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The concepts of Weyl fermions and topological semimetals emerging in three-dimensional momentum space are extensively explored owing to the vast variety of exotic properties that they give rise to. On the other hand, very little is known about semimetallic states emerging in two-dimensional magnetic materials, which present the foundation for both present and future information technology. Here, we demonstrate that including the magnetization direction into the topological analysis allows for a natural classification of topological semimetallic states that manifest in two-dimensional ferromagnets as a result of the interplay between spin-orbit and exchange interactions. We explore the emergence and stability of such mixed topological semimetals in realistic materials, and point out the perspectives of mixed topological states for current-induced orbital magnetism and current-induced domain wall motion. Our findings pave the way to understanding, engineering and utilizing topological semimetallic states in two-dimensional spin-orbit ferromagnets., Whether topological semimetal states can emerge in two-dimensional magnetic materials remains less understood. Here, Niu and Hanke et al. propose the concepts of mixed Weyl and nodal-line semimetallic phases by including the magnetization direction into the topological analysis in two-dimensional ferromagnets.

In topological semimetals the Dirac points can form zero-dimensional and one-dimensional manifolds, as predicted for Dirac/Weyl semimetals and topological nodal line semimetals, respectively. Here, based on first-principles calculations, we predict a topological nodal line semimetal phase in the two-dimensional compounds ${X}_{2}Y$ ($X$ = Ca, Sr, and Ba; $Y$ = As, Sb, and Bi) in the absence of spin-orbit coupling (SOC) with a band inversion at the M point. A nontrivial ${\mathbb{Z}}_{2}$ invariant of ${\mathbb{Z}}_{2}=1$ remains although a tiny gap appears at the nodal line when SOC is included. The mirror symmetry as well as the electrostatic interaction, which can be engineered via strain, are responsible for the nontrivial phase. In addition, the nontrivial phase is further explicitly confirmed via the existence of exotic edge states without and with SOC.

We demonstrate that topological invariants of band insulators can be derived efficiently from the eigenvalues of the local-orbital (LO) based embedding potential, called also the contact (lead) self-energy. The LO based embedding potential is a bulk quantity. Given the tight-binding Hamiltonian describing the bulk valence and conduction bands, it is constructed straightforwardly from the bulk wave functions satisfying the generalized Bloch condition. When the one-electron energy ɛ is located within a projected bulk band gap at a given planar wave vector k, the embedding potential becomes Hermitian. Its real eigenvalues exhibit distinctly different behavior depending on the topological properties of the valence bands, thus enabling unambiguous identification of bulk topological invariants. We consider the Bernevig-Hughes-Zhang model as an example of a time-reversal invariant topological insulator and tin telluride (SnTe) crystallized in a rock-salt structure as an example of a topological crystalline insulator

The search for new large band gap quantum spin Hall (QSH) and quantum anomalous Hall (QAH) insulators is critical for their realistic applications at room temperature. Here we predict, based on first principles calculations, that the band gap of QSH and QAH states can be as large as 1.01 eV and 0.35 eV in an H-decorated Bi(111) film. The origin of this giant band gap lies both in the large spin-orbit interaction of Bi and the H-mediated exceptional electronic and structural properties. Moreover, we find that the QAH state also possesses the properties of quantum valley Hall state, thus intrinsically realising the so-called valley-polarized QAH effect. We further investigate the realization of large gap QSH and QAH states in an H-decorated Bi(\={1}10) film and X-decorated (X=F, Cl, Br, and I) Bi(111) films., submitted to Physical Reveiw Letters on 25th of September 2014

Different from the two-dimensional (2D) topological insulator, the 2D topological crystalline insulator (TCI) phase disappears when the mirror symmetry is broken, e.g., upon placing on a substrate. Here, based on a new family of 2D TCIs - SnTe and PbTe monolayers - we theoretically predict the realization of the quantum anomalous Hall effect with Chern number C = 2 even when the mirror symmetry is broken. Remarkably, we also demonstrate that the considered materials retain their large-gap topological properties in quantum well structures obtained by sandwiching the monolayers between NaCl layers. Our results demonstrate that the TCIs can serve as a seed for observing robust topologically non-trivial phases., 5 pages, submitted on 27th Feb 2015

