Degree Of Chirality Research Articles

Chirality control of the spin structure in monoaxial helimagnets by charge current

Chirality control of the spin structure in monoaxial helimagnets by using charge current is theoretically investigated. The classical J1−J2 Heisenberg model has two degenerate helical states that are characterized by the chirality. In a recent experiment, it has been shown that the chirality of the spin structure can be controlled by applying a charge current during the field-decreasing process [Jiang et al., Nat. Commun. 11, 1601 (2020)]. We reproduced this experiment by numerical calculations based on the Landau–Lifshitz–Gilbert equation with the spin-transfer torque. We show that the damping torque and spin-transfer torque are responsible for the controllability. In addition, we theoretically propose more convenient forms of chirality control: instantaneous switching of chirality and zero-field control by using a ferromagnet junction. Such improved controllability may pave the way to spintronics based on the chirality degree of freedom.

Interlocked attosecond pulse trains in slightly bi-elliptical high harmonic generation

The ellipticity of high harmonics driven by bi-chromatic (e.g. ) co-propagating fields can be fully tuned by varying the polarization of the pump components. In order to start revealing the underlying mechanism of this control, we explore a relatively simple regime of this scheme that still gives rise to full control over the harmonics ellipticities. In this regime, the pumps are only slightly elliptical and the high harmonic radiation consists of two (different) interlocked attosecond pulse trains (APTs). We formulate a semi-analytic model that maps the high harmonic ellipticity to properties of the APTs harmonic decompositions. Utilizing this model, we reconstruct these APTs variables from measurements of the high harmonics ellipticities. This ellipticity-resolved spectroscopy of interlocked APTs may be useful for ultrafast probing of chiral degrees of freedom.

Degree of chirality of electromagnetic fields and maximally chiral light

Recently, synthetic chiral light was introduced and theoretically shown to be highly effective for chiral light-matter interactions [D. Ayuso, O. Neufeld, A. F. Ordonez, P. Decleva, G. Lerner, O. Cohen, M. Ivanov, and O. Smirnova, Nat. Photonics 13, 866 (2019)]. This electromagnetic (EM) field possesses a new intrinsic property denoted ``local chirality.'' Contrary to standard circularly polarized light, it is chiral within the electric dipole approximation, even if the field is spatially uniform. The degree of chirality (DOC) of such light was defined, but has not yet been explored. Here we provide a comprehensive study of the DOC of locally chiral EM fields. We present numerical schemes that are capable of calculating this quantity for arbitrary fields at a low computational cost (we provide open access codes). We utilize these approaches to explore the functional dependence of the degree of chirality of bichromatic laser beams on their various degrees of freedom such as beam intensities, polarization states, and so on. We perform an extensive numerical search for the bichromatic EM field that possesses the maximal possible value of local chirality, and find a field that exhibits a 69.6% degree of chirality (out of the theoretical limit of 200%). This geometry sets the current record for a maximally chiral EM field. The numerical approach and results presented here will be useful for future investigations of chiral light-matter interactions.

Templated Growth of a Homochiral Thin Film Oxide.

Chiral surfaces are of growing interest for enantioselective adsorption and reactions. While metal surfaces can be prepared with a wide range of chiral surface orientations, chiral oxide surface preparation is more challenging. We demonstrate the chirality of a metal surface can be used to direct the homochiral growth of a thin film chiral oxide. Specifically, we study the chiral "29" copper oxide, formed by oxidizing a Cu(111) single crystal at 650 K. Surface structure spread single crystals, which expose a continuous distribution of surface orientations as a function of position on the crystal, enable us to systematically investigate the mechanism of chirality transfer between the metal and the surface oxide with high-resolution scanning tunneling microscopy. We discover that the local underlying metal facet directs the orientation and chirality of the oxide overlayer. Importantly, single homochiral domains of the "29" oxide were found in areas where the Cu step edges that templated growth were ≤20 nm apart. We use this information to select a Cu(239 241 246) oriented single crystal and demonstrate that a "29" oxide surface can be grown in homochiral domains by templating from the subtle chirality of the underlying metal crystal. This work demonstrates how a small degree of chirality induced by slight misorientation of a metal surface (∼1 sites/20 nm2) can be amplified by oxidation to yield a homochiral oxide with a regular array of chiral oxide pores (∼75 sites/20 nm2). This offers a general approach for making chiral oxide surfaces via oxidation of an appropriately "miscut" metal surface.

