Double-cone Structure Research Articles

Guided modes near the Dirac point in negative-zero-positive index metamaterial waveguide

Motivated by the realization of the Dirac point (DP) with a double-cone structure for optical field in the negative-zero-positive index metamaterial (NZPIM), we make theoretical investigations of the guided modes in the NZPIM waveguide near the DP by using the graphical method. Due to the linear Dirac dispersion, the fundamental mode is absent when the angular frequency is smaller than the DP, while the behaviors of NZPIM waveguide are similar to the conventional dielectric waveguide when the angular frequency is larger than the DP. The unique properties of the guided modes are analogous to the propagation of electron waves in graphene waveguide [Appl. Phys. Lett., 94, 212105 (2009)], corresponding to the classical motion and the Klein tunneling. These results suggest that many exotic phenomena in graphene can be simulated by the relatively simple optical NZPIM.

Transmission gap, Bragg-like reflection, and Goos-Hänchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab

Motivated by the realization of the Dirac point (DP) with a double-cone structure for optical field in the negative-zero-positive index metamaterial (NZPIM), the reflection, transmission, and Goos-H\"anchen (GH) shifts inside the NZPIM slab are investigated. Due to the linear Dirac dispersion, the transmission as the function of the frequency has a gap, thus, the corresponding reflection has a frequency or wavelength window for the perfect reflection, which is similar to the Bragg reflection in the one-dimensional photonic crystals. Near the DP, the associated GH shifts in the transmission and reflection can be changed from positive to negative with increasing the wavelength. These negative and positive shifts can also be enhanced by transmission resonances when the frequency is far from that at the DP. All these phenomena will lead to some potential applications in the integrated optics and optical devices.

Realization of Dirac point with double cones in optics

The Dirac point (DP) with a double-cone structure for optical fields can be realized in optically homogenous media. The condition for the realization of DP in optical systems is the varying of refractive index from negative to zero and then to positive. Our analysis verify that, similar to electrons in graphene, the light field near DP possesses of the pseudodiffusive property obeying the 1/L scaling law, where L is the propagation distance inside the media.

Cyclic, trinuclear PdII complex of cytidine with pronounced double cone structure

Reaction of PdII(tmeda) (tmeda=N,N,N',N'-tetramethylethylenediamine) with the RNA nucleoside cytidine (Cytd) yields a cyclic nucleoside complex containing three metal entities and three cytidine anions, with metal cross-links involving N(3) and N(4)H(-) sites. [{Pd(Cytd(-)-N3,N4)(tmeda)}3](ClO4)3.6H2O has a characteristic double cone structure with the methyl groups of the tmeda ligands representing the lower rim and the ribose moieties forming the upper rim. The Pd3 triangle is equilateral (5.193(1)A). In the solid state structure, one of the ClO(4)(-) counter ions links the lower and the upper rims of adjacent cones, thereby leading to a 1D chain. No host-guest chemistry has been detected with a series of N-heterocyclic ligands in water.

The [Ga2(C5Me5)]+ Ion: Bipyramidal Double‐Cone Structure and Weakly Coordinated, Monovalent Ga+

The [Ga₂(C₅Me₅)]⁺ Ion: Bipyramidal Double‐Cone Structure and Weakly Coordinated, Monovalent Ga⁺

An Analysis of Average Pulsar Profiles and A Study of the ρ-Prelation of Pulsars

Using the method of Gaussian Fit Separation of Average Profile (GFSAP), we re-examine the average profiles of nine pulsars at several frequencies, ranging from 408–1642 MHz. This method enables us to obtain the number of components for each pulsar, and the parameters for each component, the width, position and amplitude. The ρ-P relation for the inner cone and outer cone are studied separately, and the results are, respectively, ρ = P−0.51±0.05 and ρ = P−0.42±0.06. The results can be interpreted as a confirmation of the double-cone structure of pulsar emission beams. The altitudes of emission region, and the radius-to-frequency-map (RFM) are also examined; for the outer cone, we obtained r(v) ∝ v−0.19±0.09.

