There have been growing efforts to find new two-dimensional (2D) materials with anisotropic properties due to their potential applications in electronics. Although in such a search, a symmetry based analysis can be useful, it has not been reported so far. Using group theory we have found sufficient conditions for the existence of a linear dispersion in one direction and quadratic one in perpendicular direction, in the vicinity of points of symmetry in the Brillouin zone (BZ) of any non-magnetic, 2D material with negligible spin-orbit coupling. We have formulated a set of symmetry conditions that lead to the semi-Dirac dispersion and analyzed all possible symmetries of 2D materials. In four, out of all eighty symmetry groups, combined time-reversal and crystal symmetry leads, at given points in the BZ, to such dispersion. The result is valid irrespectively of strength of electronic correlations in the system, model used to calculate the band structure, or the actual crystal structure that realizes given groups. We have illustrated our findings using a tight-binding example.
We present studies of structural, magnetic, and electrical properties of Zn1-x Mn x SnSb2+MnSb nanocomposite ferromagnetic semiconductors with the average Mn-content, [Formula: see text], changing from 0.027 up to 0.138. The magnetic force microscope imaging done at room temperature shows the presence of a strong signal coming from MnSb clusters. Magnetic properties show the paramagnet-ferromagnet transition with the Curie temperature, T C, equal to about 522 K and the cluster-glass behavior with the transition temperature, T CG, equal to about 465 K, both related to MnSb clusters. The magnetotransport studies show that all investigated samples are p-type semiconductors with high hole concentration, p, changing from 10(21) to 10(22) cm(-3). A large increase in the resistivity as a function of the magnetic field is observed at T < 10 K and small magnetic fields, [Formula: see text] mT, for all the studied samples with a maximum amplitude of the magnetoresistance about 460% at T = 1.4 K. The large increase in the resistivity is most probably caused by the appearance of the superconducting state in the samples at T < 4.3 K.
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.
The design of electromagnetic invisibility cloaks is based on singular mappings prescribing zero or infinite values for material parameters on the inner surface of the cloak. Since this is only approximately feasible, an asymptotic analysis is necessary for a sound description of cloaks. We adopt a simple and effective approach for analyzing electromagnetic cloaks - instead of the originally proposed singular mapping, nonsingular mappings asymptotically approaching the ideal one are considered. Scattering and radiation from this type of imperfect cylindrical cloaks is solved analytically and the results are confirmed by full-wave finite element simulations. Our analysis sheds more light on the influence of this kind of imperfection on the cloaking performance and further explores the physics of cloaking devices.
Algorithms , Electromagnetic Fields , Models, Theoretical , Radiometry/methods , Security Measures , Computer Simulation , Radiation Dosage , Scattering, Radiation
In this paper we theoretically study refraction effects in the 2D square-like Archimedean photonic crystals (3(2), 4, 3, 4) and (4, 8(2)) made of dielectric rods in air. In addition, we investigated a band isotropy and band gap structure in these lattices. We compared the square and square-like structures as well, their refraction characteristics, zone structures and the level of band and band gap isotropy (bandwidth and band gap dependence on the wave vector). We found that square-like structures can have some advantages over the square ones regarding the completeness of the gap, its isotropy and the gap width. Also, due to the same square primitive unit cell and the first Brillouin zone, the square and square-like lattices have similar optical response in lower bands.
Crystallization/methods , Models, Theoretical , Refractometry/methods , Computer Simulation , Light , Photons , Scattering, Radiation
We report on a study of the wave propagation and refraction in a 2D square-lattice photonic crystal for the first two photonic bands as well as the coupling of the external waves and criteria for flat-lens focusing. Microwave experiments and numerical simulations are performed. Main results concern the transition from positive to negative refraction below the first band gap, the flat-lens focusing using a novel criterion, viz. the constancy of the ratio of the tangents of the incident and refracted angle. Focusing results for medium ( approximately 10) and ultra-large dielectric contrast ( approximately 100) are presented. In the latter case focusing with a spot size below one wavelength at distances several wavelengths behind the photonic crystal is achieved.
We present a study on relation between the refraction and rightness effects in photonic crystals applied on a 2D square lattice photonic crystal. The plane wave (the band and equifrequency contour analyses) and FDTD calculations for both TM and TE modes revealed all possible refraction and rightness cases in photonic crystal structures in the first three bands. In particular, we show for the first time, a possibility of the left-handed positive refraction. This means that left-handedness does not necessarily imply negative refraction in photonic crystals.