Learning how planarization can affect dichroic patterns in polyfluorenes.

The circular dichroism spectra of a single chain of polyfluorene was predicted for a p-twisted helix conformation and local planarized polymer sections in the presence and in the absence of thermal vibrations. Under thermal vibrations at 300 K, the planarized section of polyfluorene affords a red-shifted positive dichroic band between 446 and 456 nm, preserving a degree of chirality. The S1 ← S0 excitation energy decreases from 3.29 eV, for the p-twisted helix to 2.77 or 2.71 eV, for planarized sections with one or two coplanar twists, respectively. Thermal vibrations and intramolecular rotations eventually affect the circular dichroism spectrum patterns, where planarized bent conformers induce a positive band towards 450 nm.

Fullerene Stability by Geometrical Thermodynamics

AbstractThis work proves that stability of C60 is a geometrical property of the thermodynamics of the system: a significant methodological advance since a detailed treatment of the energetics may be avoidable. This approach may be fruitful, not only for fullerenes but also for general problems of molecular stability and in other applications of conformational chemistry. For the non‐chiral C60, C384, and the weakly‐chiral C28, C76 and C380 (of these, C380 and C384 are classed as “unspirallable”), Schlegel projections are used to show that these fullerenes can all be represented by pairs of spirals counter‐propagating in anti‐parallel (C2) symmetry. For C60, the high symmetry is used to construct an analytical approximation for the spherical double‐spirals, shown mathematically to be Maximum Entropy (MaxEnt) using the formalism of Quantitative Geometrical Thermodynamics (QGT). Therefore C60 is necessarily stable. This MaxEnt stability criterion is general, depending only on the geometry and not the kinematics of the system. The sense and degree of chirality for C76 and C380 is also quantified using a Shannon entropy‐based fragmentation metric.

Odd-frequency Berezinskii superconductivity in Dirac semimetals

We formulate a general framework for addressing both odd- and even-frequency superconductivity in Dirac semimetals and demonstrate that the odd-frequency or the Berezinskii pairing can naturally appear in these materials because of the chirality degree of freedom. We show that repulsive frequency-dependent interactions favor the Berezinskii pairing while an attractive electron-electron interaction allows for the BCS pairing. In the case of compensated Dirac and Weyl semimetals, both the conventional BCS and odd-frequency Berezinskii pairings require critical coupling. Since these pairings could originate from physically different mechanisms, our findings pave the way for controlling the realization of the Berezinskii superconductivity in topological semimetals. We also present the density of states with several cusp-like features that can serve as an experimentally verifiable signature of the odd-frequency gap.

Optical Helicity and Optical Chirality in Free Space and in the Presence of Matter

The inherently weak nature of chiral light–matter interactions can be enhanced by orders of magnitude utilizing artificially-engineered nanophotonic structures. These structures enable high spatial concentration of electromagnetic fields with controlled helicity and chirality. However, the effective design and optimization of nanostructures requires defining physical observables which quantify the degree of electromagnetic helicity and chirality. In this perspective, we discuss optical helicity, optical chirality, and their related conservation laws, describing situations in which each provides the most meaningful physical information in free space and in the context of chiral light–matter interactions. First, an instructive comparison is drawn to the concepts of momentum, force, and energy in classical mechanics. In free space, optical helicity closely parallels momentum, whereas optical chirality parallels force. In the presence of macroscopic matter, the optical helicity finds its optimal physical application in the case of lossless, dual-symmetric media, while, in contrast, the optical chirality provides physically observable information in the presence of lossy, dispersive media. Finally, based on numerical simulations of a gold and silicon nanosphere, we discuss how metallic and dielectric nanostructures can generate chiral electromagnetic fields upon interaction with chiral light, offering guidelines for the rational design of nanostructure-enhanced electromagnetic chirality.

