Lifting Of Degeneracy Research Articles

Research on transmission characteristics of aperture-coupled square-ring resonator based filter

In this study, a nanometric surface plasmon polariton (SPP) filter based on an aperture-coupled square-ring resonator is presented and the transmission characteristics of the SPP filter are analyzed in detail by using the finite difference time domain (FDTD) method. Results show that lifting of degeneracy exists in both even-modes and odd-modes for the regular side-coupled square-ring resonator. By introducing the aperture between the ring and bus waveguide, semi-integer resonance modes with high drop efficiency emerge in the optical transmission spectrum. Further simulation results show that semi-integer modes can be efficiently modified and linearly tuned by adjusting the parameters of the resonators such as side length of the ring, the width of the aperture and the medium inside the aperture. The simple band-stop SPP filter is very promising for high-density SPP waveguide integrations.

Oxygen-Vacancy-Induced Orbital Reconstruction of Ti Ions at the Interface ofLaAlO3/SrTiO3Heterostructures: A Resonant Soft-X-Ray Scattering Study

Resonant soft-x-ray scattering measurements have been performed to investigate interface electronic structures of (LaAlO(3)/SrTiO(3)) superlattices. Resonant scattering intensities at superlattice reflections show clear evidence of degeneracy lifting in t(2g) states of interface Ti ions. Polarization dependence of intensities indicates the energy of d(xy) states is lower by ~1 eV than two other t(2g) states. The energy splitting is insensitive to epitaxial strain. The orbital reconstruction is induced by oxygen vacancies and confined to the interface within two unit cells, indicating charge compensation at the polar interfaces.

Environmental perturbations lift the degeneracy of the genetic code to regulate protein levels in bacteria

The genetic code underlying protein synthesis is a canonical example of a degenerate biological system. Degeneracies in physical and biological systems can be lifted by external perturbations, thus allowing degenerate systems to exhibit a wide range of behaviors. Here we show that the degeneracy of the genetic code is lifted by environmental perturbations to regulate protein levels in living cells. By measuring protein synthesis rates from a synthetic reporter library in Escherichia coli, we find that environmental perturbations, such as reduction of cognate amino acid supply, lift the degeneracy of the genetic code by splitting codon families into a hierarchy of robust and sensitive synonymous codons. Rates of protein synthesis associated with robust codons are up to 100-fold higher than those associated with sensitive codons under these conditions. We find that the observed hierarchy between synonymous codons is not determined by usual rules associated with tRNA abundance and codon usage. Rather, competition among tRNA isoacceptors for aminoacylation underlies the robustness of protein synthesis. Remarkably, the hierarchy established using the synthetic library also explains the measured robustness of synthesis for endogenous proteins in E. coli. We further found that the same hierarchy is reflected in the fitness cost of synonymous mutations in amino acid biosynthesis genes and in the transcriptional control of σ-factor genes. Our study suggests that organisms can exploit degeneracy lifting as a general strategy to adapt protein synthesis to their environment.

Structural Studies and Valence Band Splitting Parameters in Ordered Vacancy Compound AgGa7Se12

The threefold absorption in the fundamental absorption region of the ternary chalcopyrite AgGa7Se12, an ordered defect compound of AgGaSe2, is analyzed to elucidate the three closely spaced band gaps in its valence band due to the lifting of degeneracy of the Γ15 level. Hopfield’s quasi cubic model is employed to extract the crystal-field and spin–orbit splitting parameters and the linear hybridisation of orbitals model for evaluating the percentage contribution of Ag d-orbital and Ga and Se p-orbitals to the p–d hybridization of orbitals. The observed optical properties are correlated with the structural parameters like deformation parameter, anion displacement and anion–cation bond lengths that are deduced from X-ray diffraction data. The compound films for the studies are prepared by a modified form of Gunther’s three temperature technique and the compositional analysis was done by energy dispersive analysis of X-rays. X-ray photoelectron spectroscopy confirms the compound formation while atomic force microscopic technique was used for surface morphological analysis. The electrical resistivity of these n-type semi-conducting films is assessed to be ~5 Ωm and the films are found to be photosensitive.

Small-Sized PbSe/PbS Core/Shell Colloidal Quantum Dots

The work focuses on the synthesis of small-sized PbSe/PbS core/shell colloidal quantum dots with the core diameter of 2–2.5 nm and the shell thickness of 0.5–1.0 nm. The PbSe/PbS core/shell CQDs are chemically stable under time-limited air exposure and have emission quantum efficiency of 60% at room temperature. The PbSe/PbS core/shell CQDs have a tunable absorption edge around 1 μm, large exciton emission Stokes shift (∼150 meV), and small exchange interaction (∼1.5 meV). Theoretical calculations associate the mentioned parameters to the small-size regime as well as to a lift of band-edge degeneracy due to slight shape anisotropy. The specific parameters are of special interest in photovoltaic applications.

