Symmetry Arguments Research Articles

Guanine and 7,8-Dihydroxanthopterin Reflecting Crystals in the Zander Fish Eye: Crystal Locations, Compositions, and Structures.

The eyes of many fish contain a reflecting layer of organic crystals partially surrounding the photoreceptors of the retina, which are commonly believed to be composed of guanine. Here we study an unusual fish eye from Stizostedion lucioperca that contains two layers of organic crystals. The crystals in the outer layer are thin plates, whereas the crystals in the inner tapetum layer are block-shaped. We show that the outer layer indeed contains guanine crystals. Analyses of solutions of crystals from the inner layer indicated that the block-shaped crystals are composed of xanthopterin. A model of the structure of the block-shaped crystals was produced using symmetry arguments based on electron diffraction data followed by dispersion-augmented DFT calculations. The resulting crystal structure of xanthopterin included, however, a problematic repulsive interaction between C═O and N of two adjacent molecules. Knowing that dissolved 7,8-dihydroxanthopterin can oxidize to xanthopterin, we replaced xanthopterin with 7,8-dihydroxanthopterin in the model. An excellent fit was obtained with the powder X-ray diffraction pattern of the biogenic crystals. We then analyzed the biogenic block-shaped crystals in their solid state, using MALDI-TOF and Raman spectroscopy. All three methods unequivocally prove that the block-shaped crystals in the eye of S. lucioperca are crystals of 7,8-dihydroxanthopterin. On the basis of the eye anatomy, we deduce that the guanine crystals form a reflective layer producing the silvery color present on part of the eye surface, whereas the block-shaped crystals backscatter light into the retina in order to increase the light sensitivity of the eye.

Origin of the electromagnetic anisotropy in monolayer black phosphorus

Contrary to empirical observations, lowest-order $k\cdot\hat{p}$ theory predicts that monolayer black phosphorus ("phosphorene") is completely immune to zigzag-polarized optical excitation at the bandgap energy. Using symmetry arguments, we derive a $2\times2$ Hamiltonian under the $k\cdot\hat{p}$ formalism including higher-order corrections, which is used to show that the experimentally-measured band-gap transition with zigzag polarization is dominated by the third order $k\cdot\hat{p}$ perturbation in the interband optical matrix element, whereas the effects of spin-orbit interaction are negligible in this material, consistent with a trivial orbital diamagnetic contribution to the $\textit{g}$-factor.

Thermal Hall Effect Induced by Magnon-Phonon Interactions.

We propose a new mechanism for the thermal Hall effect in exchange spin-wave systems, which is induced by the magnon-phonon interaction. Using symmetry arguments, we first show that this effect is quite general, and exists whenever the mirror symmetry in the direction of the magnetization is broken. We then demonstrate our result in a collinear ferromagnet on a square lattice, with perpendicular easy-axis anisotropy and Dzyaloshinskii-Moriya interaction from mirror symmetry breaking. We show that the thermal Hall conductivity is controlled by the resonant contribution from the anticrossing points between the magnon and phonon branches, and estimate its size to be comparable to that of the magnon-mediated thermal Hall effect.

Electronic hydrodynamics in graphene

In this paper I report a pedagogical derivation of the unconventional electronic hydrodynamics in graphene on the basis of the kinetic theory. While formally valid in the weak coupling limit, this approach allows one to derive the unconventional hydrodynamics in the system which is neither Galilean- nor Lorentz-invariant, such that hydrodynamic equations cannot be inferred from symmetry arguments. I generalize earlier work to include external magnetic fields and give explicit expressions for dissipative coefficients, the shear viscosity and electrical conductivity. I also compare the resulting theory with relativistic hydrodynamics.

Protected cat states from kinetic driving of a boson gas

We investigate the behavior of a one-dimensional Bose-Hubbard gas in both a ring and a hard-wall box, whose kinetic energy is made to oscillate with zero time-average, which suppresses first-order particle hopping. For intermediate and large driving amplitudes the system in the ring has similarities to the Richardson model, but with a peculiar type of pairing and an attractive interaction in momentum space. This analogy permits an understanding of some key features of the interacting boson problem. The ground state is a macroscopic quantum superposition, or cat state, of two many-body states collectively occupying opposite momentum eigenstates. Interactions give rise to a reduction (or modified depletion) cloud that is common to both macroscopically distinct states. Symmetry arguments permit a precise identification of the two orthonormal macroscopic many-body branches which combine to yield the ground state. In the ring, the system is sensitive to variations of the effective flux but in such a way that the macroscopic superposition is preserved. We discuss other physical aspects that contribute to protect the cat-like nature of the ground state.

