Triple Degeneracy Research Articles

RMSD and Symmetry.

A common approach for comparing the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the pointwise root-mean-square deviation (RMSD). We present a new, robust numerical algorithm that computes the RMSD between two molecules or all the mutual RMSDs of a list of molecules and, if desired, the corresponding rotation matrix in a minimal number of operations as compared to previous algorithms. The RMSD gradient can also be computed. We address the problem of symmetry, both in alignment (possible alternative alignments due to indistinguishable atoms) as well as geometry. In the latter case, it is possible to have degenerate superposition. A necessary condition is optimal superimposability to one's mirror image. Double (respectively, triple) degeneracy results in a one- (respectively, two)-parameter family of rotations leaving the superposition invariant. The software, frmsd, is freely available at http://www.ams.stonybrook.edu/~coutsias/codes/frmsd.tgz. © 2019 Wiley Periodicals, Inc.

Phase structure of the twisted SU(3)/U(1)2 flag sigma model on \u211d \xd7 S1

We investigate the phase structure of the compactified 2-dimensional nonlinear SU(3)/U(1)2 flag sigma model with respect to two θ-terms. Based on the circle compactification with the ℤ3-twisted boundary condition, which preserves an ’t Hooft anomaly of the original uncompactified theory, we perform the semiclassical analysis based on the dilute instanton gas approximation (DIGA). We clarify classical vacua of the theory and derive fractional instanton solutions connecting these vacua. The resulting phase structure based on DIGA exhibits the quantum phase transitions and triple degeneracy at special points in the (θ1, θ2)-plane, which is consistent with the phase diagram obtained from the anomaly matching and global inconsistency conditions. This result indicates the adiabatic continuity between the flag sigma models on ℝ2 and ℝ × S1 with small compactification radius. We further estimate contributions from instanton-anti-instanton configuration (bion) and show the existence of the imaginary ambiguity, which is expected to be cancelled by that of the perturbative Borel resummation.

Deaf band based engineered Dirac cone in a periodic acoustic metamaterial: A numerical and experimental study

A Dirac-cone-like dispersion at the center of the Brillouin zone where the wave number $\stackrel{P\vec}{k}=0$ [L. Brillouin, Wave Propagation in Periodic Structures (Dover, New York, 1953)], is rare and only happens due to accidental degeneracy. At certain frequencies, the Dirac cone breaks the time-reversal symmetry of acoustic waves, which has not yet been fully explored. In this paper, even the simplest geometric microarchitecture of phononic crystals (PnCs) in a periodic structure can be modulated to obtain the accidental triple degeneracies that make a Dirac-like cone at the \ensuremath{\Gamma} point ($\stackrel{P\vec}{k}=0$). While doing so, it was observed that the frequency of a nondispersive band obtained from any arbitrary periodic structure made of similar PnCs remains unaltered. Then, a deaf band based predictive modulation of the PnCs is realized, and multiple occurrences of the Dirac-like points are demonstrated. The claims are validated using a numerical and experimental study of a baseline periodic structure having a square array of cylindrical polyvinylchloride inclusions in an air matrix. Phenomena such as orthogonal wave transport, negative refraction, and wave vortex are verified to exist at the deaf band based engineered Dirac cone.

Electron Transport in Configurational Model of Ferromagnetic Fulleride with Triple Orbital Degeneracy

Phenomenon of ferromagnetic ordering was for a long time associated exclusively with transition metal and rare-earth compounds. Nowadays this view is challenged by growing evidence that in molecular carbon-based systems the ferromagnetic alignment of spins can be observed as well. We have developed a microscopical model of a fulleride electronic subsystem taking into account triple orbital degeneracy of energy states within the configurational-operator approach. Using the Green function method the energy spectrum of the model has been calculated. Conditions for the ferromagnetic state stabilization have been determined. Static electrical conductivity and effective masses of current carriers in the system with orbitally degenerated energy band have been obtained. In the ground state and for low temperatures at different forms of unperturbed density of electronic states the concentration dependences of transport characteristics for less-then-half-filled lower quasiparticle subband have been calculated.

