Degeneracy

In breathing pyrochlores and kagomes, couplings between neighbouring tetrahedra and triangles are free to differ. Breathing lattices thus offer the possibility to explore a different facet of the rich physics of these systems. Here we consider nearest-neighbour classical Heisenberg interactions, both ferromagnetic and antiferromagnetic, and study how the anisotropy of breathing lattices modifies the mode spectrum of pyrochlore and kagome systems. The nature and degeneracy of the flat bands are shown to be preserved for any value of the anisotropy...

Based on the Shannon's information communication theory, information amount of the entire length of a polymeric macromolecule can be calculated in bits through adding the entropies of each building block. Proteins, DNA and RNA are such macromolecules. When only the building blocks' variation is considered as the source of entropy, there is seemingly lower information in case of the protein if this approach is applied directly on a protein of specific size and the coding sequence size of the mRNA corresponding to the particular length of the protein...

We identify two orthogonal sources of structural entropy in rattler-free granular systems: affine, involving structural changes that only deform the contact network, and topological, corresponding to different topologies of the contact network. We show that a recently developed connectivity-based granular statistical mechanics separates the two naturally by identifying the structural degrees of freedom with spanning trees on the graph of the contact network. We extend the connectivity-based formalism to include constraints on, and correlations between, degrees of freedom as interactions between branches of the spanning tree...

One of the most promising platforms for spintronics and topological quantum computation is the two-dimensional electron gas (2DEG) with strong spin-orbit interaction and out-of-plane ferromagnetism. In proximity to an s-wave superconductor, such 2DEG may be driven into a topologically non-trivial superconducting phase, predicted to support zero-energy Majorana fermion modes. Using angle-resolved photoemission spectroscopy and ab initio calculations, we study the 2DEG at the surface of the vanadium-doped polar semiconductor with a giant Rashba-type splitting, BiTeI...

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...

We analyze four ways of formulating the Kohn-Sham (KS) density functionals with a fractional number of electrons, through extending the constrained search space from the Kohn-Sham and the generalized Kohn-Sham (GKS) non-interacting v-representable density domain for integer systems to four different sets of densities for fractional systems. In particular, these density sets are (I) ensemble interacting N-representable densities, (II) ensemble non-interacting N-representable densities, (III) non-interacting densities by the Janak construction, and (IV) non-interacting densities whose composing orbitals satisfy the Aufbau occupation principle...

We classify line nodes in superconductors with strong spin-orbit interactions and time-reversal symmetry, where the latter may include nonprimitive translations in the magnetic Brillouin zone to account for coexistence with antiferromagnetic order. We find four possible combinations of irreducible representations of the order parameter on high-symmetry planes, two of which allow for line nodes in pseudospin-triplet pairs and two that exclude conventional fully gapped pseudospin-singlet pairs. We show that the former can only be realized in the presence of band-sticking degeneracies, and we verify their topological stability using arguments based on Clifford algebra extensions...

Motivated by recent realizations of Dy_{2}Ti_{2}O_{7} and Ho_{2}Ti_{2}O_{7} spin ice thin films, and more generally by the physics of confined gauge fields, we study a model spin ice thin film with surfaces perpendicular to the [001] cubic axis. The resulting open boundaries make half of the bonds on the interfaces inequivalent. By tuning the strength of these inequivalent "orphan" bonds, dipolar interactions induce a surface ordering equivalent to a two-dimensional crystallization of magnetic surface charges...

Monolayer manganese chalcogenophosphates MnPSe3 possess a pair of non-degenerate energy valleys in the vicinities of the vertices of the hexagonal Brillouin zone, which exhibit fascinating optical valley polarization. However, the spin is still degenerate due to antiferromagnetic coupling between Mn ions. In this paper we propose a strategy to realize simultaneously the spin and valley degeneracy splitting by the doping-induced Zeeman effect in monolayer MnPSe3. Using first-principles calculations we demonstrate that in Zn-doped monolayer MnPSe3 a valley splitting of larger than 20 meV and a spin splitting of larger than 100 meV can be achieved simultaneously...

The molybdenum trisamidoamine (TAA) complex [Mo] {[3,5-(2,4,6-i-Pr3C6H2)2C6H3NCH2CH2N]Mo} carries out catalytic reduction of N2 to ammonia (NH3) by protons and electrons at room temperature. A key intermediate in the proposed [Mo] nitrogen reduction cycle is nitridomolybdenum(VI), [Mo(VI)]N. The addition of [e(-)/H(+)] to [Mo(VI)]N to generate [Mo(V)]NH might, in principle, follow one of three possible pathways: direct proton-coupled electron transfer; H(+) first and then e(-); e(-) and then H(+). In this study, the paramagnetic Mo(V) intermediate {[Mo]N}(-) and the [Mo]NH transfer product were generated by irradiating the diamagnetic [Mo]N and {[Mo]NH}(+) Mo(VI) complexes, respectively, with γ-rays at 77 K, and their electronic and geometric structures were characterized by electron paramagnetic resonance and electron nuclear double resonance spectroscopies, combined with quantum-chemical computations...