Tetraneutron condensation in neutron rich matter

.In this work we investigate the possible condensation of tetraneutron resonant states in the lower density neutron rich gas regions inside Neutron Stars (NSs). Using a relativistic density functional approach we characterize the system containing different hadronic species including, besides tetraneutrons, nucleons and a set of light clusters (3He, alpha particles, deuterium and tritium). sigma, omega and rho mesonic fields provide the interaction in the nuclear system. We study how the tetraneutron presence could significantly impact the nucleon pairing fractions and the distribution of baryonic charge among species. For this we assume that they can be thermodynamically produced in an equilibrated medium and scan a range of coupling strengths to the mesonic fields from prescriptions based on isospin symmetry arguments. We find that tetraneutrons may appear over a range of densities belonging to the outer NS crust carrying a sizable amount of baryonic charge thus depleting the nucleon pairing fractions.

Construction of breather solutions for nonlinear Klein-Gordon equations on periodic metric graphs

The purpose of this paper is to construct small-amplitude breather solutions for a nonlinear Klein-Gordon equation posed on a periodic metric graph via spatial dynamics and center manifold reduction. The major difficulty occurs from the irregularity of the solutions. The persistence of the approximately constructed pulse solutions under higher order perturbations is obtained by symmetry and reversibility arguments.

Non-Markovian barrier crossing with two-time-scale memory is dominated by the faster memory component.

We investigate non-Markovian barrier-crossing kinetics of a massive particle in one dimension in the presence of a memory function that is the sum of two exponentials with different memory times, [Formula: see text] and [Formula: see text] . Our Langevin simulations for the special case where both exponentials contribute equally to the total friction show that the barrier-crossing time becomes independent of the longer memory time if at least one of the two memory times is larger than the intrinsic diffusion time. When we associate memory effects with coupled degrees of freedom that are orthogonal to a one-dimensional reaction coordinate, this counterintuitive result shows that the faster orthogonal degrees of freedom dominate barrier-crossing kinetics in the non-Markovian limit and that the slower orthogonal degrees become negligible, quite contrary to the standard time-scale separation assumption and with important consequences for the proper setup of coarse-graining procedures in the non-Markovian case. By asymptotic matching and symmetry arguments, we construct a crossover formula for the barrier crossing time that is valid for general multi-exponential memory kernels. This formula can be used to estimate barrier-crossing times for general memory functions for high friction, i.e. in the overdamped regime, as well as for low friction, i.e. in the inertial regime. Typical examples where our results are important include protein folding in the high-friction limit and chemical reactions such as proton-transfer reactions in the low-friction limit.

Koopman operator and its approximations for systems with symmetries.

Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, often described by complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and to simplify their analysis. The Koopman operator is an infinite dimensional linear operator that fully captures a system's nonlinear dynamics through the linear evolution of functions of the state space. Importantly, in contrast with local linearization, it preserves a system's global nonlinear features. We demonstrate how the presence of symmetries affects the Koopman operator structure and its spectral properties. In fact, we show that symmetry considerations can also simplify finding the Koopman operator approximations using the extended and kernel dynamic mode decomposition methods (EDMD and kernel DMD). Specifically, representation theory allows us to demonstrate that an isotypic component basis induces a block diagonal structure in operator approximations, revealing hidden organization. Practically, if the symmetries are known, the EDMD and kernel DMD methods can be modified to give more efficient computation of the Koopman operator approximation and its eigenvalues, eigenfunctions, and eigenmodes. Rounding out the development, we discuss the effect of measurement noise.

Light intensity as mechanical potential: a symmetry-based approach

ABSTRACTLight-induced motion is of increasing importance in materials development. In many situations, modelling the detailed dynamics of light-induced phenomena is not practical, yet a description of the behaviour is needed. We attempt to show here that in some such situations, symmetry arguments can prove useful. We outline a simple scheme where symmetry arguments can be useful in modelling the dynamics, and show, in three examples, that in some instances, light intensity may be regarded as a mechanical potential. Such an approach may help in understanding photoactuations in situations where more detailed analyses are impractical.

Where are the next Higgs bosons?