Analytical study of mode degeneracy in non-Hermitian photonic crystals with TM-like polarization

We present an analytical study of the mode degeneracy in non-Hermitian photonic crystals (PC) with $C_{4v}$ symmetry, from the perspective of the coupled-wave-theory (CWT). The wave couplings and leakages within the non-Hermitian PCs are depicted, and the condition of accidental triple degeneracy is derived which leads to a Dirac-cone like dispersion. We prove that, similar to the real Dirac-cone, the Dirac-cone like band in non-Hermitian PC possesses good linearity and isotropy in the vicinity of the $\Gamma$ point. Moreover, some topological transit of the band may occur when the parameters adiabatically evolve. However, the Berry phase remains zero at the $\Gamma$ point, indicated the Dirac-like-cone dosen't obey Dirac equation and it is only Dirac-cone.

Topological Phases in InAs_{1-x}Sb_{x}: From Novel Topological Semimetal to Majorana Wire.

Superconductor proximitized one-dimensional semiconductor nanowires with strong spin-orbit interaction (SOI) are, at this time, the most promising candidates for the realization of topological quantum information processing. In current experiments the SOI originates predominantly from extrinsic fields, induced by finite size effects and applied gate voltages. The dependence of the topological transition in these devices on microscopic details makes scaling to a large number of devices difficult unless a material with dominant intrinsic bulk SOI is used. Here, we show that wires made of certain ordered alloys InAs_{1-x}Sb_{x} have spin splittings up to 20 times larger than those reached in pristine InSb wires. In particular, we show this for a stable ordered CuPt structure at x=0.5, which has an inverted band ordering and realizes a novel type of a topological semimetal with triple degeneracy points in the bulk spectrum that produce topological surface Fermi arcs. Experimentally achievable strains can either drive this compound into a topological insulator phase or restore the normal band ordering, making the CuPt-ordered InAs_{0.5}Sb_{0.5} a semiconductor with a large intrinsic linear in k bulk spin splitting.

Level of helium enhancement among M3’s horizontal branch stars

(Abridged) The color and luminosity distribution of horizontal branch (HB) stars in globular clusters are sensitive probes of their original helium abundances. However, recent analyses based on visual and near-ultraviolet (UV) CMDs have provided conflicting results. To clarify the situation, we address the optimum ranges of applicability (in terms of the $T_{eff}$ range covered by the HB stars) for visual and near-UV CMDs, as far as application of this HB $Y$ test goes. We consider both Stromgren and Hubble Space Telescope (HST) bandpasses. Our results indicate that the distributions of HB stars in the y vs (b-y) plane can be a reliable indicator of the He content in cool blue HB (BHB) stars, particularly when a differential comparison between blue and red HB stars is carried out in the range $T_{eff}<8300$K. Conversely, we demonstrate that CMDs using the F336W filter have a much less straightforward interpretation at the cool end of the BHB, as the distributions of HB stars in the F336W vs (F336W-F555W) plane are affected by a triple degeneracy effect. In other words, the position of an HB star is exactly the same, for a given chemical composition, for multiple combinations of the parameters $Y$, $M_{HB}$, and age along the HB evolutionary track. Other HST UV filters do not appear to be as severely affected by this degeneracy effect, to which visual bandpasses are also immune. We do find, on the other hand, that such near-UV CMDs can be extremely useful for the hottest stars along the cool BHB end. Based on a reanalysis of the distribution of HB stars in the y vs (b-y) plane, we find that the coolest among the BHB stars in M3 are likely enhanced in helium by $\Delta Y\approx 0.01$, compared with the red HB stars in the same cluster. Using near-UV HST photometry we find evidence of a progressive increase in $Y$ with increasing temperature, reaching $\Delta Y=0.02$ at $T_{eff}=10900$K.

ℤ3 parafermionic chain emerging from Yang-Baxter equation.

We construct the 1D parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the parafermionic model is a direct generalization of 1D Kitaev model. Both the and model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian based on Yang-Baxter equation. Different from the Majorana doubling, the holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, ω-parity P and emergent parafermionic operator Γ, which are the generalizations of parity PM and emergent Majorana operator in Lee-Wilczek model, respectively. Both the parafermionic model and can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation.

