Chiral Term Research Articles

Quantum chemistry study on the hyper-Rayleigh scattering optical activity of R-carvone and (1R,5R)-α-pinene.

In this work, the HRS-OA circular differential scattering ratios of medium-size chiral molecules, R-carvone and (1R,5R)-α-pinene, has been computed by means of TD-DFT calculations. The results have been discussed as a function of the basis set size. For R-carvone a conformational analysis has been taken into account. In particular, the three most stable conformations of R-carvone present chiral terms that contribute to the HRS-OA circular differential scattering ratio, with opposite signs. Finally, the modified unit sphere representations (mUSR) have been produced for the molecules under study.

Pre-Smectic Ordering and the Unwinding Helix in Monte Carlo Simulations of Cholesteric Liquid-Crystals.

In this paper, molecular chirality is studied for liquid-crystal fluids represented by hard rods with the addition of an attractive chiral dispersion term. Chiral forces between molecular pairs are assumed to be long-ranged and are described in terms of the pseudotensor of Goossens [W. J. A. Goossens, Mol. Cryst. Liq. Cryst. 1971, 12, 237-244]. Following Varga and Jackson [S. Varga and G. Jackson, Chem. Phys. Lett. 2003, 377, 6-12], this is combined with a hard-spherocylinder core. We investigate the relationship between molecular chirality and the helical pitch of the system, which occurs in the absence of full three-dimensional periodic boundary conditions. The dependence of the wavenumber of this pitch on the thermodynamic variables, temperature, and density is measured. We also explore the use of a novel surface boundary interaction model. As a result of this approach, we are able to lower the temperature of the system without the occurrence of nematic droplets, which would interfere with the formation of a uniaxial pitch. Regarding the theoretical predictions of Wensink and Jackson [H. H. Wensink and G. Jackson, J. Chem. Phys. 2009, 130, 234911], on the one hand, we have qualitative agreement with the observed non-monotonic density dependence of the wavenumber. Initially increasing with density, the wavenumber reaches a maximum, before falling as the density moves toward the point of phase transition from cholesteric to smectic. However, further analysis for shorter rods, in the presence of novel boundary conditions, reveals some disagreement with the theory, at least in this case; the unwinding of the cholesteric helix in the cholesteric phase occurs simultaneously with subtle increases in smectic ordering. These pre-smectic fluctuations have not been accounted for so far in theories on cholesterics but turn out to play a key role in controlling the pitch of cholesteric phases of rod-shaped mesogens with a small to moderate aspect ratio.

The Correction of Quantum Tunneling Rate and Entropy of Non-Stationary Spherically Symmetric Black Hole by Lorentz Breaking

With the introduction of CFJ correction term, Chiral correction term, and aether-like correction term, based on Lorentz breaking, WKB approximate, and quantum tunneling radiation theory of black holes, the modified fermion dynamics equation is studied in the general non-stationary spherically symmetric black hole space-time, and the new modified expressions of the fermion tunneling rate, the Hawking temperature, and the Bekenstein–Hawking entropy of the black hole are obtained. This black hole has both thermal and non-thermal radiation. In this article, the influence of Lorentz breaking on the energy levels of Dirac particles was also studied, and the distribution characteristics of Dirac energy levels in the space-time and the maximum value of the crossing of positive and negative energy levels were obtained. The necessary discussion and the explanation of the corresponding results are made.

Narushenie kiral'noy simmetrii i neodnorodnye sostoyaniya v deformirovannykh ferromagnetikakh

The general form of chiral terms associated with deformation of a ferromagnet is determined. The possibility of a transition from the helical state to the vortex state is demonstrated for a ferromagnetic rod subjected to elastic torsional strain. In the case of a single screw dislocation, the formation of the skyrmion state due to elastic strains and the helical distribution of magnetization induced by strains in the dislocation core is indicated. The conditions in which a transition from one chiral magnetization distribution to another distribution in an ensemble of identical dislocations are determined.

