Abstract:
The semiconducting half-Heulser compound DyNiBi shows a negative giant magnetoresistance (GMR) below 200 K. Except for a weak deviation, this magnetoresistance scales roughly with the square of the magnetization in the paramagnetic state, and is related to the metal-insulator transition. At low temperature, a positive magnetoresistance is found, which can be suppressed by high fields. The magnitude of the positive magnetoresistance changes slightly with the amount of impurity phase.

Abstract:
Berry curvatures are computed for a set of Heusler compounds using density functional (DF) calculations and the wave functions that DF provide. The anomalous Hall conductivity is obtained from the Berry curvatures. It is compared with experimental values in the case of Co$_2$CrAl and Co$_2$MnAl. A notable trend cannot be seen but the range of values is quite enormous. The results for the anomalous Hall conductivities and their large variations can be qualitatively understood by means of the band structure and the Fermi-surface topology.

In contrast to the normal operator approach, our reverse approach starts from the state vector in the Hilbert space. In this work, we give a concise introduction to our recent work in this aspect. By postulating a superconducting state (SCS) to be a generalized coherent state (GCS) constructed by pure group theory, we show that some important properties such as the Cooper pairs of the SCS naturally appear in this new framework without resorting to the microscopic origin. This latter characteristic renders this theory a more universal feature in comparison with other theories developed by the operator approach. The studies on the residue of the pair-wise constraint due to the collapse of the GCS lead to a “flat/steep” band model for searching new superconductors.

Abstract:
In the present work, the elastic constants and derived properties of tetragonal Heusler compounds were calculated using the high accuracy of the full-potential linearized augmented plane wave (FPLAPW) method. To find the criteria required for an accurate calculation, the consequences of increasing the numbers of k-points and plane waves on the convergence of the calculated elastic constants were explored. Once accurate elastic constants were calculated, elastic anisotropies, sound velocities, Debye temperatures, malleability, and other measurable physical properties were determined for the studied systems. The elastic properties suggested metallic bonding with intermediate malleability, between brittle and ductile, for the studied Heusler compounds. To address the effect of off-stoichiometry on the mechanical properties, the virtual crystal approximation (VCA) was used to calculate the elastic constants. The results indicated that an extreme correlation exists between the anisotropy ratio and the stoichiometry of the Heusler compounds, especially in the case of Ni_{2}MnGa. Metastable cubic Ni_{2}MnGa exhibits a very high anisotropy (≈28) and hypothetical cubic Rh_{2}FeSn violates the Born-Huang stability criteria in the L2_{1} structure. The bulk moduli of the investigated tetragonal compounds do not vary much (≈130 ...190 GPa). The averaged values of the other elastic moduli are also rather similar, however, rather large differences are found for the elastic anisotropies of the compounds. These are reflected in very different spatial distributions of Young’s moduli when comparing the different compounds. The slowness surfaces of the compounds also differ considerably even though the average sound velocities are in the same order of magnitude (3.2 ... 3.6 km/s). The results demonstrate the importance of the elastic properties not only for purely tetragonal Heusler compounds but also for phase change materials that exhibit magnetic shape memory or magnetocaloric effects.

Abstract:
The anomalous Hall effect is investigated theoretically by means of density functional calculations for the non-collinear antiferromagnetic order of the hexagonal compounds Mn$_3$Ge and Mn$_3$Sn using various planar triangular magnetic configurations as well as unexpected non-planar configurations. The former give rise to anomalous Hall conductivities (AHC) that are found to be extremely anisotropic. For the planar cases the AHC is connected with Weyl-points in the energy-band structure, which are described in detail. If this case were observable in Mn$_3$Ge, a large AHC of about 900 S/cm should be expected. However, in Mn$_3$Ge it is the non-planar configuration that is energetically favored, in which case it gives rise to an AHC of 100 S/cm. The non-planar configuration allows a quantitative evaluation of the topological Hall effect that is seen to determine this value of the conductivity to a large extent. For Mn$_3$Sn it is the planar configurations that are predicted to be observable. In this case the AHC can be as large as 250 S/cm.

Abstract:
We studied the square-octagonal lattice of the transition metal dichalcogenide MX$_2$ (with $M$=Mo, W; $X$=S, Se and Te), as an isomer of the normal hexagonal compound of MX$_2$. By band structure calculations, we observe the graphene-like Dirac band structure in a rectangular lattice of MX$_2$ with nonsymmorphic space group symmetry. Two bands with van Hove singularity points cross each at the Fermi energy, leading to two Dirac cones that locates at opposite momenta. Spin-orbit coupling can open a nontrivial gap at these Dirac points and induce the quantum spin Hall (QSH) phase, the 2D topological insulator. Here, square-octagonal MX$_2$ structures realize the interesting graphene physics, such as Dirac bands and QSH effect, in the transition metal dichalcogenides.

Abstract:
The inconclusive results of the previous first-principles studies on the \S3 \ grain boundaries (GBs) in \CISe\ reveal the importance of employing a method that can correctly describe the electronic structure of this solar-cell material. We have employed hybrid functional calculations to study the \S3 (112) and \S3 (114) GBs in \CISe\ and \CGSe. The electronic structure changes introduced by the formation of GBs are threefold: creation of gap states, shift in band edges, and alteration of bandgap sizes. Gap states commonly behave as recombination centers, but the band alignment and the change in the bandgap size induced by GBs mitigate the destructive effect of these states in \CISe. That means, \S3 \ GBs are not detrimental for the carrier transport in devices based on \CISe. Conversely, these GBs are destructive for the carrier transport in \CGSe. The different behaviors of the \S3 \ GBs in CISe and CGSe might be considered by experimentalists to optimize the device fabrication to achieve high-performance solar cells.

Abstract:
We report the discovery of weak topological insulators by ab initio calculations in a honeycomb lattice. We propose a structure with an odd number of layers in the primitive unit-cell as a prerequisite for forming weak topological insulators. Here, the single-layered KHgSb is the most suitable candidate for its large bulk energy gap of 0.24 eV. Its side surface hosts metallic surface states, forming two anisotropic Dirac cones. Though the stacking of even-layered structures leads to trivial insulators, the structures can host a quantum spin Hall layer with a large bulk gap, if an additional single layer exists as a stacking fault in the crystal. The reported honeycomb compounds can serve as prototypes to aid in the finding of new weak topological insulators in layered small-gap semiconductors.

Abstract:
We present a systematic study of the high-pressure FeSe phase performed by means of the first-principle electronic structure calculations. Basing on available experimental information about the unit cell geometry we calculate the band structure and characterize the related properties during their pressure driven evolution. The electronic structure including the hybrid functional B3LYP or the Hubbard parameter U for the iron d states lead to the correct semiconducting ground state for the hexagonal stoichiometric FeSe within the broad pressure range (up to 30 GPa).

Abstract:
Although topological surface states are known to be robust against non-magnetic surface perturbations, their band dispersions and spatial distributions are still sensitive to the surface defects. Take Bi2Se3 as an example, we demonstrated that Se vacancies modifies the surface band structures considerably. When large numbers of Se vacancies exist on the surface, topological surface states may sink down from the first to second quintuple layer and get separated from the vacancies. We simulated STM images to distinguish the surfaces with Se- and Bi-terminations.