The electronic structure of f-element compounds is complex due to a combination of relativistic effects, strong electron correlation and weak crystal field environments. However, a quantitative understanding of bonding in these compounds is becoming increasingly technologically relevant. Recently, bonding interpretations based on analyses of the physically observable electronic density have gained popularity and, in this Feature Article, the utility of such density-based approaches is demonstrated. Application of Bader's Quantum Theory of Atoms in Molecules (QTAIM) is shown to elucidate many properties including bonding trends, orbital overlap and energy degeneracy-driven covalency, oxidation state identification and bond stability, demonstrating the increasingly important role that simulation and analysis play in the area of f-element bond characterisation...

Predicting ground- and excited-state properties of open-shell organic molecules by electronic structure theory can be challenging because an accurate treatment has to correctly describe both static and dynamic electron correlation. Strongly correlated systems, i.e., systems with near-degeneracy correlation effects, are particularly troublesome. Multiconfigurational wave function methods based on an active space are adequate in principle, but it is impractical to capture most of the dynamic correlation in these methods for systems characterized by many active electrons...

Universal properties of entangled many-body states are controlled by their symmetry and quantum fluctuations. By the magnetic-field tuning of the spin-orbital degeneracy in a Kondo-correlated quantum dot, we have modified quantum fluctuations to directly measure their influence on the many-body properties along the crossover from SU(4) to SU(2) symmetry of the ground state. High-sensitive current noise measurements combined with the nonequilibrium Fermi liquid theory clarify that the Kondo resonance and electron correlations are enhanced as the fluctuations, measured by the Wilson ratio, increase along the symmetry crossover...

The subject of topological materials has attracted immense attention in condensed-matter physics because they host new quantum states of matter containing Dirac, Majorana, or Weyl fermions. Although Majorana fermions can only exist on the surface of topological superconductors, Dirac and Weyl fermions can be realized in both 2D and 3D materials. The latter are semimetals with Dirac/Weyl cones either not tilted (type I) or tilted (type II). Although both Dirac and Weyl fermions have massless nature with the nontrivial Berry phase, the formation of Weyl fermions in 3D semimetals require either time-reversal or inversion symmetry breaking to lift degeneracy at Dirac points...

Intrinsic valley polarization can be obtained in VSe2 monolayers with broken inversion symmetry and time reversal symmetry. First-principles investigations reveal that the magnitude of the valley splitting in magnetic VSe2 induced by spin-orbit coupling reaches as high as 78.2 meV and can be linearly tuned by biaxial strain. Besides conventional polarized light, hole doping or illumination with light of proper frequency can offer effective routes to realize valley polarization. Moreover, spin-orbit coupling in monolayer VSe2 breaks not only the valley degeneracy but also the three-fold rotational symmetry in band structure...

In this paper, we construct a special kind of breather solution of the nonlinear Schrödinger (NLS) equation, the so-called breather-positon (b-positon for short), which can be obtained by taking the limit λ_{j}→λ_{1} of the Lax pair eigenvalues in the order-n periodic solution, which is generated by the n-fold Darboux transformation from a special "seed" solution-plane wave. Further, an order-n b-positon gives an order-n rogue wave under a limit λ_{1}→λ_{0}. Here, λ_{0} is a special eigenvalue in a breather of the NLS equation such that its period goes to infinity...

We study how the non-Fermi-liquid nature of the overscreened multi-channel Kondo impurity model affects the response to a BCS pairing term that, in the absence of the impurity, opens a gap Δ. We find that the low-energy spectrum in the limit Δ → 0 actually does not correspond to the spectrum strictly at Δ = 0. In particular, in the two-channel Kondo model the Δ → 0 ground state is an orbitally degenerate spin-singlet, while it is an orbital singlet with a residual spin degeneracy at Δ = 0. In addition, there are fractionalized spin-1/2 sub-gap excitations whose energy in units of Δ tends towards a finite and universal value when Δ → 0; as if the universality of the anomalous power-law exponents that characterise the overscreened Kondo effect turned into universal energy ratios when the scale invariance is broken by Δ ≠ 0...

The magnetic and nematic properties of the iron chalcogenides have recently been the subject of intense interest. Motivated by the proposed antiferroquadrupolar and Ising-nematic orders for the bulk FeSe, we study the phase diagram of an S=1 generalized bilinear-biquadratic model with multineighbor interactions. We find a large parameter regime for a (π, 0) antiferroquadrupolar phase, showing how quantum fluctuations stabilize it by lifting an infinite degeneracy of certain semiclassical states. Evidence for this C_{4}-symmetry-breaking quadrupolar phase is also provided by an unbiased density matrix renormalization group analysis...

The existence of closed loops of degeneracies in crystals has been intimately connected with associated crystal symmetries, raising the following question: What is the minimum symmetry required for topological character, and can one find an example? Triclinic CaAs_{3}, in the space group P1[over ¯] with only a center of inversion, has been found to display, without need for tuning, a nodal loop of accidental degeneracies with topological character, centered on one face of the Brillouin zone that is otherwise fully gapped...

The purpose of this study was to develop a quantitative histopathological scoring scheme to evaluate disc degeneration and regeneration using an ovine annular lesion model of experimental disc degeneration. Toluidine blue and Haematoxylin and Eosin (H&E) staining were used to evaluate cellular morphology: (i) disc structure/lesion morphology; (ii) proteoglycan depletion; (iii) cellular morphology; (iv) blood vessel in-growth; (v) cell influx into lesion; and (vi) cystic degeneration/chondroid metaplasia...