Pure gauge theory for the gravitational spin connection

The gravitational spin connection appears in gravity as a non-Abelian gauge field for the Lorentz group $SO(3,1)$, which is non-compact. The action for General Relativity is linear in the field strength associated to the spin connection, and its equation of motion corresponds to the standard metricity constraint. Consequently, the zero-torsion spin connection is never realized as an independent degree of freedom and is determined by the vierbein field. In this work, we take a different perspective and consider a pure Yang-Mills theory for the spin connection coupled to Dirac fermions, resulting in the former being a dynamical field. After discussing various approaches towards managing the pathologies associated with non-compact gauge theories, we compute the tree-level amplitude for fermion scattering via a spin connection exchange. In contrast to integrating out torsion in the presence of fermions, the model induces a chiral four-Fermi like term that involves a right-right current interaction, which is not present in the Standard Model.

Validation of broadband infrared normalization in sum-frequency generation vibrational spectroscopy through simultaneous chiral terms on α-quartz crystal

Sum-frequency generation vibrational spectroscopy (SFG-VS) has been widely used for characterizing various interfaces. However, obtaining SFG signals with a high signal-to-noise ratio can be challenging for certain interfaces, such as those involving powder particles, which scatter the SFG light and make it difficult to obtain accurate spectra. To address these challenges, we developed a new approach using a z-cut α-quartz crystal as the substrate loaded with a very small amount of powder sample. This approach not only amplifies the SFG signal from particles through the interference of the electric field from the quartz crystal, but also allows for phase reference and normalization of the broadband infrared SFG spectrum. By distinguishing the different polarizations of the SFG light, we were able to separate and simultaneously collect the achiral and chiral SFG signals. We used the chiral SFG signal to normalize the achiral SFG intensity, thereby avoiding any potential changes to the interface caused by loading substances onto the quartz, as well as coincidence differences resulting from the instability of light at different moments. We demonstrated our method by measuring the adsorption of CH3OD on a quartz substrate loaded with MoC nanoparticles. Our approach produced a high signal-to-noise ratio SFG spectrum, regardless of the interface situation.

The model for non-Abelian field topology for the multilayer fractional quantum anomalous Hall device

From the recent empirical discovery of the quantum anomalous Hall effect (QAHE), the interaction of the particle with spin–orbit coupling (SOC) plays an essential role in the cause of the QAHE, which includes three terms: external, internal, and chiral symmetric terms. Then, the non-Abelian quantum field theory was adopted to analyze and prove the conjecture on the causes that can lead to the fractional quantum Hall effect (FQHE). The spontaneously topological chiral symmetry breaking is the main contribution to the FQHE, which also includes two terms: the hopping of sublattice and Coulomb energy by the interaction of many-body particles. More generally, this exciton possesses an intermediate characteristic between the Wannier regimes and displays a peculiar two-dimensional wavefunction in the three-dimensional FQHE states. Finally, a bilayer three-dimensional model is proposed to implement the FQHE on the lattice by incorporating ferromagnetic dopants into three-dimensional topological insulative thin films. This study theoretically predicts the FQHE on the basis of other reports that have experimentally verified the rationality of the proposed model in magnetic topological insulators.

Dynamics of chiral liquid crystals between cylinders using Landau-de Gennes theory

ABSTRACT This study employs the Landau-de Gennes theory to investigate the behaviour of chiral liquid crystals (CLCs) between concentric and eccentric cylinders under different flow conditions. This theory was implemented in dynamic finite element simulations to solve the evolution of the microstructure of CLCs and couple it with linear momentum balance equation (modified Navier–Stokes equation) to capture the structure of CLCs. The study focused on the microstructure formation of CLCs and their performance as lubricants under various chirality strengths (θ), Deborah numbers (De), and eccentricity of eccentric cylinders. The hexagonal structure of the CLCs was found between cylinders at low De (0.001), where the chiral term predominates. Moreover, the number of hexagonal structures between cylinders was shown to be significantly correlated to the chiral strength. We showed that increasin De resulted in vanishing hexagonal pattern of CLCs and the De value at which the hexagonal pattern vanishes depends on the chiral strength. We also observed that a higher eccentricity ratio significantly increased the pressure force per length on the inner cylinders and caused more non-uniformity in the structure. Based on the findings, we concluded that the performance of CLCs as lubricants is greater at higher θ and eccentricity and lower De.