Simple symmetry arguments applied to the third generation lead to a prediction: there exist new sequential Higgs doublets with masses of order $\lesssim 5 $ TeV, with approximately universal Higgs-Yukawa coupling constants, $g\sim 1$. This is calibrated by the known Higgs boson mass, the top quark Higgs-Yukawa coupling, and the $b$-quark mass. A new massive weak-isodoublet, $H_b$, coupled to the $b$-quark with $g\sim 1$ is predicted, and may be accessible to the LHC at $13$ TeV, and definitively at the energy upgraded LHC of $26$ TeV. The extension to leptons generates a new $H_\tau$ and a possible $H_{\nu_\tau}$ doublet. The accessibility of the latter depends upon whether the mass of the $\tau$-neutrino is Dirac or Majorana.

Superconducting gap anisotropy and topological singularities due to lattice translational symmetry and their thermodynamic signatures

Symmetry arguments based on the point group of a system and thermodynamic measurements are often combined to identify the order parameter in unconventional superconductors. However, lattice translations, which can induce additional momenta with vanishing order parameter in the Brillouin zone, are neglected, especially in gap functions otherwise expected to be constant, such as in chiral superconductors. After a general analysis of the symmetry conditions for vanishing gap functions, we study the case of chiral $p$- and chiral $f$-wave pairing on a square lattice, a situation relevant for Sr$_2$RuO$_4$. Specifically, we calculate the impurity-induced density of states, specific heat, superfluid density and thermal conductivity employing a self-consistent T-matrix calculation and compare our results to the case of a nodal ($d$-wave) order parameter. While there is a clear distinction between a fully gapped chiral state and a nodal state, the strongly anisotropic case is almost indistinguishable from the nodal case. Our findings illustrate the difficulty of interpreting thermodynamic measurements. In particular, we find that the available measurements are consistent with a chiral ($f$-wave) order parameter. Our results help to reconcile the thermodynamic measurements with the overall picture of chiral spin-triplet superconductivity in Sr$_2$RuO$_4$.

Tuning spin filtering by anchoring groups in benzene derivative molecular junctions

One of the important issues of molecular spintronics is the control and manipulation of charge transport and, in particular, its spin polarization through single-molecule junctions. Using ab initio calculations, we explore spin-polarized electron transport across single benzene derivatives attached with six different anchoring groups (S, CH3S, COOH, CNH2NH, NC and NO2) to Ni(1 1 1) electrodes. We find that molecule-electrode coupling, conductance and spin polarization (SP) of electric current can be modified significantly by anchoring groups. In particular, a high spin polarization (SP > 80%) and a giant magnetoresistance (MR > 140%) can be achieved for NO2 terminations and, more interestingly, SP can be further enhanced (up to 90%) by a small voltage. The S and CH3S systems, on the contrary, exhibit rather low SP while intermediate values are found for COOH and CNH2NH groups. The results are analyzed in detail and explained by orbital symmetry arguments, hybridization and spatial localization of frontier molecular orbitals. We hope that our comparative and systematic studies will provide valuable quantitative information for future experimental measurements on that kind of systems and will be useful for designing high-performance spintronics devices.

Sign change of polarization rotation under time or space inversion in magnetoelectric YbAl3(BO3)4

Materials with optical activity can rotate the polarization plane of transmitted light. The most typical example is the natural optical activity, which has the symmetry property of changing sign after space inversion but being invariant to time inversion. Faraday rotation exhibits the opposite: it is invariant to space inversion but changes sign after time reversal. Here, we demonstrate that in a magnetoelectric material, another type of polarization rotation is possible. This effect is investigated in magnetoelectric YbAl3(BO3)4 under the viewpoint of time and space inversion symmetry arguments. We observe the sign change of the rotation sense under either time or space reversal. This investigation proves that the polarization rotation in YbAl3(BO3)4 must be classified as gyrotropic birefringence, which has been discussed within the idea of time-reversal breaking in underdoped cuprates. The diagonal terms in the magnetoelectric susceptibility are responsible for the observed signal of gyrotropic birefringence. Further analysis of the experimental spectra reveals a substantial contribution of the natural optical activity to the polarization rotation. We also demonstrate that the observed activity originates from the magnetoelectric susceptibility.

Boundary conditions for spin and charge diffusion in the presence of interfacial spin-orbit coupling

Breaking of the inversion symmetry at the interface between different materials may dramatically enhance spin-orbit interaction in the vicinity of the interface. We incorporate the effects of this interfacial spin-orbit coupling (ISOC) into the standard drift-diffusion theory by deriving generalized boundary conditions for diffusion equations. Our theoretical scheme is based on symmetry arguments, providing a natural classification and parametrization of all spin-charge and spin-spin conversion effects that occur due to ISOC at macroscopically isotropic interfaces between nonmagnetic materials. We illustrate our approach with specific examples of spin-charge conversion in hybrid structures. In particular, for a lateral metal-insulator structure we predict an "ISOC-gating" effect which can be used to detect spin currents in metallic films with weak bulk SOC.

