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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.

At ferroelectric longitudinal domain walls there is an uncompensated charge, which could form a two-dimensional electron gas in the insulator. However, the uncompensated charges can be accommodated by, e.g., defects or localized states that split off from the conduction band. We carried out density functional theory calculations to study these scenarios in PbTiO3 with and without consideration of strong correlation effects simulated via inclusion of a Hubbard parameter U. The optimized structure and electronic structure depend on the choice of this parameter: For vanishing U, a broad, conducting domain wall is obtained, while increasing U leads to localized Ti 3d states and an insulating, sharp domain wall. We also investigated the effects of varying the ferroelectric polarization on the electronic structure of these domain walls.

We examined by two-dimensional photoemission band mapping the electronic structure of Au films epitaxially grown on an Ag(111) substrate. The very similar structural and electronic properties of the two metals make this system extremely unfavorable for the occurrence and observation of electron confinement effects. At variance with previous spectroscopic studies, we show that the electron reflectivity at the interface sustains the formation of well-defined $sp$-derived quantum well states (QWS) and weak quantum well resonance states (QWRS) in the Au layers. The character and degree of confinement of these states are analyzed and quantitatively related to the Au/Ag interface reflectivity on the basis of density functional theory (DFT) band structure calculations.

Electronic tunneling through ferroelectric insulators is considered to be a key ingredient of future oxide electronics. We investigate the role of the electronic band structure of the decaying electronic states in the band gap by first discussing the expected behavior of tunneling in the effective mass model. We demonstrate that, even for the simple prototype ferroelectric oxides in the perovskite structures PbTiO${}_{3}$ and BaTiO${}_{3}$, the basic assumption of the effective mass model is not appropriate, and that the correct interpretation of tunneling in these materials requires a material-specific description of the evanescent states as provided by the complex band structure.

We monitored the $sp$-quantum-well states of Ag films on Pt(111) by angle-resolved photoemission in order to examine the electron transmission across the Ag/Pt interface. For thin layers up to 3.5 nm, the Ag states are characterized by broad quasiparticle peaks and a reversal of the parabolic curvature near the center of the surface Brillouin zone. Remarkable departures from the expected nearly-free-electronlike band dispersion persist in films of more than 14 nm thickness. First-principles calculations and symmetry analysis demonstrate that the observed anomalies in the spectroscopic data can be straightforwardly linked to variations in the Ag/Pt transmission coefficient in the energy-momentum space.

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

By combining the first-principles concept based on the density functional theory with a model vacuum potential, we calculate image potential states and analogous ones in the presence of an electric field applied on a nonmagnetic Ag(100) surface and a magnetic Fe(110) surface. Our investigations are based on the Green-function embedding technique, which allows us to treat a truly semi-infinite surface and whence yields a continuum of bulk states. This turns out to be of crucial importance in order to investigate the qualitative difference between localized image or field states located in a band gap of the substrate and states in resonance with bulk states present at the same energies. This difference leads to remarkable changes in the binding energy versus field dispersion of the states. Furthermore, we show that in the case of the Fe(110) surface, the calculated magnetic exchange splitting increases with the electric field and is also modified by the transition from field states to surface resonance states.

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.

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.