Neutron diffraction study of the ZrMn6Ge6, LuMn6Ge6 and ScMn6Ge6 compounds

The new hexagonal HfFe6Ge6-type ZrMn6Ge6 compound orders antiferromagnetically below TN=640K and undergoes a second transition at Tt=50K. Neutron diffraction experiments were performed on the three ZrMn6Ge6, LuMn6Ge6 and ScMn6Ge6 compounds. At 300K, they exhibit collinear easy-axis antiferromagnetic arrangements and the magnetic structure consists of ferromagnetic (001) Mn planes antiferromagnetically coupled along the c-axis with a (+−−+) sequence (μMn≈2.06, 1.86 and 1.94μB for Zr-, Lu- and ScMn6Ge6, respectively). At low temperature, spin reorientation processes occur, yielding incommensurate antiferromagnetic arrangements. Below Tt, in both ZrMn6Ge6 and LuMn6Ge6 (Tt∽30K), the Mn moments form a double-cone structure (μMn≈2.1μB, semi-cone angle α≈6°) as already found in YMn6Ge6 (Tt∽80K) whereas only preliminary results are available for ScMn6Ge6 below Tt=255K. These results lead us to strongly revise previous conclusions concerning LuMn6Ge6 and ScMn6Ge6 with more reasonable Mn magnetic moment values (∽2μB against the ∽1μB value previously published).

Magnetic ordering and phase transitions of RFe 4Al 8 (R=La, Ce, Y, Lu) compounds by neutron diffraction

We have studied the Fe magnetic ordering in the tetragonal RFe 4Al 8 (R=La, Ce, Lu, Y) antiferromagnetic compounds by neutron diffraction at temperatures between 1.5 and 240 K. The structure refinement in the paramagnetic state confirms the preference of the Fe atoms for the 8(f) positions. Below T N the four compounds were found to order with four distinct types of spiral structures requiring two sets of wave vectors for their description: (i) q 1=0, q 2=(0, 0, q z ) and (ii) q 1=0, q 3=( q x , q x , 0). Most of the structures undergo magnetic phase transitions at lower temperatures. In all cases is the Fe moment value at 1.5 K close to 2.0 μ B/Fe atom. The wave vector length(s) is slightly temperature dependent in the high temperature region. The R=La compound orders with a double cone structure with the cone axis parallel to the wave vector q 2=(0, 0, 0.265(5)). The cone axes of adjacent Fe chains extending along c have opposite signs. At 1.5 K the cone angle(s) of the Fe sublattices are Φ c=60° and Φ c+π. The rotation angle is Φ s=95(1)°. For the RFe 4Al 8 compounds with R=Ce, Lu, Y the iron site splits into two independent sets (orbits) under the action of the in-plane wave vector q 3=( q x , q x , 0), where q x has at 1.5 K the values 0.243(1), 0.145(3), 0.135(1) r.l.u., respectively. Between Fe moments of adjacent chains extending along c (different orbits) there is a non-zero phase while along the face diagonal(s) (the same orbit) the moments have the same phase. The moments of the Y and Lu compounds rotate within the plane of the wave vector (0 0 1) and form a cycloid spiral. The latter compound has in addition a small component along c which corresponds to a double cone cycloid spiral. The Ce compound has a simple spiral structure with the moments rotating in a plane perpendicular to the wave vector q 3=( q x , q x , 0). The existence of small moment component along q 3 cannot be excluded from the present data. This would give rise to a double cone structure.

Magnetic structure of YMn 6Ge 6 and room temperature magnetic structure of LuMn 6Sn 6 obtained from neutron diffraction study

Neutron diffraction measurements have been performed on the ternary compounds YMn 6Ge 6 and LuMn 6Sn 6 of HfFe 6Ge 6-type structure (space group, P6/mmm). This structure can be described as a filled derivative of the CoSn-B35-type structure. Each of the rare earth (R) and Mn atoms are successively distributed in alternate layers, stacked along the c axis with the sequence MnRMnMnRMn. At 300 K, both compounds exhibit collinear antiferromagnetic arrangements and the magnetic structures consist of a stacking of ferromagnetic (001) layers of Mn with the coupling sequence Mn(+)RMn(−)Mn(−)RMn(+) ( μ Mn ≈ 1.33(1) μ B and 1.82(3) μ B for LuMn 6Sn 6 and YMn 6Ge 6 respectively). For LuMn 6Sn 6, the magnetic moments lie in the (001) plane, while they are along the c axis in YMn 6Ge 6. At low temperature, a spin reorientation process occurs in both compounds, yielding incommensurate antiferromagnetic arrangements. For YMn 6Ge 6 ( T t ≈ 80 K), the Mn moments form a double-cone structure with a periodicity of about 105 Å ( μ Mn = 1.95(4) μ B at 2 K), while only preliminary results are available for LuMn 6Sn 6 below about 200 K. The results are compared with those obtained on the CoSnB35-type structure binary compounds FeSn and FeGe, on one hand, and the RMn 6Sn 6 compounds, on the other hand.

