Fourfold Degenerate Research Articles

Symmetry-enforced fourfold degenerate phonons in noncentrosymmetric space groups

Multifold degenerate phonons have received much attention due to their nontrivial monopole topological charge and fascinating boundary states. Although Yu et al recently provides a comprehensive list of all potential nodal points for systems with specific space groups (SGs) (2022 Sci. Bull. 67 375). However, our understanding of the fundamental mechanisms that give rise to the formation of fourfold-degenerate (FD) phonons is still limited. In this paper, we have directed our research towards investigating the generation mechanism of these FD phonons in noncentrosymmetric SGs. Using symmetry arguments and k⋅p model analysis, we have classified them into two categories: the first origins from the commutation/anticommutation relation of the little cogroup operations, and the second associates to the combination of threefold rotation, mirror and time-reversal symmetries. Moreover, the band dispersions of the FD phonons in the first group are required to be linear, whereas the band dispersions of the FD phonons in the second category may be quadratic. On the basis of first-principles calculations, we propose that K 2 Mg2O3 and Na 4 SnSe4 are representative candidates for the two categories, respectively. Furthermore, for each SG with fourfold degenerate phonons, we propose corresponding materials that must host the FD points. Our work not only deepens our understanding of the mechanisms underlying the formation of these FD phonons, but it also proposes practical materials for observing FD phonons in crystalline systems without inversion symmetry.

Contribution of tRNA sequence and modifications to the decoding preferences of E. coli and M. mycoides tRNAGlyUCC for synonymous glycine codons.

tRNA superwobbling, used by certain bacteria and organelles, is an intriguing decoding concept in which a single tRNA isoacceptor is used to decode all synonymous codons of a four-fold degenerate codon box. While Escherichia colirelies on three tRNAGly isoacceptors to decode the four glycine codons (GGN), Mycoplasma mycoidesrequires only a single tRNAGly. Both organisms express tRNAGly with the anticodon UCC, which are remarkably similar in sequence but different in their decoding ability. By systematically introducing mutations and altering the number and type of tRNA modifications using chemically synthesized tRNAs, we elucidated the contribution of individual nucleotides and chemical groups to decoding by the E. coli and M. mycoides tRNAGly. The tRNA sequence was identified as the key factor for superwobbling, revealing the T-arm sequence as a novel pivotal element. In addition, the presence of tRNA modifications, although not essential for providing superwobbling, was shown to delicately fine-tune and balance the decoding of synonymous codons. This emphasizes that the tRNA sequence and its modifications together form an intricate system of high complexity that is indispensable for accurate and efficient decoding.

Tunable Valley Splitting and Bipolar Operation in Graphene Quantum Dots.

Quantum states in graphene are 2-fold degenerate in spins, and 2-fold in valleys. Both degrees of freedom can be utilized for qubit preparations. In our bilayer graphene quantum dots, we demonstrate that the valley g-factor gv, defined analogously to the spin g-factor gs for valley splitting in a perpendicular magnetic field, is tunable by over a factor of 4 from 20 to 90, by gate voltage adjustments only. Larger gv results from larger electronic dot sizes, determined from the charging energy. On our versatile device, bipolar operation, charging our quantum dot with charge carriers of the same or the opposite polarity as the leads, can be performed. Dots of both polarities are tunable to the first charge carrier, such that the transition from an electron to a hole dot by the action of the plunger gate can be observed. Addition of gates easily extends the system to host tunable double dots.

Analysis of codon usage in the mitochondrion genome of Spirodela polyrhiza

In this study, investigation into the characteristics of codon bias and factors in shaping the codon usage pattern of the mitochondrial genome of Spirodela polyrhiza L. Schleid (strain 7498) was performed. S. polyrhiza had a very high GC content of 45.7% in the mitochondrial genome. Compared with other monocots whose mitochondrial genomes have been sequenced, the GC contents of mitochondrial genome of monocots seem to have a decreasing trend as the molecular evolution, and then finally trend to stable at about 44%. The mitochondrion of S. polyrhiz had extremely narrow GC3s distributions from 0.212 to 0.433, if taking no account of SpMatR (0.559) which was the only protein-coding genes with G/C-biased codon usages. The neutrality plot (GC12 vs. GC3s) indicated that there was no correlation between GC12 and GC3s, suggesting there was little directional mutation pressure on the mitochondrial genome of S. polyrhiza. The ENC-plot (ENC vs. GC3s) showed that there were only a small number of genes lying on the expected curve, but a majority of the points with low ENC values lied well below the expected curve. According to the frequency distributions of the ENC ratio, the dataset displayed a single peak, and the most of genes located into a narrow region of ENC ratios between 0–0.1. Context-dependent mutation was analyzed by Chi square test for contingency tables at the four fold degenerate (FFD) sites, suggesting that the frequencies of N3-position bases were definitely not independent of the N2-position bases. Correspondence analysis (COA) of relative synonymous codon usage (RSCU) yielded a first axis which accounted for only13.23% of the total variation. These results suggested that although other factors might play a role in the mitochondrion evolution of S. polyrhiza, mutation press still was the major factor in shaping the codon usage. Meantime, six codons including UUA(Leu), CAU(His), CGU(Arg), AUU(Ile), GCU(Ala) and GAA(Glu) were determined as the “optimal codons” (p < 0.01). Among them, the codon UUA(Leu), its usage was significantly more often in highly biased genes than in lowly.

