Twofold Degenerate Research Articles

Excited-state singlet-triplet inversion in hexagonal aromatic and heteroaromatic compounds.

The inversion of the energies of the lowest singlet (S1) and lowest triplet (T1) excited states in violation of Hund's multiplicity rule is a rare phenomenon in stable organic molecules. S1-T1 inversion has significant consequences for the photophysics and photochemistry of organic chromophores. In this work, wave-function based ab initio computational methods were employed to explore the possibility of S1-T1 inversion in hexagonal polycyclic aromatic and heteroaromatic compounds. In these molecules, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are two-fold degenerate. The HOMO-LUMO transition gives rise to three singlet and three triplet excited states. While the singlet-triplet energy gap ΔST, defined as the energy difference between the S1 state and the T1 state, is clearly positive for benzene, it is predicted to be close to zero for borazine, the boron nitride analogue of benzene. Although ΔST decreases with increasing size of hexagonal polycyclic aromatics, it remains positive up to circumcoronene (19 rings). However, symmetry-preserving substitution of C-C pairs by B-N groups in the interior, keeping the conjugation of the outer rim intact, results in compounds with robustly negative ΔST. These findings establish the existence of a new family of boron carbon nitrides with inverted singlet-triplet gaps.

Symmetry-enforced planar nodal chain phonons in non-symmorphic materials

Nodal chains in which two nodal rings connect at one point were recently discovered in non-symmorphic electronic systems and then generalized to symmorphic phononic systems. In this work, we identify a new class of planar nodal chains in non-symmorphic phononic systems, where the connecting rings lie in the same plane. The constituting nodal rings are protected by mirror symmetry, and their intersection is guaranteed by the combination of time-reversal and non-symmorphic twofold screw symmetry. The connecting points are fourfold degenerate while those in previous works are twofold degenerate. We found 8 out of 230 space groups that can host the proposed planar nodal chain phonons. Taking wurtzite GaN (space group No. 186) as an example, the planar nodal chain is confirmed by first-principles calculations. The planar nodal chains result in two distinct classes of drumhead surface states on the [10(–1)0] and the [0001] surface Brillouin zones. Our finding reveals a class of planar nodal chains in non-symmorphic phononic systems, expanding the catalog of topological nodal chains and enriching the family of topological surface states.

Two-dimensional semimetal states in transition metal trichlorides: A first-principles study

The two-dimensional (2D) transition metal trihalide (TMX3, X = Cl, Br, I) family has attracted considerable attention in recent years due to the realization of CrCl3, CrBr3, and CrI3 monolayers. Up to now, the main focus of the theoretically predicted TMX3 monolayers has been on the Chern insulator states, which can realize the quantum anomalous Hall effect. Here, using first-principles calculations, we theoretically demonstrate that the stable OsCl3 monolayer has a ferromagnetic ground state and a spin-polarized Dirac point without spin–orbit coupling (SOC), which disappears in the band structure of a Janus OsBr1.5Cl1.5 monolayer. We find that OsCl3 exhibits in-plane magnetization when SOC is included. By manipulating the magnetization direction along the C2 symmetry axis of the OsCl3 structure, a gapless half-Dirac semimetal state with SOC can be achieved, which is different from the gapped Chern insulator state. Both semimetal states of OsCl3 monolayer without and with SOC exhibit a linear half-Dirac point (twofold degenerate) with high Fermi velocities. The achievement of the 2D semimetal state with SOC is expected to be found in other TMX3 monolayers, and we confirm it in a TiCl3 monolayer. This provides a different perspective to study the band structure with SOC of the 2D TMX3 family.

On the conformational equilibria between isobutyl halide (CH3)2CH–CH2X (X=Cl, Br and I) rotational isomers: A combined ultrasonic relaxation spectroscopic and computational study

In this study, ultrasonic relaxation spectroscopy and molecular orbital calculations have been used to investigate the rotational-isomeric equilibria in isobutyl halide (CH3)2CH–CH2X (X = Cl, Br and I) liquids as a function of frequency and temperature under isobaric conditions. The sound absorption in the a/f2 representation appeared to deviate from straight line with frequency in the MHz region revealing a single Debye-type relaxation process, which is attributed to thermal relaxation of a rotational isomeric equilibrium for all isobutyl halide systems. From the temperature dependence of the relaxation parameters, the associated thermodynamic parameters and the respective volume changes were estimated for each liquid and discussed in view of the outcome of density functional theory electronic structure calculations. The activation enthalpy was found to be strongly dependent on the ionic radius of the halide. Furthermore, the lower energy state of all isobutyl halide systems is two-fold degenerate. The experimental results indicate that a shear viscosity relaxation is questionable in the frequency region covered in this work. The observed-to-classical absorption ratio α/αcl and the volume-to-shear viscosity ratio nV/ns have been evaluated and used as a measure to monitor the strength of the intermolecular bonding. The values and the strong temperature dependence of these ratios are typical of a relaxation process associated to rotational isomers equilibrium. The results have been discussed in the context of inter- and intra-molecular interactions.