Infrared absorption spectroscopy of a carbon–oxygen complex in gallium arsenide

AbstractInfrared absorption measurements have been carried out on a carbon–oxygen complex in gallium arsenide. The stretching mode at 2059.6 cm−1 has been investigated at low temperatures with polarized light under uniaxial stress in the 〈100〉, 〈111〉, and 〈110〉 crystallographic directions. The splitting behavior due to lifting of orientational degeneracy shows that the center has tetragonal symmetry. The intensity of the isotope shifted satellite band caused by the naturally abundant 18O isotope is not in agreement with the identification as a simple CO‐molecule. The number of incorporated oxygen atoms is 3 ± 1. The assignment of the defect to a CO2 molecule is in agreement with the experimental data available so far.

Infrared magnetospectroscopy of graphite in tilted fields

The electronic structure of Bernal-stacked graphite subjected to tilted magnetic fields has been investigated using infrared magnetotransmission experiments. With the increasing in-plane component of the magnetic field ${B}_{\ensuremath{\parallel}}$, we observe significant broadening and partially also splitting of interband inter-Landau-level transitions, which originate at the $H$ point of the graphite Brillouin zone, where the charge carriers behave as massless Dirac fermions. The observed behavior is attributed to the lifting of the twofold degeneracy of Landau levels at the $H$ point---a degeneracy which in graphite complements the standard spin and valley degeneracies typical of graphene.

Static field induced magnetic relaxations in dinuclear lanthanide compounds of [phen<sub>2</sub>Ln<sub>2</sub>(HCOO)<sub>4</sub>(HCOO)<sub>2-2<italic>x</italic>(NO<sub>3</sub>)<sub>2<italic>x</italic>] (1, Ln = Gd and <italic>x</italic> = 0.52; 2, Ln = Er and <italic>x</italic> = 0.90; phen = 1,10-phenanthroline)</sub></sub>

Two dinuclear lanthanide (Ln) complexes, formulated as [phen 2 Ln 2 (HCOO) 4 (HCOO) 2-2 x (NO 3 ) 2 x ] (1, Ln = Gd and x = 0.52; 2, Ln = Er and x = 0.90; phen = 1,10-phenanthroline), were synthesized and characterized. They are isostructural. The dinuclear molecule consists of two Ln 3+ bridged by four formate groups and chelated by phen and formate/nitrate ligands, and the Ln 3+ possesses a coordination environment of distorted tri-capped trigonal prism of LnO 7 N 2 . Both compounds behave as paramagnets between 2 and 300 K, but display two static field induced magnetic relaxation processes. One is slow and of spin-lattice type, and it results from the lifting of Kramer's degeneracy of the ground-states of both Gd 3+ and Er 3+ , and the other is fast, and it might be spin-spin type.

Static field induced magnetic relaxations in dinuclear lanthanide compounds of [phen2Ln2(HCOO)4(HCOO)2−2x (NO3)2x ] (1, Ln = Gd and x = 0.52; 2, Ln = Er and x = 0.90; phen = 1,10-phenanthroline)

Two dinuclear lanthanide (Ln) complexes, formulated as [phen 2 Ln 2 (HCOO) 4 (HCOO) 2-2 x (NO 3 ) 2 x ] (1, Ln = Gd and x = 0.52; 2, Ln = Er and x = 0.90; phen = 1,10-phenanthroline), were synthesized and characterized. They are isostructural. The dinuclear molecule consists of two Ln 3+ bridged by four formate groups and chelated by phen and formate/nitrate ligands, and the Ln 3+ possesses a coordination environment of distorted tri-capped trigonal prism of LnO 7 N 2 . Both compounds behave as paramagnets between 2 and 300 K, but display two static field induced magnetic relaxation processes. One is slow and of spin-lattice type, and it results from the lifting of Kramer's degeneracy of the ground-states of both Gd 3+ and Er 3+ , and the other is fast, and it might be spin-spin type.

Asymmetric velocities of Dirac particles and Vernier spectrum in metallic single-wall carbon nanotubes

Left- and right-going Dirac particles near the $K$ (or ${K}^{\ensuremath{'}}$) point in the two-dimensional Brillouin zone have different velocities in metallic single-wall carbon nanotubes. The metallic linear energy band is tilted by a curvature effect of the nanotube. The difference of the velocities is calculated by a numerical calculation and by an effective mass theory. Tilting as well as warping of the Dirac cones explains the diameter and chirality dependences of the velocities quantitatively. The asymmetric velocities give a ``vernier'' spectrum of an electron in a nanotube quantum dot with a sharp confinement potential containing two different sequences of levels, which is relevant to the lifting of the fourfold degeneracy of the energy levels.