Particle-hole mirror symmetries around the half-filled shell: Quantum numbers and algebraic structure of composite fermions

Composite fermions (CFs) of the fractional quantum Hall effect are described as spherical products of electron and vortex spinors, built from underlying L=1/2 ladder operators aligned so that the spinor angular momenta Le and Lv are maximal. We identify the CF's quantum numbers as the angular momentum L in (L_e L_v)L, its magnetic projection m_L, the electron number N, with L_v={N-1)/2, and magnetic \nu-spin, m_\nu=L_e-L_v. Translationally invariant FQHE states are formed by filling p subshells with their respective CFs, in order of ascending L for fixed L_e and L_v, beginning with the lowest allowed value, L=|m_\nu|. We show that this wave function has an exactly equivalent hierarchical form. FQHE states can be grouped into \nu-spin multiplets mirror symmetric around m_\nu=0, with N held constant. Electron particle-hole conjugation with respect to this vacuum is identified as the mirror symmetry relating FQHE states of the same N but distinct fillings \nu = p/(2p+1} and p/( 2p-1). Alternatively, mirror symmetric \nu-spin multiplets can be constructed in which the magnetic field strength is held fixed: the valence states are electron particle-vortex hole excitations. Particle-hole symmetry -- relating the N-particle FQHE state of filling \nu=p/(2p+1} to the $\bar{N}$-particle state of filling {p+1)/(2p+1} -- is shown to be equivalent to electron-vortex exchange. In this construction $\bar{N}$-N CFs of the higher density state occupy an extra zero-mode subshell. We link this structure, familiar from supersymmetric quantum mechanics, to the CF Pauli Hamiltonian, which we show is isospectral, quadratic in the \nu-spin raising and lowering operators, and four-fold degenerate. On linearization, it takes a Dirac form similar to that found in the integer quantum Hall effect (IQHE).

The Importance of Being Modified: The Role of RNA Modifications in Translational Fidelity.

The posttranscriptional modifications of tRNA's anticodon stem and loop (ASL) domain represent a third level, a third code, to the accuracy and efficiency of translating mRNA codons into the correct amino acid sequence of proteins. Modifications of tRNA's ASL domain are enzymatically synthesized and site specifically located at the anticodon wobble position-34 and 3'-adjacent to the anticodon at position-37. Degeneracy of the 64 Universal Genetic Codes and the limitation in the number of tRNA species require some tRNAs to decode more than one codon. The specific modification chemistries and their impact on the tRNA's ASL structure and dynamics enable one tRNA to decode cognate and "wobble codons" or to expand recognition to synonymous codons, all the while maintaining the translational reading frame. Some modified nucleosides' chemistries prestructure tRNA to read the two codons of a specific amino acid that shares a twofold degenerate codon box, and other chemistries allow a different tRNA to respond to all four codons of a fourfold degenerate codon box. Thus, tRNA ASL modifications are critical and mutations in genes for the modification enzymes and tRNA, the consequences of which is a lack of modification, lead to mistranslation and human disease. By optimizing tRNA anticodon chemistries, structure, and dynamics in all organisms, modifications ensure translational fidelity of mRNA transcripts.

Energy levels of exciton in a gapped graphene sheet

A theory is presented for exciton formation in a graphene sheet using the center-of-mass approximation. The energy levels and wavefunctions of exciton are calculated analytically which show that the exciton can form if the band gap of graphene is not zero. We show that the energy gap of graphene plays the role of the mass which if not zero, leads to formation of the excitons. It is shown that the main quantum number of the exciton ground state changes with the graphene dielectric constant. Also, all of the states are found to be four-fold degenerate. The binding energy of exciton can reach as high as 1/4 of the energy gap of graphene which is notable among the conventional quasi-2D systems. This result can play an important rule in the photonics of graphene.