Ground State, Magnetization Process and Bipartite Quantum Entanglement of a Spin-1/2 Ising-Heisenberg Model on Planar Lattices of Interconnected Trigonal Bipyramids.

The ground state, magnetization scenario and the local bipartite quantum entanglement of a mixed spin- Ising–Heisenberg model in a magnetic field on planar lattices formed by identical corner-sharing bipyramidal plaquettes is examined by combining the exact analytical concept of generalized decoration-iteration mapping transformations with Monte Carlo simulations utilizing the Metropolis algorithm. The ground-state phase diagram of the model involves six different phases, namely, the standard ferrimagnetic phase, fully saturated phase, two unique quantum ferrimagnetic phases, and two macroscopically degenerate quantum ferrimagnetic phases with two chiral degrees of freedom of the Heisenberg triangular clusters. The diversity of ground-state spin arrangement is manifested themselves in seven different magnetization scenarios with one, two or three fractional plateaus whose values are determined by the number of corner-sharing plaquettes. The low-temperature values of the concurrence demonstrate that the bipartite quantum entanglement of the Heisenberg spins in quantum ferrimagnetic phases is field independent, but twice as strong if the Heisenberg spin arrangement is unique as it is two-fold degenerate.

Exactly solvable model for anyons with non-Abelian flux

We present an exactly solvable model for synthetic anyons carrying non-Abelian flux. The model corresponds to a two-dimensional electron gas in a magnetic field with a specific spin interaction term, which allows only fully aligned spin states in the ground state; the ground state subspace is thus two-fold degenerate. This system is perturbed with identical solenoids carrying a non-Abelian gauge potential. We explore dynamics of the ground state as these solenoids are adiabatically braided and show they behave as anyons with a non-Abelian flux. Such a system represents a middle ground between the ordinary Abelian anyons and the fully non-Abelian anyons.

Low-energy subband wave-functions and effective g-factor of one-dimensional hole gas

One-dimensional (1D) hole gas confined in a cylindrical Ge nanowire has potential applications in quantum information technologies. Here, we analytically study the low-energy properties of this 1D hole gas. The subbands of the hole gas are two-fold degenerate. The low-energy subband wave-functions are obtained exactly, and the degenerate pairs are related to each other via a combination of the time-reversal and the spin-rotation transformations. In evaluating the effective g-factor of these low-energy subbands, the orbital effects of the magnetic field are shown to contribute as strongly as the Zeeman term. Also, near the center of the k z space, there is a sharp dip or a sharp peak in the effective g-factor. At the site k z = 0, the longitudinal g-factor g l is much less than the transverse g-factor g t for the lowest subband, while away from the site k z = 0, g l can be comparable to g t.

Non-Hermitian Majorana modes protect degenerate steady states

We introduce non-Hermitian generalizations of Majorana zero modes (MZMs) which appear in the topological phase of a weakly dissipative Kitaev chain coupled to a Markovian bath. Notably, the presence of MZMs ensures that the steady state in the absence of decoherence events is two-fold degenerate. Within a stochastic wavefunction approach, the effective Hamiltonian governing the coherent, non-unitary dynamics retains BDI classification of the closed limit, but belongs to one of four non-Hermitian "flavors" of the ten-fold way. We argue for the stability of MZMs due to a generalization of particle-hole symmetry, and uncover the resulting topological phase diagram. Qualitative features of our study generalize to two-dimensional chiral superconductors. The dissipative superconducting chain can be mapped to an Ising model in a complex transverse field, and we discuss potential signatures of the degeneracy.