Quantum ballistic transport by interacting two-electron states in quasi-one-dimensional channels

For quantum ballistic transport of electrons through a short conduction channel, the role of Coulomb interaction may significantly modify the energy levels of two-electron states at low temperatures as the channel becomes wide. In this regime, the Coulomb effect on the two-electron states is calculated and found to lead to four split energy levels, including two anticrossing-level and two crossing-level states. Moreover, due to the interplay of anticrossing and crossing effects, our calculations reveal that the ground two-electron state will switch from one anticrossing state (strong confinement) to a crossing state (intermediate confinement) as the channel width gradually increases and then back to the original anticrossing state (weak confinement) as the channel width becomes larger than a threshold value. This switching behavior leaves a footprint in the ballistic conductance as well as in the diffusion thermoelectric power of electrons. Such a switching is related to the triple spin degeneracy as well as to the Coulomb repulsion in the central region of the channel, which separates two electrons away and pushes them to different channel edges. The conductance reoccurrence region expands from the weak to the intermediate confinement regime with increasing electron density.

Designing perovskite BFO (111) membrane as an electrochemical sensor for detection of amino acids: A simulation study

Perovskite bismuth ferrite-BFO (111) membranes, as a potential sensitive electrochemical sensor, are investigated for the detection of amino acids by molecular dynamics (MD) and density functional theory (DFT) techniques. For the detection mechanism of the ferromagnetic phase BFO (111) membrane, the cation bridge model indicates that there is a electronic signal amplification (0.01–0.09 V), due to the enhancement of Fe3+–COO− triple degeneracy orbit (t2g). It is an excellent detection sensitivity for various AAs that can be used to distinguish the surface charges. However, the Fe-d7/2 momentum changes its orientation from upward to downward, on the anti-ferromagnetic phase BFO (111) membrane. The empty d0 orbital degenerates to the O↓ orbital that weakens the Fe–O electron transfer rate, weakening the electronic signal (0.005–0.05 V).

Spin-orbital interaction for face-sharing octahedra: Realization of a highly symmetric SU(4) model

Specific features of orbital and spin structure of transition metal compounds in the case of the face-sharing MO$_6$ octahedra are analyzed. In this geometry, we consider the form of the spin--orbital Hamiltonian for transition metal ions with double ($e_g^{\sigma}$) or triple ($t_{2g}$) orbital degeneracy. Trigonal distortions typical of the structures with face-sharing octahedra lead to splitting of $t_{2g}$ orbitals into an $a_{1g}$ singlet and $e_g^{\pi}$ doublet. For both doublets ($e_g^{\sigma}$ and $e_g^{\pi}$), in the case of one electron or hole per site, we arrive at a symmetric model with the orbital and spin interaction of the Heisenberg type and the Hamiltonian of unexpectedly high symmetry: SU(4). Thus, many real materials with this geometry can serve as a testing ground for checking the prediction of this interesting theoretical model. We also compare general trends in spin--orbital ("Kugel--Khomskii") exchange interaction for three typical situations: those of MO$_6$ octahedra with common corner, common edge, and the present case of common face, which has not been considered yet.

Silane Radical Cation: A Theoretical Account on the Jahn–Teller Effect at a Triple Degeneracy

An ab initio quantum dynamics study is performed to examine the complex nuclear motion underlying the first photoelectron band of the silane molecule due to Jahn-Teller distortion via T2⊗(e+t2+t2) coupling. The problem is investigated by employing a quadratic vibronic coupling model for the Hamiltonian. All sheets of the required potential energy surface are established through extensive electronic structure calculations using the multireference configuration-interaction method. They cover at most two dimensions of the full 9D coordinate space, with the parameters defining the model Hamiltonian being determined by a least-squares fitting procedure. The results are compared with the available experimental data and discussed in relation to those obtained for the methane radical cation. The quadratic couplings of Jahn-Teller active vibrational modes are found to have a crucial role on the irregular vibronic structure, intensity of the spectral excitations, and overall width of the first photoelectron band of the title molecule. The impact of large amplitude motions on the vibronic structure and dynamics of the first photoelectron band has also been examined by varying their linear coupling parameters up to ±10%.