The new journal of physics 15, 115009 (2013). doi:10.1088/1367-2630/15/11/115009, Published by IOP Publ. [u.a.], London

We report on the implementation of the Wannier Functions (WFs) formalism within the full-potential linearized augmented plane wave method (FLAPW), suitable for bulk, film and one-dimensional geometries. The details of the implementation, as well as results for the metallic SrVO3, ferroelectric BaTiO3 grown on SrTiO3, covalently bonded graphene and a one-dimensional Pt-chain are given. We discuss the effect of spin-orbit coupling on the Wannier Functions for the cases of SrVO3 and platinum. The dependency of the WFs on the choice of the localized trial orbitals as well as the difference between the maximally localized and "first-guess" WFs are discussed. Our results on SrVO3 and BaTiO3, e.g. the ferroelectric polarization of BaTiO3, are compared to results published elsewhere and found to be in excellent agreement., 13 pages, 9 figures, accepted for publication in Phys. Rev. B

The influence of local Coulomb correlations on the surface electronic structure of ${\mathrm{SrVO}}_{3}$, a strongly-correlated metal in a perovskite structure, is investigated for both the $\mathrm{SrO}$-layer and ${\mathrm{VO}}_{2}$-layer-terminated (001) surfaces. The electronic structure within the local density approximation of a semi-infinite surface is determined using the embedded Green-function approach, and the resultant density of states projected on the V ${t}_{2g}$ orbitals is used as an input to a subsequent many-body calculation within the dynamical mean field theory (DMFT) and the multiorbital quantum Monte Carlo technique. Qualitatively, the present study confirms the conclusion of recent photoemission experiments and tight-binding DMFT calculations which both indicate that the electronic structure at the surface is more strongly correlated than in the bulk. On a quantitative level significant differences are obtained as a function of orbital polarization at the surface, surface layer relaxation, and $\mathrm{SrO}$ vs ${\mathrm{VO}}_{2}$ surface termination.

Results are presented of a first-principles calculation of the spin-polarized field emission from ferromagnetic Ni(111) and Ni(001) surfaces. The electronic structure of both surfaces exposed to an external field is determined by combining the surface-embedded Green function approach and the full-potential linearized augmented plane-wave (FLAPW) method within the local spin density approximation. We discuss the contributions of different states to the field-emission current. In particular, we show that delocalized states make similar contributions to that obtained at jellium surfaces while localized Ni d states contribute mostly through surface states and resonances. These contributions dominate in the minority spin and lead to a negative spin polarization of the emitted current.

A method for the first-principles calculation of the transfer matrix is presented. The method is based on a Green-function formulation and allows one to relate the wave functions and their derivatives on boundaries at opposite sides of a film or junction of finite thickness. Both the underlying theory and an actual implementation in the full-potential linearized augmented plane wave method are described. Currently the embedding method is used to evaluate the Green-function matrix elements and in turn we show that the transfer matrix can be used to construct the embedding potential. Some possible applications of the transfer-matrix method such as the calculations of the complex band structure or the calculation of the transmission and reflection coefficients for ballistic transport are discussed. As a first example, complex band structures of Cu, Fe, and Si are presented.

We present an efficient method for calculating the conductance of ballistic electrons through an interface from first principles using the embedding approach of Inglesfield. In our method the Landauer-B\"uttiker formula for ballistic transport is expressed in terms of two quantities that are available in the embedded Green-function formalism without additional calculations. One is the embedding potential of bulk crystals on both sides of the interface and the other is the Green function in the interface region. As a proof of principle we calculate on the basis of the density-functional theory the spin-resolved electron transmission through a model system of ferromagnetic Co monolayers sandwiched between bulk Cu crystals. The relationship between our formulation and the Green-function formulation of Baranger and Stone is discussed.