Chiral and helical p -wave superconductivity in doped bilayer BiH

We investigate the superconductivity (SC) driven by correlation effects in electron-doped bilayer BiH near a type-II van Hove singularity (vHS). By functional renormalization group, we find triplet $p$-wave pairing prevails in the interaction parameter space, except for spin density wave (SDW) closer to the vHS or when the interaction is too strong. Because of the large atomic spin-orbital coupling (SOC), the $p$-wave pairing occurs between equal-spin electrons, and is chiral and two-fold degenerate. The chiral state supports in-gap edge states, even though the low energy bands in the SC state are topologically trivial. The absence of mirror symmetry allows Rashba SOC that couples unequal spins, but we find its effect is of very high order, and can only drive the chiral $p$-wave into helical $p$-wave deep in the SC state. Interestingly, there is a six-fold degeneracy in the helical states, reflected by the relative phase angle $\theta=n\pi/3$ (for integer $n$) between the spin components of the helical pairing function. The phase angle is shown to be stable in the vortex state.

Hybrid two-qubit gate using a circuit QED system with a triple-leg stripline resonator

We theoretically propose a circuit QED system implemented with triple-leg stripline resonator (TSR). Unlikely from linear stripline resonator, the fundamental intra-cavity microwave modes of the TSR are two-fold degenerate. When a superconducting qubit is placed near one of the TSR legs, one fundamental mode is directly coupled to the qubit, while the other one remains uncoupled. Our system closely resembles an optical cavity QED system, where an atom in a cavity couples only to the incident photon with a specific polarization by placing a polarization beamsplitter in front of the optical cavity. Using our circuit QED system, we have theoretically studied a two-qubit quantum gate operation in a hybrid qubit composed of flying microwave qubit and superconducting qubit. We have demonstrated that for the hybrid qubit, the quantum controlled phase flip (CPF) gate can be reliably implemented for the experimentally available set of parameters.

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.

Evidence for spin-triplet odd-parity superconductivity close to type-II van Hove singularities

Searching for unconventional Cooper pairing states has been at the heart of superconductivity research since the discovery of BCS superconductors. In particular, spin-triplet odd-parity pairing states were recently revisited due to the possibility of tuning towards topological superconductors. In this context, it is interesting to note a recent proposal that such a spin-triplet pairing instability occurs when the band filling is near van Hove singularities (vHS) associated with momenta away from time-reversal invariant momenta named type-II vHS. However, this result was obtained within a weak coupling renormalization group with Fermi surface patch approximation. To explore superconducting instabilities beyond this weak coupling Fermi surface patch approximation, we perform systematic study on Hubbard model in a two-dimensional square lattice using three different methods: random phase approximation, large-scale dynamical mean field theory simulations with continuous time quantum Monte Carlo (CTQMC) impurity solver, and large-scale dynamical cluster simulations with CTQMC cluster solver. We find, in a wide doping range centered around the type-II van Hove filling, a two-fold degenerate, spin-triplet, odd-parity $p$-wave pairing state emerges due to repulsive interaction, when the Fermi surface is not sufficiently nested. Possible relevance of our findings to the recently discovered superconductors LaO$_{1-x}$F$_{x}$BiS$_{2}$, Ir$_{1-x}$Pt$_{x}$Te$_{2}$ and proposed doped BC$_{3}$ are also discussed.

Odd-parity triplet superconducting phase in multiorbital materials with a strong spin-orbit coupling: application to doped Sr₂IrO₄.

We explore possible superconducting states in t(2g) multiorbital correlated electron systems with strong spin-orbit coupling (SOC). In order to study such systems in a controlled manner, we employ large-scale dynamical mean-field theory (DMFT) simulations with the hybridization expansion continuous-time quantum Monte Carlo (CTQMC) impurity solver. To determine the pairing symmetry, we go beyond the local DMFT formalism using parquet equations to introduce the momentum dependence in the two-particle vertex and correlation functions. In the strong SOC limit, a singlet, d-wave pairing state in the electron-doped side of the phase diagram is observed at weak Hund's coupling, which is triggered by antiferromagnetic fluctuations. When the Hund's coupling is comparable to SOC, a twofold degenerate, triplet p-wave pairing state with relatively high transition temperature emerges in the hole-doped side of the phase diagram, which is associated with enhanced charge fluctuations. Experimental implications to doped Sr2IrO4 are discussed.