Spectral properties of embedded Gaussian unitary ensemble of random matrices with Wigner’s SU(4) symmetry

For m fermions in Ω number of single particle orbitals, each fourfold degenerate, we introduce and analyze in detail embedded Gaussian unitary ensemble of random matrices generated by random two-body interactions that are SU(4) scalar [EGUE(2)- SU(4)]. Here the SU(4) algebra corresponds to the Wigner’s supermultiplet SU(4) symmetry in nuclei. Embedding algebra for the EGUE(2)- SU(4) ensemble is U(4 Ω) ⊃ U( Ω) ⊗ SU(4). Exploiting the Wigner–Racah algebra of the embedding algebra, analytical expression for the ensemble average of the product of any two m particle Hamiltonian matrix elements is derived. Using this, formulas for a special class of U( Ω) irreducible representations (irreps) {4 r , p}, p = 0, 1, 2, 3 are derived for the ensemble averaged spectral variances and also for the covariances in energy centroids and spectral variances. On the other hand, simplifying the tabulations of Hecht for SU( Ω) Racah coefficients, numerical calculations are carried out for general U( Ω) irreps. Spectral variances clearly show, by applying Jacquod and Stone prescription, that the EGUE(2)- SU(4) ensemble generates ground state structure just as the quadratic Casimir invariant ( C 2) of SU(4). This is further corroborated by the calculation of the expectation values of C 2[ SU(4)] and the four periodicity in the ground state energies. Secondly, it is found that the covariances in energy centroids and spectral variances increase in magnitude considerably as we go from EGUE(2) for spinless fermions to EGUE(2) for fermions with spin to EGUE(2)- SU(4) implying that the differences in ensemble and spectral averages grow with increasing symmetry. Also for EGUE(2)- SU(4) there are, unlike for GUE, non-zero cross-correlations in energy centroids and spectral variances defined over spaces with different particle numbers and/or U( Ω) [equivalently SU(4)] irreps. In the dilute limit defined by Ω → ∞, r ≫ 1 and r/ Ω → 0, for the {4 r , p} irreps, we have derived analytical results for these correlations. All correlations are non-zero for finite Ω and they tend to zero as Ω → ∞.

Nucleotide Content Gradients in Maternally and Paternally Inherited Mitochondrial Genomes of the Mussel Mytilus

Several studies have shown that in vertebrate mtDNAs the nucleotide content at fourfold degenerate sites is well correlated with the site's time of exposure to the single-strand state, as predicted from the asymmetrical model of mtDNA replication. Here we examine whether the same explanation may hold for the regional variation in nucleotide content in the maternal and paternal mtDNAs of the mussel Mytilus galloprovincialis. The origin of replication of the heavy strand (O(H)) of these genomes has been previously established. A systematic search of the two genomes for sequences that are likely to act as the origin of replication of the light strand (O(L)) suggested that the most probable site lies within the ND3 gene. By adopting this O(L) position we calculated times of exposure for 0(FD) (nondegenerate), 2(FD) (twofold degenerate), and 4(FD) (fourfold degenerate) sites of the protein-coding part of the genome and for the rRNA, tRNA and noncoding parts. The presence of thymine and absence of guanine at 4(FD) sites was highly correlated with the presumed time of exposure. Such an effect was not found for the 2(FD) sites, the rRNA, the tRNA, or the noncoding parts. There was a trend for a small increase in cytosine at 0(FD) sites with exposure time, which is explicable as the result of biased usage of 4(FD) codons. The same analysis was applied to a recently sequenced mitochondrial genome of Mytilus trossulus and produced similar results. These results are consistent with the asymmetrical model of replication and suggest that guanine oxidation due to single-strand exposure is the main cause of regional variation of nucleotide content in Mytilus mitochondrial genomes.

