Single crystals of iron(IV) rich oxides $\mathrm{Sr}\mathrm{Fe}{\mathrm{O}}_{3-\delta }$ with controlled oxygen content $(0⩽\delta ⩽0.31)$ have been studied by Mössbauer spectroscopy, magnetometry, magnetotransport measurements, Raman spectroscopy, and infrared ellipsometry in order to relate the large magnetoresistance (MR) effects in this system to phase composition and magnetic and charge order. It is shown that three different types of MR effects occur. In cubic $\mathrm{Sr}\mathrm{Fe}{\mathrm{O}}_3$ $(\delta =0)$ a large negative MR of 25% at $9\mathrm{T}$ is associated with a hitherto unknown $60\mathrm{K}$ magnetic transition and a subsequent drop in resistivity. The $60\mathrm{K}$ transition appears in addition to the onset of helical ordering at $\sim 130\mathrm{K}$. In crystals with vacancy-ordered tetragonal $\mathrm{Sr}\mathrm{Fe}{\mathrm{O}}_{3-\delta }$ as the majority phase $(\delta \sim 0.15)$ a coincident charge-antiferromagnetic ordering transition near $70\mathrm{K}$ is considered as the origin of a negative giant MR effect of 90% at $9\mathrm{T}$. A positive MR effect is observed in tetragonal and orthorhombic materials with increased oxygen deficiency $(\delta =0.19,0.23)$ which are insulating at low temperatures. Phase mixtures can result in a complex superposition of these different MR phenomena. The MR effects in $\mathrm{Sr}\mathrm{Fe}{\mathrm{O}}_{3-\delta }$ differ from those in manganites as no ferromagnetic states are involved.

Dirac-like electronic states are the main engines powering tremendous advancements in the research of graphene, topological insulators and other materials with these states. Zero effective mass, high carrier mobility and numerous applications are some consequences of linear dispersion that distinguishes Dirac states. Here we report a new class of linear electronic bands in two-dimensional materials with zero electron effective mass and sharp band edges, and predict stable materials with such electronic structures utilizing symmetry group analysis and an ab initio approach. We make a full classification of completely linear bands in two-dimensional materials and find that only two classes exist: Dirac fermions on the one hand and fortune teller-like states on the other hand. The new class supports zero effective mass similar to that of graphene and anisotropic electronic properties like that of phosphorene.

Vibrational frequencies and phonon displacement patterns of the H-site doped graphene are calculated by the density functional theory (DFT). DFT calculations, as well as the group theory study, are used to describe these structures as interesting materials for single layer superconductivity. In this paper, graphene doped with Li, Ca and Ba adatoms is systematically analysed and compared. Due to the effect of zone folding, displacement patterns of calculated modes correspond to the ones of the K and Γ point phonons of graphene and this offers the possibility for comparison with the experimental results for graphene. Our objective was to provide compendious and practical guidelines for the experimental research and characterization of these structures.

We have considered non-magnetic materials with weak spin–orbit coupling, that are periodic in two non-collinear directions, and finite in the third, orthogonal direction. In some cases, the combined time-reversal and crystal symmetry of such systems, allows the existence of Dirac cones at certain points in the reciprocal space. We have investigated in a systematic way, all points of the Brillouin zone of all 80 diperiodic groups and have found sufficient conditions for the existence of s = 1/2 Dirac fermions, with symmetry-provided band touching at the vertex of the Dirac cones. Conversely, complete linear dispersion is forbidden for orbital wave functions belonging to two-dimensional (2D) irreducible representations (irreps) of little groups that do not satisfy certain group theoretical conditions given in this paper. Our results are illustrated by a tight-binding example.

Magnesium diboride gained significant interest in the materials science community after the discovery of its superconductivity, with an unusually high critical temperature of 39 K. Many aspects of the electronic properties and superconductivity of bulk MgB ${}_2$ and thin sheets of MgB ${}_2$ have been determined; however, a single layer of MgB ${}_2$ has not yet been fully theoretically investigated. Here, we present a detailed study of the structural, electronic, vibrational, and elastic properties of monolayer MgB ${}_2$ , based on ab initio methods. First-principles calculations reveal the importance of reduction of dimensionality on the properties of MgB ${}_2$ and thoroughly describe the properties of this novel 2D material. The presence of a negative Poisson ratio, higher density of states at the Fermi level, and a good dynamic stability under strain make the MgB ${}_2$ monolayer a prominent material, both for fundamental research and application studies.