Local well-posedness of the Landau–Lifshitz equation with helicity term

We consider the initial value problem for the Landau–Lifshitz equation with a helicity term (chiral interaction term), which arises from the Dzyaloshinskii–Moriya interaction energy. We prove that it is well-posed locally in-time in the space k̄+Hs for s ≥ 3 with s∈Z and k̄=(0,0,1)t. We also show that if we further assume that the solution is homotopic to constant maps, then local well-posedness holds in the space k̄+Hs for s > 2 with s∈R. Our proof is based on two different approaches: One is the geometric energy method by McGahagan and the other is via the modified Schrödinger map equation. In the present analysis, we exploit a special structure of the helicity term, which enables us to overcome the difficulty in the quadratic derivative nonlinearity of the helicity term.

Achieving maximum scattering circular dichroism through the excitation of anapole states within chiral Mie nanospheres

The chirality-dependent asymmetric light-matter interaction can be enhanced using various artificial photonic structures as well as engineered incident field. Compared with chiral photonic structures, the engineered optical field is less explored and recently recognized as a new regime in tailoring light-matter interaction. In this work, we demonstrate that weakly chiral spheres can exhibit the maximum scattering circular dichroism (CD) by tailoring the incident field to construct chirality-sensitive anapole states. By considering the chiral terms radiated from Mie nanospheres as perturbation, a multiscattering model is established to predict the chiroptical Mie scattering response of these nanospheres. This model provides a specific guideline to tailor the incident field to realize the upper limit of the achievable scattering CD.

Phase behavior of the generalized chiral Lebwohl-Lasher model in bulk and confinement.

One of the simplest models that is used to study the isotropic-nematic tranition in liquid crystalline systems is the Lebwohl-Lasher model. Several extensions of this model further enhanced its applicability. We combine two of these extensions (a generalization and the inclusion of a chiral term) and study the phase behavior and the nature of phase transitions of the resulting generalized chiral Lebwohl-Lasher model using Monte Carlo simulations. We find that the type (and even the existence) of the transition depends on the combination of the width of the interaction potential, the strength of the chiral part of the interaction, and the geometry of the system. As well, the pitch of the cholesteric bulk phase changes on approaching the phase transition if the interaction width differs from the one of the original Lebwohl-Lasher model. Thus, we identify parameter combinations that allow one to tune the properties of the ordered phase and the nature of the order-disorder transition.

Significance of chiral three-nucleon force contact terms for understanding of elastic nucleon-deuteron scattering

We investigate the importance of the three-nucleon (3N) force contact terms in elastic nucleon-deuteron (Nd) scattering by applying the N$^4$LO$^+$ chiral semi-local momentum space (SMS) regularized nucleon-nucleon (NN) chiral potential supplemented by N$^2$LO and all subleading N$^4$LO three-nucleon force (3NF) contact terms. Strength parameters of the contact terms were obtained by least squares fitting of theoretical predictions to cross section and analyzing powers data at three energies of the impinging nucleon. Although the N$^3$LO contributions to the 3N force were completely neglected, the results calculated with the contact terms multiplied by the fitted strength parameters yield an improved description of the elastic Nd scattering observables in a wide range of incoming nucleon energies below the pion production threshold.

Self-consistent field theory of chiral nematic worm-like chains.

Many macromolecules of biological and technological interest are both chiral and semi-flexible. DNA and collagen are good examples. Such molecules often form chiral nematic (or cholesteric) phases, as is well-documented in collagen and chitin. This work presents a method for studying cholesteric phases in the highly successful self-consistent field theory of worm-like chains, offering a new way of studying many biologically relevant molecules. The method involves an effective Hamiltonian with a chiral term inspired by the Oseen-Frank (OF) model of liquid crystals. This method is then used to examine the formation of cholesteric phases in chiral-nematic worm-like chains as a function of polymer flexibility, as well as the optimal cholesteric pitch and distribution of polymer segment orientations. Our approach not only allows for the determination of the isotropic-cholesteric transition and segment distributions, beyond what the OF model promises, but also explicitly incorporates polymer flexibility into the study of the cholesteric phase, offering a more complete understanding of the behavior of semiflexible chiral-nematic polymers.