Lorentz boosts of bispinor Bell-like states

We describe in this paper the effects of Lorentz boost on the quantum entanglement encoded in two-particle Dirac bispinor Bell-like states. Each particle composing the system described in this formalism has three degrees of freedom: spin, chirality, and momentum, and the joint state can be interpreted as a 6 qubit state. Given the transformation law of bispinor under boosts, we compute the change of the Meyer-Wallach global measure of quantum entanglement due to the frame transformation and study its equivalence to the results obtained for the relativistic spin 1/2 Bell-like states, constructed in the framework of the irreducible representations of the Lorentz group. We verify that the monotonic increase of the global entanglement under boosts for ultra-relativistic states is solely due to an increasing of the entanglement associated with the spins subsystems. For such ultra-relativistic states, the entanglement related to the chirality degrees of freedom is invariant, and the variation of the global entanglement of bispinor states is the same as the one calculated for relativistic spin 1/2 states. We also show that the particle-particle entanglement is invariant under boosts for any Bell-like state.

Quantum ferromagnetic transition in clean Dirac metals

The ferromagnetic quantum phase transition in clean metals with a negligible spin-orbit interaction is known to be first order due to a coupling of the magnetization to soft fermionic particle-hole excitations. A spin-orbit interaction gives these excitations a mass, suggesting the existence of a ferromagnetic quantum-critical point in metals with a strong spin-orbit interaction. We show that this expectation is not borne out in a large class of materials with a Dirac spectrum, since the chirality degree of freedom leads to new soft modes that again render the transition first order.

Physicochemical Properties and Complexity of Amino Acids beyond Our Biosphere: Analysis of the Isoleucine Group from Meteorites

Understanding the physicochemical properties of biomolecules and how these properties drive the emergence of complexity in the assembly/condensation of such systems is important for understanding a variety of reactions taking place in astrophysical environments, in particular those where polymerization processes occur on mineral surfaces or solid organic matter form in cold-chemistry processes. Here, a computational study of the structural and electronic properties of the gas and condensed phases of the isoleucine group of amino acids, found with large enantiomeric excess in Antarctic meteorites, is presented. An analysis of a statistical complexity measure related to their electronic properties, of the degree of chirality, and of the H-bond patterns is also reported. The results, based on Density Functional Theory, Many Body Perturbation Theory, and Moller–Plesset perturbation theory, show that a) the condensed amino acids keep reminiscence of structural and electronic properties of the gas phase molecules, b) the proteinogenic l-isoleucine gains in complexity and chirality upon condensation, contrary to its diastereomer, which is absent in living systems, and c) the complexity based on electronic properties can contrast with the notion of structural/geometrical complexity. The findings suggest that future scoring strategies of organic molecules should rely on both structural/geometrical molecular complexity and on the electronic properties, which in different states of matter are determined by other degrees of freedom (configurational or chiral) to a different extent, as well as on information storage capability of self-assembly configurations constrained by an atomistic chemistry perspective.

Tunable Sorting of Mesoscopic Chiral Structures by External Noise in Achiral Periodic Potentials

Efficient chirality sorting is now highly in demand to separate assembled mesoscopic chiral structures which are of very special physical properties rather than their achiral counterparts or those at the single-particle level. However, the efficiency of conventional methods usually suffers from the thermal or external noise. Here, we propose a mechanism utilizing external noise to attain a tunable sorting of mesoscopic chiral particles in an achiral periodic potential. The complete chirality separation stems from the path selection by a noise-induced biased flux in a nonequilibrium landscape. Such a mechanism provides a practical way to control the motion of chiral particles by simply adjusting the noise intensity, which is demonstrated by simultaneous separation of several kinds of enantiomorphs with different degrees of chirality. The robustness and generalizability of noise-tuned chirality sorting is further verified in systems with other types of periodic potentials or spatially/temporally correlated noise.

