infinite chain presenting geometric defects or magnetic walls and with that of a finite chain connected to infinite one-dimensional or three-dimensional leads. In the presence of defects or contacts the transmission probability of $d$ electrons is much more affected than that of $s$ electrons, in particular, contact effects may suppress some transmission channels. It is shown that the behaviour of an infinite wire is never obtained even in the limit of long chains connected to electrodes. The introduction of the spin-orbit coupling term in the Hamiltonian enables us to calculate the anisotropy of the magneto-resistance. Finally whereas the variation of the magneto-resistance as a function of the magnetization direction is step-like for an infinite wire, it becomes smooth in the presence of defects or contacts.

The orbital contribution to the magnetic properties of Fe in systems of decreasing dimensionality (bulk, surfaces, wire and free clusters) is investigated using a tight-binding hamiltonian in an $s, p,$ and $d$ atomic orbital basis set including spin-orbit coupling and intra-atomic electronic interactions in the full Hartree-Fock (HF) scheme, i.e., involving all the matrix elements of the Coulomb interaction with their exact orbital dependence. Spin and orbital magnetic moments and the magnetocrystalline anisotropy energy (MAE) are calculated for several orientations of the magnetization. The results are systematically compared with those of simplified hamiltonians which give results close to those obtained from the local spin density approximation. The full HF decoupling leads to much larger orbital moments and MAE which can reach values as large as 1$\mu_B$ and several tens of meV, respectively, in the monatomic wire at the equilibrium distance. The reliability of the results obtained by adding the so-called Orbital Polarization Ansatz (OPA) to the simplified hamiltonians is also discussed. It is found that when the spin magnetization is saturated the OPA results for the orbital moment are in qualitative agreement with those of the full HF model. However there are large discrepancies for the MAE, especially in clusters. Thus the full HF scheme must be used to investigate the orbital magnetism and MAE of low dimensional systems.

We show that considerable orbital magnetic moments and magneto-crystalline anisotropy energies are obtained for a Fe monatomic wire described in a tight-binding method with intra-atomic electronic interactions treated in a full Hartree Fock (HF) decoupling scheme. Even-though the use of the orbital polarization ansatz with simplified Hamiltonians leads to fairly good results when the spin magnetization is saturated this is not the case of unsaturated systems. We conclude that the full HF scheme is necessary to investigate low dimensional systems.

The magnetic properties of iron (spin and orbital magnetic moments, magnetocrystalline anisotropy energy) in various geometries and dimensionalities are investigated by using a parametrized tight-binding model in an $s$, $p$ and $d$ atomic orbital basis set including spin polarization and the effect of spin-orbit coupling. The validity of this model is well established by comparing the results with those obtained by using an ab-initio code. This model is applied to the study of iron in bulk bcc and fcc phases, $(110)$ and $(001)$ surfaces and to the monatomic wire, at several interatomic distances. New results are derived. The variation of the component of the orbital magnetic moment on the spin quantization axis has been studied as a function of depth, revealing a significant enhancement in the first two layers, especially for the $(001)$ surface. It is found that the magnetic anisotropy energy is drastically increased in the wire and can reach several meV. This is also true for the orbital moment, which in addition is highly anisotropic. Furthermore it is shown that when the spin quantization axis is neither parallel nor perpendicular to the wire the average orbital moment is not aligned with the spin quantization axis. At equilibrium distance the easy magnetization axis is along the wire but switches to the perpendicular direction under compression. The success of this model opens up the possibility of obtaining accurate results on other elements and systems with much more complex geometries.