Densities of degeneracies and near-degeneracies.

The eigenvalues of a quantum system depending on two parameters become degenerate at isolated points in the parameter space, which are called diabolical points because of their double-cone structure. Varying one parameter produces near-degeneracies termed avoided crossings. Some results on the density of these objects in parameter space can be obtained by requiring consistency with the level repulsion exhibited by the distribution of energy-level spacings. The density of diabolical points and the distribution of their ellipticities are obtained exactly for the Gaussian orthogonal ensemble random-matrix model. The distribution of their separations in parameter space is also investigated.

Diabolical points in one-dimensional Hamiltonians quartic in the momentum

The authors study the family of quantal Hamiltonians defined on -1<x<+1 by H=p4=d4/dx4 which depend via the boundary conditions on four real parameters a, b, c, d. The spectra of states with even and odd parity have degeneracies with codimension three, that is, on lines in abcd space; near the degeneracies, the level splitting has a double-cone (diabolical) structure, and during a circuit of a diabolical point in the subspace of real H (i.e. d=0) the wavefunctions change sign. These are generic properties which in this model can be studied analytically. The degeneracies could be realised classically in vibrating beams with positive and negative linear feedback in the boundary conditions.

Double-cone structure of an optical beam in a nonlinear medium

A double-cone structure for an optical beam in an amplifying medium with appreciable multiphoton absorption and Kerr nonlinearity is predicted and investigated. An analysis is made of the width of the principal maximum and of the contrast of the ring structure (which divides the double-cone structure of the optical beam into outer and inner regions), and also of the distance at which this is formed as a function of the parameters of the active medium. Attention is drawn to the possibility of measuring multiphoton absorption and Kerr nonlinearity constants by observing the double-cone structure. It is also noted that high-order cylindrical guided light waves, which are not subject to self-focusing even at powers substantially higher than the critical value, may be excited in the adjacent medium.

The Semi-Cone Angles in Conical Tb-Er and Dy-Er Alloys

The semi-cone angles of Tb and Er in Tb-Er alloys and of Dy and Er in Dy-Er alloys both in conical structure are calculated by analyzing the results of our spin echo measurements on these alloys. It was found that the angles of individual components are different with each other, indicating a double cone structure. A simple molecular field calculation shows that really such double cone structure is the most stable one in these alloys, provided that the exchange and anisotropy constants are properly chosen.

Localized versus itinerant electrons in hexagonal FeGe

Hexagonal FeGe is a metallic antiferromagnet with T N = 411K. At higher temperatures FeGe is a uniaxial antiferromagnet with spins parallel to the c-axis and ferromagnetic alignment within each c-plane. Susceptibility and magnetization measurements show that the spins leave the c-axis below 30K. From the molecular field model (MF) we propose that the spins then form a double cone structure. The spin components parallel to the c-axis retain the uniaxial structure while the c-plane components have a turn angle in the vicinity of 180° between neighbour planes, which implies absence of long range order. The MF results are in good agreement with Fermi surface calculations, which show the existence of several spin density wave vectors in the vicinity of Q = π c , thus explaining the indeterminacy of the turn angle in the MF model.

Susceptibility Measurements and Magnetic Ordering of Hexagonal FeGe

The spin structure of the metallic hexagonal B 35 phase of FeGe has been studied by means of susceptibility and magnetization measurements. Below the Neel temperature TN = 411 K hexagonal FeGe is a uniaxial antiferromagnet with the spins parallel to the c-axis. In each c-plane all spins are ferromagnetically coupled with an exchange constant J0 ≈ 22 meV. The antiferromagnetic exchange constant between nearest neighbour and next nearest neighbour c-planes are J1 = -3.5 meV and J2 = -0.9 meV resp. in the molecular field model. Susceptibility and spin flop experiments indicate that the spins tilt away from the c-axis below 30 K. We suggest that the spins then form a double cone structure with a cone halfangle of 20° at 4.2 K. In the double cone the c-plane components have a turn angle in the vicinity of 180° between nearest neighbour planes, which implies absence of long range order. The result is in good agreement with Fermi surface calculations by Sundström (Physica Scripta, following paper), which show the existence of several spin density wave vectors between Q = 0.89 π/c and Q = 1.3 π/c calipering different parts of the Fermi surface in a direction parallel to the c-axis.