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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.

Spin caloric transport refers to the coupling of heat with spin transport. Its applications primarily concern the generation of spin currents and control of magnetisation by temperature gradients for information technology, known by the synonym spin caloritronics. Within the framework of ab initio theory, new tools are being developed to provide an additional understanding of these phenomena in realistic materials, accounting for the complexity of the electronic structure without adjustable parameters. Here, we review this progress, summarising the principles of the density-functional-based approaches in the field and presenting a number of application highlights. Our discussion includes the three most frequently employed approaches to the problem, namely the Kubo, Boltzmann, and Landauer-Büttiker methods. These are showcased in specific examples that span, on the one hand, a wide range of materials, such as bulk metallic alloys, nano-structured metallic and tunnel junctions, or magnetic overlayers on heavy metals, and, on the other hand, a wide range of effects, such as the spin-Seebeck, magneto-Seebeck, and spin-Nernst effects, spin disorder, and the thermal spin-transfer and thermal spin-orbit torques.

A hybrid MPI+OpenMP parallelization strategy has been implemented into the density functional theory code FLEUR. Based on the full-potential linearized augmented plane-wave (FLAPW) method, FLEUR is a well-established all-electron code specialized on the simulation of materials properties of crystalline bulk solids and surfaces with significant electronic and magnetic complexity. Developed in over 30 years the Fortran implementation included two layers of MPI-based distributed memory parallelization that serves as a reference for our work. The revised code version shows superior performance, improved scalability and thereby opens the path to exploit current and future high performance computing architectures efficiently. Multiple threads per MPI process can be utilized by interfacing with optimized linear algebra subroutines from the BLAS and LAPACK libraries as well as in code sections with explicit OpenMP statements. We demonstrate that the additional multithreading helps to avoid the communication induced scalability limit of the pure-MPI version and simultaneously boosts the single node-performance on current multi-core systems. This enables FLEUR calculations for unit cells with over 1000 atoms to simulate extended defects, surfaces and disordered solids.

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 properties that distinguish topological crystalline insulator (TCI) and topological insulator (TI) rely on crystalline symmetry and time-reversal symmetry, respectively, which encodes different bulk and surface/edge properties. Here, we predict theoretically that electron-doped TlM (M = S and Se) (110) monolayers realize a family of two-dimensional (2D) TCIs characterized by mirror Chern number CM = -2. Remarkably, under uniaxial strain (≈ 1%), a topological phase transition between 2D TCI and 2D TI is revealed with the calculated spin Chern number CS = -1 for the 2D TI. Using spin-resolved edge states analysis, we show different edge-state behaviors, especially at the time reversal invariant points. Finally, a TlBiSe2/NaCl quantum well is proposed to realize an undoped 2D TCI with inverted gap as large as 0.37 eV, indicating the high possibility for room-temperature observation.

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