Effects of halogen substitutes on the electronic and magnetic properties of BiFeO3

To observe the high-temperature ferro-electricity at room-temperature, we used a halogen to create a 2p-hole for improving O–Fe p–d electronic transition, and calculated the systematic variations in electronic and magnetic properties using first-principle calculation. The systems prefer to charge disproportionate as Fe3+–O2−–Fe2+ with the highly localized halogen concentration increasing, where the O-site halogen creates a 2p-hole to disproportionate Fe charge from Fe3+-d5 orbital with a full-filled triple degeneracy orbits (t2g) orbital to Fe2+-d5–d0 with a partially filled t2g orbital. Whatever at room-temperature or high-temperature phase, the halogen substitutes, typically, for F (or Cl)-doping, induce the electrons to transfer from O-2p4 → unoccupied Fe3+-3d5 to O-2p4→Bi3+-6p3, while the ferromagnetic (FM)–anti-ferromagnetic (AFM) phase transits at about 1 atom per cell. Furthermore, to retain O–Fe electron transfer process, we applied the crystallographic anisotropy to produce the strong Fe–O orbital hybridization which offsets the effect of 2p-hole, and it causes more significant O-2p4 → unoccupied Fe3+-d5 electronic transitions at the valence band. This study opens a new perspective to the development of multiferroic devices with independent temperature.

Dirac Dispersion in Two-Dimensional Photonic Crystals

We show how one may obtain conical (Dirac) dispersions in photonic crystals, and in some cases, such conical dispersions can be used to create a metamaterial with an effective zero refractive index. We show specifically that in two-dimensional photonic crystals with C4v symmetry, we can adjust the system parameters to obtain accidental triple degeneracy at Γ point, whose band dispersion comprises two linear bands that generate conical dispersion surfaces and an additional flat band crossing the Dirac-like point. If this triply degenerate state is formed by monopole and dipole excitations, the system can be mapped to an effective medium with permittivity and permeability equal to zero simultaneously, and this system can transport wave as if the refractive index is effectively zero. However, not all the triply degenerate states can be described by monopole and dipole excitations and in those cases, the conical dispersion may not be related to an effective zero refractive index. Using multiple scattering theory, we calculate the Berry phase of the eigenmodes in the Dirac-like cone to be equal to zero for modes in the Dirac-like cone at the zone center, in contrast with the Berry phase of π for Dirac cones at the zone boundary.

Mott−Hubbard Lacalization in a Model of the Electronic Subsystem of Doped Fullerides

A microscopical model of doped fulleride electronic subsystem taking the triple orbital degeneracy of energy states into account is considered within the configurational-operator approach. Using the Green function method, the energy spectrum at the integer band filling n = 1 corresponding to AC60 compounds is calculated. A possible correlation-driven metal-insulator transition within the model is discussed.

Orthorhombic fulleride (CH3NH2)K3C60close to Mott-Hubbard instability:Ab initiostudy

We study the electronic structure and magnetic interactions in methylamine-intercalated orthorhombic alkali-doped fullerene $({\mathrm{CH}}_{3}{\mathrm{NH}}_{2}){\mathrm{K}}_{3}{\mathrm{C}}_{60}$ within the density functional theory. As in the simpler ammonia intercalated compound $({\mathrm{NH}}_{3}){\mathrm{K}}_{3}{\mathrm{C}}_{60}$, the orthorhombic crystal-field anisotropy $\ensuremath{\Delta}$ lifts the ${t}_{1}\mathrm{u}$ triple degeneracy at the $\ensuremath{\Gamma}$ point and drives the system deep into the Mott-insulating phase. However, the computed $\ensuremath{\Delta}$ and conduction electron bandwidth $W$ cannot alone account for the abnormally low experimental N\'eel temperature, ${T}_{\mathrm{N}}=11$ K, of the methylamine compound, compared to the much higher value ${T}_{\mathrm{N}}=40$ K of the ammonia one. Significant interactions between ${\mathrm{CH}}_{3}{\mathrm{NH}}_{2}$ and ${\mathrm{C}}_{60}^{3\ensuremath{-}}$ are responsible for the stabilization of particular fullerene-cage distortions and the ensuing low-spin $S=1/2$ state. These interactions also seem to affect the magnetic properties, as interfullerene exchange interactions depend on the relative orientation of deformations of neighboring ${\mathrm{C}}_{60}^{3\ensuremath{-}}$ molecules. For the ferro-orientational order of ${\mathrm{CH}}_{3}{\mathrm{NH}}_{2}$-K${}^{+}$ groups we find an apparent reduced dimensionality in magnetic exchange interactions, which may explain the suppressed N\'eel temperature. The disorder in exchange interactions caused by orientational disorder of ${\mathrm{CH}}_{3}{\mathrm{NH}}_{2}$-K${}^{+}$ groups could further contribute to this suppression.