Homochirality in biomineral suprastructures induced by assembly of single-enantiomer amino acids from a nonracemic mixture

Since Pasteur first successfully separated right-handed and left-handed tartrate crystals in 1848, the understanding of how homochirality is achieved from enantiomeric mixtures has long been incomplete. Here, we report on a chirality dominance effect where organized, three-dimensional homochiral suprastructures of the biomineral calcium carbonate (vaterite) can be induced from a mixed nonracemic amino acid system. Right-handed (counterclockwise) homochiral vaterite helicoids are induced when the amino acid l-Asp is in the majority, whereas left-handed (clockwise) homochiral morphology is induced when d-Asp is in the majority. Unexpectedly, the Asp that incorporates into the homochiral vaterite helicoids maintains the same enantiomer ratio as that of the initial growth solution, thus showing chirality transfer without chirality amplification. Changes in the degree of chirality of the vaterite helicoids are postulated to result from the extent of majority enantiomer assembly on the mineral surface. These mechanistic insights potentially have major implications for high-level advanced materials synthesis.

Viedma Ripening of Chiral Coordination Polymers Based on Achiral Molecules

When the chiral coordination polymers were composed of achiral molecules, the deracemization of the bulk product remains a great challenge if without any chiral induction. The Viedma ripening theory was adopted herein to help the achievement of mirror symmetry breaking for the bulk chirality of two chiral coordination polymers. The enantiomeric excess of the bulk chirality for the first compound is about 100%, which means absolute asymmetric synthesis. The deracemization degree of the bulk chirality for the second compound fluctuates occasionally. Further study has discussed the different deracemization degree of the bulk chirality for two compounds with the consideration of enantioselective incorporation in crystal cluster.

Helical Ordering of Spin Trimers in a Distorted Kagome Lattice of Gd3Ru4Al12Studied by Resonant X-ray Diffraction

Successive magnetic phase transitions at $T_1$=17.5 K and $T_2$=18.5 K in Gd$_3$Ru$_4$Al$_{12}$, with a distorted kagome lattice of Gd ions, is studied using resonant X-ray diffraction with polarization analysis. It has been suggested that in this compound the $S=7/2$ spins on the nearest-neighbor Gd-triangle form a ferromagnetic trimer and the Gd lattice can be effectively considered as an antiferromagnetic triangular lattice of $S=21/2$ spin trimers [S. Nakamura et al., Phys. Rev. B 98, 054410 (2018)]. We show that the magnetic order in this system is described by an incommensurate wave vector $q$~(0.27, 0, 0), which varies slightly with temperature. In the low temperature phase below $T_1$, the experimental results are well explained by considering that the spin trimers form a helical order with both the $c$-axis and $c$-plane components. In the intermediate phase above $T_1$, the $c$-axis component vanishes, resulting in a sinusoical structure within the $c$-plane. The sinusoidal-helical transition at $T_1$ can be regarded as an ordering of chiral degree of freedom, which is degenerate in the intermediate phase.

Probing chiral electronic excitations in bilayer graphene by Raman scattering

We report a symmetry resolved electronic Raman scattering (ERS) study of a bilayer graphene device under gate voltage. We show that the ERS continuum is dominated by interband chiral excitations of $A_{2}$ symmetry and displays a characteristic Pauli-blocking behavior similar to the monolayer case. Crucially, we show that non-chiral excitations make a vanishing contribution to the Raman cross-section due to destructive interference effects in the Raman amplitude matrix elements. This is in a marked contrast to optical absorption measurements and opens interesting venues for the use of Raman scattering as a selective probe of chiral degrees of freedom in topological matter and other 2D crystals.

Chirality in Au9 clusters protected by chiral/achiral mixed bidentate phosphine ligands: influence of the metal core and ligand array.