Curvature effects on valley splitting and degeneracy lifting: Case of Si/Ge rolled-up nanotubes

We numerically investigate electronic states, degeneracy lifting, and valley splitting in the conduction band of rolled-up Si/Ge nanotubes. Results are derived from a tight-binding model where the input equilibrium positions of the atoms are obtained by means of continuum elasticity theory. We find three inequivalent $\ensuremath{\Delta}$ valleys. The lifting of their energy degeneracy and the spatial distribution of the corresponding states are interpreted in terms of nonbiaxial strain and confinement effects. The intervalley interaction in Si/Ge nanotubes is studied as a function of the thickness and curvature of the tube. We demonstrate that the curvature affects the intervalley interaction, in close analogy to what happens with the application of a perpendicular electric field in planar quantum well Si/Ge systems.

Quantum Hall Effect and Semimetallic Behavior of Dual-Gated ABA-Stacked Trilayer Graphene

The electronic structure of multilayer graphenes depends strongly on the number of layers as well as the stacking order. Here we explore the electronic transport of purely ABA-stacked trilayer graphenes in a dual-gated field-effect device configuration. We find that both the zero-magnetic-field transport and the quantum Hall effect at high magnetic fields are distinctly different from the monolayer and bilayer graphenes, and that they show electron-hole asymmetries that are strongly suggestive of a semimetallic band overlap. When the ABA trilayers are subjected to an electric field perpendicular to the sheet, Landau level splittings due to a lifting of the valley degeneracy are clearly observed.

Assignment of Aluminum Corroles Absorption Bands to Electronic Transitions by Femtosecond Polarization Resolved VIS-Pump IR-Probe Spectroscopy

We combine femtosecond polarization resolved VIS-pump IR-probe spectroscopy with DFT and TD-DFT calculations to identify and assign absorption bands to electronic transitions for corroles. These macrocycles and their corresponding metal complexes are receiving great attention because of their utility in many fields, while many of their spectroscopic features have not yet been fully described. Analysis of the perturbed free induction decay provides information about the bleaching signal at time zero and allows for determination of overlapping excited state and bleaching signal amplitudes. The S(0) → S(1) and S(0) → S(2) transitions in the Q-band of the hexacoordinated Al(tpfc)(py)(2) and Br(8)Al(tpfc)(py)(2) absorption spectra are explicitly assigned. Angles between these electronic transition dipole moments (tdms) with a single vibrational transition dipole moment of (53 ± 2)° and (34 ± 2)° when excited at 580 and 620 nm for hexacoordinated Al(tpfc)(py)(2) and (51 ± 2)° and (43 ± 2)° when excited at 590 and 640 nm for hexacoordinated Br(8)Al(tpfc)(py)(2) were determined. The relative angles between the two lowest electronic tdms are (90 ± 8)° and (94 ± 3)° for Al(tpfc)(py)(2) and Br(8)Al(tpfc)(py)(2), respectively. Angles are determined before time zero by polarization resolved perturbed free induction decay and after time zero by polarization resolved transients. Comparison of corrole's wave functions with those of porphine show that the reduced symmetry in the corrole molecules results in lifting of Q-band degeneracy and major reorientation of the electronic transition dipole moments within the molecular scaffold. This information is necessary in designing optimal corrole-based electron and energy transfer complexes.

Structure and electronic properties of a benzene-water solution

Electronic properties of benzene in water were investigated by a sequential quantum mechanical/molecular dynamics approach. Emphasis was placed on the analysis of the structure, polarization effects, and ionization spectrum. By adopting a polarizable model for both benzene and water the structure of the benzene-water solution is in good agreement with data from first principles molecular dynamics. Further, strong evidence that water molecules acquire enhanced orientational order near the benzene molecule is found. Upon hydration, the quadrupole moment of benzene is not significantly changed in comparison with the gas-phase value. We are also reporting results for the dynamic polarizability of benzene in water. Our results indicate that the low energy behaviour of the dynamic polarizability of gas-phase and hydrated benzene is quite similar. Outer valence Green's function calculations for benzene in liquid water show a splitting of the gas-phase energy levels associated with the 1e(1g)(π), 2e(2g), and 2e(1u) orbitals upon hydration. Lifting of the orbitals degeneracy and redshift of the outer valence bands is related to symmetry breaking of the benzene structure in solution and polarization effects from the surrounding water molecules.