Current Control of Magnetism in Two-Dimensional Fe3GeTe2

The recent discovery of magnetism in two-dimensional van der Waals systems opens the door to discovering exciting physics. We investigate how a current can control the ferromagnetic properties of such materials. Using symmetry arguments, we identify a recently realized system in which the current-induced spin torque is particularly simple and powerful. In Fe_{3}GeTe_{2}, a single parameter determines the strength of the spin-orbit torque for a uniform magnetization. The spin-orbit torque acts as an effective out-of-equilibrium free energy. The contribution of the spin-orbit torque to the effective free energy introduces new in-plane magnetic anisotropies to the system. Therefore, we can tune the system from an easy-axis ferromagnet via an easy-plane ferromagnet to another easy-axis ferromagnet with increasing current density. This finding enables unprecedented control and provides the possibility to study the Berezinskiǐ-Kosterlitz-Thouless phase transition in the 2D XY model and its associated critical exponents.

16O within the Semimicroscopic Algebraic Cluster Model and the importance of the Pauli Exclusion Principle

The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 16O, assumed to consist of a system of four alpha-clusters. For the 4-alpha cluster system a microscopic model space is constructed, which observes the Pauli-Exclusion-Principle (PEP) and is symmetric under permutation of the 4-alpha-particles. A phenomenological Hamiltonian is used, justifying the name Semi in the SACM. The spectrum and transition values are determined. One of the main objectives is to test the importance of the Pauli Exclusion Principle (PEP), comparing the results with the Algebraic Cluster Model (ACM), which does not include the PEP, and claims that the 16O shows evidence of a tetrahedral structure, which can be explained easily by symmetry arguments. We show that PEP is very important and cannot be neglected, otherwise it leads to a wrong interpretation of the band structure and to too many states at low energy.

Bacterial range expansions on a growing front: Roughness, fixation, and directed percolation.

Directed percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has appeared as a generic model for the evolutionary and ecological dynamics of competing bacterial populations. Range expansion-the stochastic reproduction of bacteria competing for space to be occupied by their progeny-leads to a fluctuating and rough growth front, which is known from experiment and simulation to affect the underlying critical behavior of the DP transition. In this work, we employ symmetry arguments to construct a pair of nonlinear stochastic partial differential equations describing the coevolution of surface roughness with the composition field of DP. Macroscopic manifestations (phenomenology) of these equations on growth patterns and genealogical tracks of range expansion are discussed; followed by a renormalization group analysis of possible scaling behaviors at the DP transition.

Chiral selection rules for multi-photon processes in two-dimensional honeycomb materials.

We examine the chirality-dependent optical selection rules in two-dimensional monolayer materials with honeycomb lattices, and, based on symmetry argument, we generalize these rules to multi-photon transitions of arbitrary orders. We also present the phase relations between incident and outgoing photons in such processes. The results agree nicely with our experimental observations of second- and third-harmonic generation. In particular, we demonstrate that the phase relation of chiral second-harmonic generation can serve as a handy tool for imaging domains and domain boundaries of these monolayers. Our results can benefit future studies on chirality-related optical phenomena and opto-electronic applications of such materials.

In-Medium Strangeness Production and Hyperon-Potentials

A hot topic of current research concerns the Equation of State (EoS) of nucleons and, in particular, of hyperons in dense nucleonic media. The study of the EoS at nucleon densities far beyond saturation has been initiated several decades ago, however, the behavior of the EoS for strangeness particles is still an open issue. The strangeness part of the EoS is very important not only for the physics of exotic (hyper)nuclei, but also crucial for nuclear astrophysics, e.g., neutron star physics.Here we present our recent investigations related to the theoretical treatment of in-medium hyperon-interactions as well as first preliminary experimental results from pion-induced reactions. The theoretical study is based on the well-established Non-Linear Derivative (NLD) model, which is extended to the strangeness sector via SU(6) symmetry arguments. It turns out that the NLD-predictions are consistent with microscopic models based on the chiral-EFT theory. On the other hand, recent experimental HADES-data on hyperon and kaon production from pion-induced reactions indicate sensitivities on the underlying in-medium hyperon potentials. We thus conclude that, the recent experimental data from pion-induced reactions will definitely set stringent constraints on the still less understood hyperon-potentials in nucleonic matter.