Strand bias in complementary single-nucleotide polymorphisms of transcribed human sequences: evidence for functional effects of synonymous polymorphisms

BackgroundComplementary single-nucleotide polymorphisms (SNPs) may not be distributed equally between two DNA strands if the strands are functionally distinct, such as in transcribed genes. In introns, an excess of A↔G over the complementary C↔T substitutions had previously been found and attributed to transcription-coupled repair (TCR), demonstrating the valuable functional clues that can be obtained by studying such asymmetry. Here we studied asymmetry of human synonymous SNPs (sSNPs) in the fourfold degenerate (FFD) sites as compared to intronic SNPs (iSNPs).ResultsThe identities of the ancestral bases and the direction of mutations were inferred from human-chimpanzee genomic alignment. After correction for background nucleotide composition, excess of A→G over the complementary T→C polymorphisms, which was observed previously and can be explained by TCR, was confirmed in FFD SNPs and iSNPs. However, when SNPs were separately examined according to whether they mapped to a CpG dinucleotide or not, an excess of C→T over G→A polymorphisms was found in non-CpG site FFD SNPs but was absent from iSNPs and CpG site FFD SNPs.ConclusionThe genome-wide discrepancy of human FFD SNPs provides novel evidence for widespread selective pressure due to functional effects of sSNPs. The similar asymmetry pattern of FFD SNPs and iSNPs that map to a CpG can be explained by transcription-coupled mechanisms, including TCR and transcription-coupled mutation. Because of the hypermutability of CpG sites, more CpG site FFD SNPs are relatively younger and have confronted less selection effect than non-CpG FFD SNPs, which can explain the asymmetric discrepancy of CpG site FFD SNPs vs. non-CpG site FFD SNPs.

Electronic structure of ZnO wurtzite quantum wires

The electronic structure and optical properties of ZnO wurtzite quantum wires with radius R >= 3 nm are studied in the framework of six-band effective-mass envelope function theory. The hole effective-mass parameters of ZnO wurtzite material are calculated by the empirical pseudopotential method. It is found that the electron states are either two-fold or four-fold degenerate. There is a dark exciton effect when the radius R of the ZnO quantum wires is in the range of [3,19.1] nm (dark range in our model). The dark ranges of other wurtzite semiconductor quantum wires are calculated for comparison. The dark range becomes smaller when the |Delta(so)| is larger, which also happens in the quantum-dot systems. The linear polarization factor of ZnO quantum wires is larger when the temperature is higher.

Epitaxial variations of Ni films grown on MgO(0 0 1)

Epitaxial Ni films were deposited on (0 0 1)MgO by DC magnetron sputtering under ultra-high vacuum conditions for studies involving magnetic-multilayer applications. The deposition temperatures of the Ni films studied in this work were 100 and 400°C. Examination by transmission electron microscopy (TEM) and electron diffraction revealed that the film deposited at the lower temperature was predominately Ni[0 0 1]‖MgO[0 0 1] and Ni(0 1 0)‖MgO(0 1 0) oriented and smooth, as expected. However, the higher temperature films were predominately of the Ni [7 5 1 ̄ ] ‖MgO[0 0 1] and Ni ( 1 ̄ 1 2 ̄ ) ‖MgO(1 0 0) orientation and facetted. The [7 5 1 ̄ ] orientation has been confirmed by X-ray diffraction, where this orientation was observed to be four-fold degenerate. For each of these four orientations there also existed a twin orientation, reflected about the MgO(1 0 0) planes, giving eight possible orientations for the Ni crystallites on MgO. This [7 5 1 ̄ ] epitaxial relationship was studied by dark-field TEM and electron diffraction. Because these films were polycrystalline and hence produced many diffraction spots from both the Ni and MgO with similar lattice spacings, electron diffraction patterns of the films were indexed using an electron diffraction image processing (EDIP) technique. In this technique, the polycrystalline electron diffraction pattern was converted into a graph, with the x-axis displaying lattice spacings and the y-axis, integrated intensity.

Thomas Precession, Berry Potential, and the Meron

We begin with a prior observation by one of us that Thomas precession in the nonrelativistic limit of the Dirac equation may be attributed to a nonabelian Berry vector potential. We ask what object produces the nonabelian potential in parameter space, in the same sense that the abelian vector potential arising in the adiabatic transport of a nondegenerate level is produced by a monopole, (centered at the point where the level becomes degenerate with another), as shown by Berry. We find that it is a {\em meron}, an object in four euclidean dimensions with instanton number ${1 \over 2}$, centered at the point where the doubly degenerate positive and negative energy levels of the Dirac equation become fourfold degenerate.

Statistics of the excitations of the resonating-valence-bond state.

By extending recent proposals for choosing the phases in resonating-valence-bond ground states to the case of excited states, we show for these wave functions that the hole excitations are charged, spinless fermions and the spin excitations are neutral, spin-(1/2 bosons. We also show that for a system with periodic boundary conditions, all states are at least fourfold degenerate.