Graph theory and the Jahn–Teller theorem

The Jahn–Teller (JT) theorem predicts spontaneous symmetry breaking and lifting of degeneracy in degenerate electronic states of (nonlinear) molecular and solid-state systems. In these cases, degeneracy is lifted by geometric distortion. Molecular problems are often modelled using spectral theory for weighted graphs, and the present paper turns this process around and reformulates the JT theorem for general vertex- and edge-weighted graphs themselves. If the eigenvectors and eigenvalues of a general graph are considered as orbitals and energy levels (respectively) to be occupied by electrons, then degeneracy of states can be resolved by a non-totally symmetric re-weighting of edges and, where necessary, vertices. This leads to the conjecture that whenever the spectrum of a graph contains a set of bonding or anti-bonding degenerate eigenvalues, the roots of the Hamiltonian matrix over this set will show a linear dependence on edge distortions, which has the effect of lifting the degeneracy. When the degenerate level is non-bonding, distortions of vertex weights have to be included to obtain a full resolution of the eigenspace of the degeneracy. Explicit treatments are given for examples of the octahedral graph, where the degeneracy to be lifted is forced by symmetry, and the phenalenyl graph, where the degeneracy is accidental in terms of the automorphism group.

Molecular thermometers based on phosphorescent porphin metal complexes

We study the temperature dependence of the radiative deactivation of triplet states of Pdand Pt-porphin molecules in n-alkane matrices in the temperature range 4.2–210 K. The nature of the thermally activated “hot” lines that are observed in phosphorescence spectra of Pdand Pt-porphin is discussed in detail. We show that, because of the degeneracy lifting of the triplet state T1, 2 in the crystal field of n-alkane matrices, lines of the transitions T1 → S0 and T2 → S0 are spectrally spaced and, in all cases, the T2 state is the first state that is activated with increasing temperature. We analyze the dependences of the T2-T1 splitting on the chelated metal ion and the type of the matrix. The possibility of measuring cryogenic temperatures with molecular thermometers that use the thermochromic properties of Pdand Pt-porphin in n-alkane matrices is discussed.

Fiber based polarization filter for radially and azimuthally polarized light

We demonstrate a new fiber based concept to filter azimuthally or radially polarized light. This concept is based on the lifting of the modal degeneracy that takes place in high numerical aperture fibers. In such fibers, the radially and azimuthally polarized modes can be spectrally separated using a fiber Bragg grating. As a proof of principle, we filter azimuthally polarized light in a commercially available fiber in which a fiber Bragg grating has been written by a femtosecond pulsed laser.

Optical properties of photonic molecules and elliptical pillars made of ZnSe-based microcavities

The influence of the geometric shape of optically confining structures on the emission properties of ZnSe-based microcavities is studied. Elliptical as well as coupled circular structures were fabricated with quantum wells or quantum dots as optical active material. For the elliptical pillars a lifting of the polarization degeneracy of the resonator modes is observed as it is favorable to control the polarization state of the emitted photons. The influence of the ellipticity on the polarization splitting of the fundamental mode as well as on the quality factor of the sample is discussed. For the coupled pillar microcavities the effect of their distance on the energy splitting of the fundamental resonator mode is analyzed. Furthermore, detailed measurements of the spatial mode distribution in elliptically shaped pillars and photonic molecules are performed. By comparing these results to the calculated mode distribution their analogy to a diatomic molecule is illustrated. It turns out that the observed mode splitting into localized bonding and delocalized antibonding states in ZnSe-based microcavities is more pronounced for elliptical geometries. The realization of delocalized mode profiles is favorable for the coupling of spatially separated quantum dots.

Quantum Monte Carlo study of molecular polarization and antiferroelectric ordering in squaric acid crystals

Effects of geometrical frustration and quantum fluctuation are theoretically investigated for the proton ordering in a quasi-two-dimensional hydrogen-bonded system, squaric acid crystal. We elucidate the phase diagram for an effective model, the transverse-field Ising model on a frustrated checkerboard lattice, by using quantum Monte Carlo simulation. A crossover to liquidlike paraelectric state with well-developed molecular polarizations is identified, distinguishably from long-range ordering. Emergence of long-range order from the liquidlike state exhibits peculiar aspects originating from the lifting of quasi-macroscopic degeneracy, such as colossal enhancement of the transition temperature and a vanishingly small anomaly in the specific heat.

Unveiling the Magnetic Structure of Graphene Nanoribbons

We perform magnetotransport measurements in lithographically patterned graphene nanoribbons down to a 70 nm width. The electronic spectrum fragments into an unusual Landau levels pattern, characteristic of Dirac fermion confinement. The two-terminal magnetoresistance reveals the onset of magnetoelectronic subbands, edge currents and quantized Hall conductance. We bring evidence that the magnetic confinement at the edges unveils the valley degeneracy lifting originating from the electronic confinement. Quantum simulations suggest some disorder threshold at the origin of mixing between chiral magnetic edge states and disappearance of quantum Hall effect.