Creation of the CMB spectrum: precise analytic solutions for the blackbody photosphere

The blackbody spectrum of CMB was created in the blackbody photosphere at redshifts z≳2 × 106. At these early times, the Universe was dense and hot enough that complete thermal equilibrium between baryonic matter (electrons and ions) and photons could be established on time scales much shorter than the age of the Universe. Any perturbation away from the blackbody spectrum was suppressed exponentially. New physics, for example annihilation and decay of dark matter, can add energy and photons to CMB at redshifts z≳105 and result in a Bose-Einstein spectrum with a non-zero chemical potential (μ). Precise evolution of the CMB spectrum around the critical redshift of z ≃ 2 × 106 is required in order to calculate the μ-type spectral distortion and constrain the underlying new physics. Although numerical calculation of important processes involved (double Compton process, comptonization and bremsstrahlung) is not difficult with present day computers, analytic solutions are much faster and easier to calculate and provide valuable physical insights. We provide precise (better than 1%) analytic solutions for the decay of μ, created at an earlier epoch, including all three processes, double Compton, Compton scattering on thermal electrons and bremsstrahlung in the limit of small distortions. This is a significant improvement over the existing solutions with accuracy ∼ 10% or worse. We also give a census of important sources of energy injection into CMB in standard cosmology. In particular, calculations of distortions from electron-positron annihilation and primordial nucleosynthesis illustrate in a dramatic way the strength of the equilibrium restoring processes in the early Universe. Finally, we point out the triple degeneracy in standard cosmology, i.e., the μ and y distortions from adiabatic cooling of baryons and electrons, Silk damping and annihilation of thermally produced WIMP dark matter are of similar order of magnitude ( ∼ 10−8–10−10).

Zero-curvature transonic states and one-component surface waves in anisotropic elastic media

The existence of one-component surface waves requires a degeneracy in the Stroh sextic equation. An extraordinary zero-curvature transonic state, a point on the slowness surface where both the curvature and its first derivative equal zero, will yield a triple degeneracy in the Stroh equation. Relationship between extraordinary zero-curvature transonic states and one-component surface waves is investigated showing that they are linked via a space of degeneracy associated with the Stroh equation. Moreover, some generalized subsonic surface waves containing generalized Stroh eigenvectors are also found along the space of degeneracy.

Unusual Yang-Lee edge singularity in the one-dimensional axial-next-to-nearest-neighbor Ising model

We show here for the one-dimensional spin-1/2 axial-next-to-nearest-neighbor Ising model in an external magnetic field that the linear density of Yang-Lee zeros may diverge with critical exponent σ=-2/3 at the Yang-Lee edge singularity. The necessary condition for this unusual behavior is the triple degeneracy of the transfer-matrix eigenvalues. If this condition is absent we have the usual value σ=-1/2 . Analogous results have been found in the literature in the spin-1 Blume-Emery-Griffths model and in the three-state Potts model in a magnetic field with two complex components. Our results support the universality of σ=-2/3 which might be a one-dimensional footprint of a tricritical version of the Yang-Lee edge singularity possibly present also in higher-dimensional spin models.

Ab-initio calculations of Co-based diluted magnetic semiconductors Cd 1− xCo xX (X=S, Se, Te)

Ab-initio calculations are performed to investigate the structural, electronic and magnetic properties of spin-polarized diluted magnetic semiconductors composed of II–VI compounds Cd 1− x Co x X (X=S, Se, Te) at x=0.25. From the calculated results of band structure and density of states, the half-metallic character and stability of ferromagnetic state for Cd 1− x Co x S, Cd 1− x Co x Se and Cd 1− x Co x Te alloys are determined. It is found that the tetrahedral crystal field gives rise to triple degeneracy t 2 g and double degeneracy e g . Furthermore, we predict the values of spin-exchange splitting energies Δ x ( d) and Δ x ( p− d) and exchange constants N 0 α and N 0 β produced by the Co 3 d states . Calculated total magnetic moments and the robustness of half-metallicity of Cd 1− x Co x X (X=S, Se, Te) with respect to the variation in lattice parameters are also discussed. We also extend our calculations to x=0.50, 0.75 for S compounds in order to observe the change due to increase in Co.