Driven Hubbard model on a triangular lattice: Tunable Heisenberg antiferromagnet with a chiral three-spin term

We study the effects of a periodically varying electric field on the Hubbard model at half-filling on a triangular lattice. The electric field is incorporated through the phase of the nearest-neighbor hopping amplitude via the Peierls prescription. When the on-site interaction $U$ is much larger than the hopping, the effective Hamiltonian $H_{eff}$ describing the spin sector can be found using a Floquet perturbation theory. To third order in the hopping, $H_{eff}$ is found to have the form of a Heisenberg antiferromagnet with three different nearest-neighbor couplings $(J_\alpha,J_\beta,J_\gamma)$ on bonds lying along the different directions. Remarkably, when the periodic driving does not have time-reversal symmetry (TRS), $H_{eff}$ is also found to have a chiral three-spin interaction in each triangle, with the coefficient $C$ of the interaction having opposite signs on up- and down-pointing triangles. Thus periodic driving which breaks TRS can simulate the effect of a perpendicular magnetic flux which is known to generate such a chiral term in the spin sector, even though our model does not have a magnetic flux. The four parameters $(J_\alpha,J_\beta,J_\gamma,C)$ depend on the amplitude, frequency and direction of the oscillating electric field. We then study the spin model as a function of these parameters using exact diagonalization and find a rich phase diagram of the ground state with seven different phases consisting of two kinds of ordered phases (colinear and coplanar) and disordered phases. Thus periodic driving of the Hubbard model on the triangular lattice can lead to an effective spin model whose couplings can be tuned over a range of values thereby producing a variety of interesting phases.

Chiral and non-chiral spinning string dynamo instability from quantum torsion sources

In this paper dynamo instability is investigated by making use of a condensed matter screw dislocation model of spinning cosmic strings in the framework of teleparallel T4 spacetime, The magnetic field is encoded into the T4 metric tensor. By using quantum torsion from quantisation flux dependence on the spin angular momentum of strings, one is able to obtain dynamo instability where chiral currents grow exponentially as in Witten superconducting cosmic string (SCS) dynamos. Our results are compared to Galitsky et al. (2018), who have investigated dynamo instability from Weyl semimetals, showing that chiral anomaly term reduces the Reynolds number for dynamo instability. String dynamos in the framework of Einstein–Cartan (EC) (Garcia de Andrade, 2014) cosmology have been previously addressed. Moreover, it is shown that dynamo strings possess a monopole singularity at Big Bang. Topological defects dynamos, such as torsion spin-polarised fermions orthogonal to the wall (Garcia de Andrade, 2021) have been obtained from torsional anomalies sources. Galitski et al also discovered that chiral anomalies help dynamo effect in real magnetic fields. Non-chiral solutions where the current is along the string but the magnetic field is not, such as in pion string dynamo [Gwyn et al. Phys Rev D] are obtained from the Heaviside step function which tells us that the magnetic field grows, in the plane above z=0 where the spinning string crosses the plane, and vanishes below the crossing plane.

Non-collinear ground state and stable bimerons from four-spin chiral interactions in D3h magnet

We demonstrate that four-spin interactions in crystals with D3h point group of symmetry can cause a phase transition from a collinear state to a non-collinear magnetic ground state (such as magnetic vortices or magnetic skyrmions), while all anti-symmetric chiral terms are forbidden by symmetry in such crystals. Moreover, D3h point group rather common among two dimensional magnets. Taking into account possible four-spin chiral exchange interactions is important for understanding noncollinear magnetic order in these systems. We also address a possible stabilization of bimerons by the same contribution.

Gutzwiller projected states for the J1−J2 Heisenberg model on the Kagome lattice: Achievements and pitfalls

We assess the ground-state phase diagram of the $J_1$-$J_2$ Heisenberg model on the kagome lattice by employing Gutzwiller-projected fermionic wave functions. Within this framework, different states can be represented, defined by distinct unprojected fermionic Hamiltonians that include hopping and pairing terms, as well as a coupling to local Zeeman fields to generate magnetic order. For $J_2=0$, the so-called U(1) Dirac state, in which only hopping is present (such as to generate a $\pi$-flux in the hexagons), has been shown to accurately describe the exact ground state [Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Phys. Rev. B 87, 060405 (2013); Y.-C. He, M. P. Zaletel, M. Oshikawa, and F. Pollmann, Phys. Rev. X 7, 031020 (2017)]. Here, we show that its accuracy improves in presence of a small antiferromagnetic super-exchange $J_2$, leading to a finite region where the gapless spin liquid is stable; then, for $J_2/J_1=0.11(1)$, a first-order transition to a magnetic phase with pitch vector ${\bf q}=(0,0)$ is detected, by allowing magnetic order within the fermionic Hamiltonian. Instead, for small ferromagnetic values of $|J_2|/J_1$, the situation is more contradictory. While the U(1) Dirac state remains stable against several perturbations in the fermionic part (i.e., dimerization patterns or chiral terms), its accuracy clearly deteriorates on small systems, most notably on $36$ sites where exact diagonalization is possible. Then, upon increasing the ratio $|J_2|/J_1$, a magnetically ordered state with $\sqrt{3} \times \sqrt{3}$ periodicity eventually overcomes the U(1) Dirac spin liquid. Within the ferromagnetic $J_{2}$ regime, evidence is shown in favor of a first-order transition at $J_2/J_1=-0.065(5)$.