In this article, the chiroptical responses of Au9 clusters protected by chiral/achiral mixed bidentate phosphine ligands are reported. The mixed phosphine we use is (S)-BINAP/Xantphos in the molar ratio of 1/0 (= pure (S)-BINAP), 3/1, 1/1, or 0/1 (= pure Xantphos), where BINAP and Xantphos represent 2,2'-bis(diphenylphosphino)-1,1'-binaphthyl and 4,5-bis(diphenylphosphino)-9,9-dimethylxanthene, respectively. Electronic absorption spectra of the clusters are similar between the samples with different molar diphosphine ratios, but the chiroptical activity or g-factor decreases nonlinearly with an increase in the fraction of Xantphos. Quantum chemical calculations and geometrical quantifications based on the Hausdorff chirality measure (HCM) for model Au9 cluster species suggest that (i) two types of metal core structures with pseudo-P- and M-chirality are found, and their appropriate contributions would cancel out the chiroptical response in the low-energy region; (ii) the origin of optical activity in pure (S)-BINAP-protected Au9 clusters can mainly be attributed to the metal core chirality, whereas that of other mixed-ligand protected clusters would be due to the chiral ligand arrangement. This work demonstrates that the modulation of chiroptical activity in Au9 clusters by chiral/achiral mixed-diphosphine ligation is controlled by the difference in the degree of chirality existing in the cluster core and/or the ligand array.

Chiral entanglement in massive quantum field theories in 1+1 dimensions

We determine both analytically and numerically the entanglement between chiral degrees of freedom in the ground state of massive perturbations of 1+1 dimensional conformal field theories quantised on a cylinder. Analytic predictions are obtained from a variational Ansatz for the ground state in terms of smeared conformal boundary states recently proposed by J. Cardy, which is validated by numerical results from the Truncated Conformal Space Approach. We also extend the scope of the Ansatz by resolving ground state degeneracies exploiting the operator product expansion. The chiral entanglement entropy is computed both analytically and numerically as a function of the volume. The excellent agreement between the analytic and numerical results provides further validation for Cardy’s Ansatz. The chiral entanglement entropy contains a universal O(1) term γ for which an exact analytic result is obtained, and which can distinguish energetically degenerate ground states of gapped systems in 1+1 dimensions.

Chiral physics in the magnetic field with quark confinement contribution

The standard chiral perturbation theory is known to predict much weaker effects in magnetic field, than found in numerical lattice data. To overcome this disagreement we are using the effective chiral confinement Lagrangian, L_{ECCL}, containing both chiral and quark degrees of freedom, in the presence of external magnetic field. Without magnetic fields L_{ECCL} reduces to the ordinary chiral Lagrangian L_{EC L}, yielding in the lowest order O(partial _mu varphi )^2 all known relations, and providing explicit numerical coefficients in the higher O(p^4, p^6) orders. The inclusion of the magnetic field in L_{ECCL} strongly modifies ECL results for chiral condensates, coupling constants f_pi , f_K and masses of chiral mesons. The resulting behavior contains the only parameter – the string tension sigma , is roughly proportional to Oleft( frac{eB}{sigma }right) and agrees very well with lattice data. These results show that the magnetic field acts not only on the chiral degrees of freedom (varphi _pi ), but also on quarks in the quark-chiral Lagrangian, which produce much stronger effect.

Chiral Ramachandran Plots II: General Trends and Protein Chirality Spectra.

The degree of chirality of protein backbone residues is used to enrich the Ramachandran plot (RP) and create three-dimensional chiral RPs with much more structural information. Detailed comparative analysis of the four classical RPs (general, glycine, proline, and pre-proline) is provided, including statistical analysis of quantitative chirality distributions in the maps and in the secondary structures. Our results show that points with outlier chirality levels represent special transitional points in the folded protein such as α-helix kinks, twists of β-strands, and transition points between secondary structures. A protein chirality spectrum in which the degree of chirality of each residue is plotted against the sequence number explores these special points. More than 65000 residues extracted from 200 high-quality proteins are used for this study, which shows that quantitative chirality is a general and useful structural parameter for protein conformational studies.