Lifshitz-Allen-Cahn domain-growth kinetics of Ising models with conserved density.

The domain-growth kinetics of p=fourfold degenerate (2\ifmmode\times\else\texttimes\fi{}1) ordering in two-dimensional Ising models with conserved density is studied as a function of temperature and range of Kawasaki spin exchange. It is found by computer simulations that the zero-temperature freezing-in behavior for nearest-neighbor exchange is released when next-nearest-neighbor exchange is included. The Lifshitz-Allen-Cahn growth law is obeyed for all temperatures indicating that the density conservation is irrelevant also for p&gt;2. .AE

II. Reduced SU(3) matrix elements

For m fermions in Ω number of single particle orbitals, each fourfold degenerate, we introduce and analyze in detail embedded Gaussian unitary ensemble of random matrices generated by random two-body interactions that are SU(4) scalar [EGUE(2)-SU(4)]. Here the SU(4) algebra corresponds to the Wigner’s supermultiplet SU(4) symmetry in nuclei. Embedding algebra for the EGUE(2)-SU(4) ensemble is U(4Ω) ⊃ U(Ω) ⊗ SU(4). Exploiting the Wigner–Racah algebra of the embedding algebra, analytical expression for the ensemble average of the product of any two m particle Hamiltonian matrix elements is derived. Using this, formulas for a special class of U(Ω) irreducible representations (irreps) {4r, p}, p = 0, 1, 2, 3 are derived for the ensemble averaged spectral variances and also for the covariances in energy centroids and spectral variances. On the other hand, simplifying the tabulations of Hecht for SU(Ω) Racah coefficients, numerical calculations are carried out for general U(Ω) irreps. Spectral variances clearly show, by applying Jacquod and Stone prescription, that the EGUE(2)-SU(4) ensemble generates ground state structure just as the quadratic Casimir invariant (C2) of SU(4). This is further corroborated by the calculation of the expectation values of C2[SU(4)] and the four periodicity in the ground state energies. Secondly, it is found that the covariances in energy centroids and spectral variances increase in magnitude considerably as we go from EGUE(2) for spinless fermions to EGUE(2) for fermions with spin to EGUE(2)-SU(4) implying that the differences in ensemble and spectral averages grow with increasing symmetry. Also for EGUE(2)-SU(4) there are, unlike for GUE, non-zero cross-correlations in energy centroids and spectral variances defined over spaces with different particle numbers and/or U(Ω) [equivalently SU(4)] irreps. In the dilute limit defined by Ω → ∞, r ≫ 1 and r/Ω → 0, for the {4r, p} irreps, we have derived analytical results for these correlations. All correlations are non-zero for finite Ω and they tend to zero as Ω → ∞.

E.S.R. spectra and hyperfine structure of symmetric trinuclear clusters

The E.S.R. spectrum hyperfine structure of trigonal trinuclear exchange clusters with half-integral spins is presented. In the case of antiferromagnetic exchange coupling, the ground state with the total spin S = ½ is four-fold degenerate. The Heisenberg-Dirac-Van Vleck model is shown to be incorrect for the problem of hyperfine interactions. The theory of E.S.R. hyperfine structure presented here arises from the group-theoretical analysis of exchange multiplets. By means of irreducible tensor methods the hyperfine interaction effective hamiltonian is constructed. The angular and field dependence of the hyperfine structure is investigated.

Deformation Potentials in Silicon. I. Uniaxial Strain

The rate of splitting with uniaxial strain of the fourfold degenerate ($J=\frac{3}{2}$) valence-band edge of silicon is computed by applying perturbation theory to the Si wave functions calculated previously by Kleinman and Phillips. Based on a "self-consistent" model the calculated values for strain along the [100] and [111] directions are 40% larger than Hensel's experimental values. A primary objective of this calculation was to test the rigid-ion and deformable-ion models often used in the theory of electron-phonon coupling. The rigid-ion model agrees with experiment to within the accuracy of the calculation while the deformable-ion model disagrees with experiment by 300%. For [111] strain the crystal symmetry is so reduced that the separation of the two atoms in each unit cell is not uniquely determined from the macroscopic strain. We have used a model in which the atoms locate themselves in such a way that nearest-neighbor covalent bonds are unchanged in length by shearing strains. This "bond-bending" model is contrasted with a model in which the atomic separation changes with strain like a macroscopic vector. The latter model yields a deformation potential of opposite sign to the experimental one.