Noncollinear Ground State from a Four-Spin Chiral Exchange in a Tetrahedral Magnet

We propose a quartic chiral term m_{x}m_{y}m_{z}∇·m for the energy density of a cubic ferromagnet with broken parity symmetry (point group T_{d}). We demonstrate that this interaction causes a phase transition from a collinear ferromagnetic state to a noncollinear magnetic cone ground state provided its strength exceeds the geometric mean of magnetic exchange and cubic anisotropy. The corresponding noncollinear ground state may also be additionally stabilized by an external magnetic field pointing along certain crystallographic directions. The four-spin chiral exchange does also manifest itself in peculiar magnon spectra and favors spin waves with the wave vector that is perpendicular to the average magnetization direction.

Radiative and chiral corrections to elastic lepton-proton scattering in chiral perturbation theory

A unified treatment of both chiral and radiative corrections to the low-energy elastic lepton-proton scattering processes is presented in Heavy Baryon Chiral Perturbations Theory. The proton hadronic chiral corrections include the next-to-next-to leading order corrections whereas the radiative corrections include the next-to-leading order terms in our novel power counting scheme. We find that the net fractional well-defined chiral corrections with respect to the leading order Born cross section can be as large as $10\%$ ($20\%$) for electron (muon) scattering process for MUon proton Scattering Experiment (MUSE) kinematics. We show {\it via} our model-independent treatment of the low-energy lepton-proton kinematics, that the largest theoretical uncertainty is due to the recent different published values of the proton's rms radius while, e.g., the next higher order hadronic chiral terms are expected to give rather nominal errors. For the radiative corrections we demonstrate a systematic order by order cancellation of all infrared singularities and present our finite ultraviolet regularization results. We find that the radiative corrections for muon-proton scattering is of the order of $2\%$, whereas for electron scattering the radiative corrections could be as large as $25\%$. We attribute such a contrasting result partially to the fact that in muon scattering the leading radiative order correction goes through zero in some intermediate low-momentum transfer region, leaving the sub-leading radiative chiral order effects to play a dominant role in this particular kinematic region. For the low-energy MUSE experiment, the often neglected lepton mass as well as the Pauli form factor contributions of the relativistic leptons are incorporated in all our computations.

Exploring self-consistency of the equations of axion electrodynamics in Weyl semimetals

Recent works have provided evidence that an axial anomaly can arise in Weyl semimetals. If this is the case, then the electromagnetic response of Weyl semimetals should be governed by the equations of axion electrodynamics. These equations capture both the chiral magnetic and anomalous Hall effects in the limit of linear response, while at higher orders their solutions can provide detectable electromagnetic signatures of the anomaly. In this work, we consider three versions of axion electrodynamics that have been proposed in the Weyl semimetal literature. These versions differ in the form of the chiral magnetic term and in whether or not the axion is treated as a dynamical field. In each case, we look for solutions to these equations for simple sample geometries subject to applied external fields. We find that in the case of a linear chiral magnetic term generated by a nondynamical axion, self-consistent solutions can generally be obtained. In this case, the magnetic field inside of the Weyl semimetal can be magnified significantly, providing a testable signature for experiments. Self-consistent solutions can also be obtained for dynamical axions, but only in cases where the chiral magnetic term vanishes identically. Finally, for a nonlinear form of the chiral magnetic term frequently considered in the literature, we find that there are no self-consistent solutions aside from a few special cases.