Symmetries and boundary theories for chiral projected entangled pair states

We investigate the topological character of lattice chiral Gaussian fermionic states in two dimensions possessing the simplest descriptions in terms of projected entangled pair states (PEPS). They are ground states of two different kinds of Hamiltonians. The first one, ${\mathcal{H}}_{\mathrm{ff}}$, is local, frustration free, and gapless. It can be interpreted as describing a quantum phase transition between different topological phases. The second one, ${\mathcal{H}}_{\mathrm{fb}}$, is gapped, and has hopping terms scaling as $1/{r}^{3}$ with the distance $r$. The gap is robust against local perturbations, which allows us to define a Chern number for the PEPS. As for (nonchiral) topological PEPS, the nontrivial topological properties can be traced down to the existence of a symmetry in the virtual modes that are used to build the state. Based on that symmetry, we construct stringlike operators acting on the virtual modes that can be continuously deformed without changing the state. On the torus, the symmetry implies that the ground state space of the local parent Hamiltonian is twofold degenerate. By adding a string wrapping around the torus, one can change one of the ground states into the other. We use the special properties of PEPS to build the boundary theory and show how the symmetry results in the appearance of chiral modes, and a universal correction to the area law for the zero R\'enyi entropy.

Nonperturbative effects of a topological theta term on principal chiral nonlinear sigma models in 2 + 1 dimensions.

We study the effects of a topological Theta term on 2+1-dimensional principal chiral models, which are nonlinear sigma models defined on Lie group manifolds. We find that when Θ=π, the nature of the disordered phase of the principal chiral model is strongly affected by the topological term: it is either a gapless conformal field theory, or it is gapped and twofold degenerate. The result of our Letter can be used to analyze the boundary states of three-dimensional symmetry protected topological phases.

Gauge freedom for degenerate Bloch states

In nonmagnetic crystals with inversion symmetry the electronic bands are twofold degenerate. As a consequence, any orthonormalized linear combination of the two corresponding eigenfunctions can represent the electron wave function. A priori it is not obvious which superposition, gauge, should be chosen to calculate a quantity which is not gauge invariant within a certain approximation. Here we consider gauge options appropriate under particular physical conditions.

Full correspondence between asymmetric filling of slits and first-order phase transition lines

Adsorption on single planar walls and filling of slits with identical planar walls are investigated in the frame of the density functional theory. In this sort of slits the external potential is symmetric with respect to its central plane. Calculations were carried out by applying both the canonical and grand canonical ensembles (CE and GCE, respectively). The behavior is analyzed by varying the strength of the adsorbate-substrate attraction, the temperature T, and the coverage Γℓ. Results obtained for physisorption of Xe on alkaline surfaces are reported in the present work. Prewetting (PW) lines and wetting temperatures, Tw, are determined from the analysis of adsorption on single walls. The filling of slits is analyzed for temperatures T > Tw. It is found that whenever for a given Xe-substrate combination the adsorption on a single wall exhibits a first-order wetting transition then asymmetric profiles that break the left-right symmetry of the external potential appear in the filling of an equivalent slit. These spontaneously symmetry breaking (SSB) solutions occur in a restricted range of Γℓ with a T-dependent width. In the case of closed slits analyzed in the CE scheme, the obtained asymmetric profiles exhibit lower Helmholtz free energies than the symmetric species and, therefore, could be stabilized in this geometry. For open slits, the GCE scheme yields all the symmetric and SSB states in the corresponding convex regimes of the free energy. It is shown that both the CE and the GCE frames yield three coexistent states, two symmetric and one asymmetric twofold degenerate. Both a PW line and the related SSB effect terminate at the same temperature. For rather strongly attractive surfaces reentrant SSB states are found at a fixed value of T.

Magnetic ground state and spin waves in A(A = K, Rb or Cs)Fe 1.5Se 2

We present theoretical results on the ground state phase diagram, spin waves and dynamic structure factor on the J 1 – J 2 model. In the reasonable physical parameter region corresponding to AFe 1.5Se 2, the A-collinear antiferromagnetic phase is stable. The spin wave spectra have two acoustic branches and four optical branches for this phase on the rhombus-ordered vacancy lattice, and each of them is twofold degenerate. However, they have one nondegenerate acoustic branch and two nondegenerate optical branches on the square-ordered vacancy lattice. To offer the theoretical guidance for the further experiments, we also discuss the magnetic excitation spectra and the inelastic neutron scattering pattern based on linear spin wave theory.

Spontaneous parity violation in a quantum spin chain

We report on a spontaneous breakdown of parity in the ground state of a spin Hamiltonian involving nearest-neighbor interactions. This occurs for a one-dimensional model where spins transform under the gauge field representation of QCD, the eight-dimensional adjoint representation of SU(3). The ground state spontaneously violates parity and is two-fold degenerate. In addition, the model possesses a non-vanishing topological string order parameter which we explicate analytically.

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.