Chiral Parameter Research Articles

Electron bubbles and Weyl fermions in chiral superfluidHe3−A

Electrons embedded in liquid $^3$He form mesoscopic bubbles with radii large compared to the interatomic distance between $^3$He atoms, voids of $N_{bubble}\approx 200$ $^3$He atoms, generating a negative ion with a large effective mass that scatters thermal excitations. We develop scattering theory of Bogoliubov quasiparticles by negative ions embedded in $^3$He-A that incorporates the broken symmetries of $^3$He-A, particularly time-reversal and mirror symmetry in a plane containing the chiral axis $\hat{\bf l}$. Multiple scattering by the ion potential, combined with Andreev scattering by the chiral order parameter, leads to a spectrum of Weyl Fermions bound to the ion that support a mass current circulating the electron bubble - the mesoscopic realization of chiral edge currents in superfluid $^3$He-A films. A consequence is that electron bubbles embedded in $^3$He-A acquire angular momentum, ${\bf L}\approx -(N_{bubble}/2)\hbar\,\hat{\bf l}$, inherited from the chiral ground state. We extend the scattering theory to calculate the forces on a moving electron bubble, both the Stokes drag and a transverse force, ${\bf F}_{W} = \frac{e}{c}{\bf v}\times{\bf B}_{W}$, defined by an effective magnetic field, ${\bf B}_{W}\propto\hat{\bf l}$, generated by the scattering of thermal quasiparticles off the spectrum of Weyl Fermions bound to the moving ion. The transverse force is responsible for the anomalous Hall effect for electron bubbles driven by an electric field reported by the RIKEN group. Our results for the scattering cross section, drag and transverse forces on moving ions are compared with experiments, and shown to provide a quantitative understanding of the temperature dependence of the mobility and anomalous Hall angle for electron bubbles in normal and superfluid $^3$He-A. We also discuss our results in relation to earlier theoretical work on negative ions in superfluid $^3$He.

Chiral matrix model of the semi-QGP in QCD

A chiral matrix model applicable to QCD with 2+1 flavors is developed. This requires adding a SU(3)_L x SU(3)_R x Z(3)_A nonet of scalar fields, with both parities, and coupling these to quarks through a Yukawa coupling, y. Treating the scalar fields in mean field approximation, the effective Lagrangian is computed by integrating out quarks to one loop order. In addition to the usual symmetry breaking term, linear in the current quark mass m_qk, at a nonzero temperature T it is necessary to add a new term, ~ m_qk T^2. The parameters of the gluon part of the matrix model are identical to that for the pure glue theory without quarks. The parameters in the chiral matrix model are fixed by the values, at zero temperature, of the pion decay constant and the masses of the pions, kaons, eta, and eta'. The temperature for the chiral crossover at T_chi = 155 MeV is determined by adjusting the Yukawa coupling y. We find reasonable agreement with the results of numerical simulations on the lattice for the pressure and related quantities. In the chiral limit, besides the divergence in the chiral susceptibility there is also a milder divergence in the susceptibility between the Polyakov loop and the chiral order parameter, with critical exponent beta - 1. We compute derivatives with respect to a quark chemical potential to determine the susceptibilities for baryon number, the chi_2n. Especially sensitive tests are provided by chi_4 - chi_2 and by chi_6, which changes in sign about T_chi. The behavior of the susceptibilities in the chiral matrix model strongly suggests that as the temperature increases from T_chi, that the transition to deconfinement is significantly quicker than indicated by the measurements of the (renormalized) Polyakov loop on the lattice.

High Frequency Fields of the PEMC Elliptical Reflector Placed in Chiral Medium Using Maslov’s Method

The high frequency field expressions are analyzed for perfect electromagnetic conducting (PEMC) elliptical reflector embedded in isotropic, homogeneous and reciprocal chiral medium. Geometric optics (GO) method is used to find the caustic region field for the PEMC elliptical reflector. However, GO fields are not valid around the caustic region due to the occurrence of un-realistic singularity around the caustic region. Therefore, Maslov’s method is used to derive the high frequency fields which are also valid in the vicinity of the caustic region. The effect of admittanceM of the PEMC boundary and the chirality parameter kβ on the high frequency fields are illustrated by plotting the numerical results using MATLAB software. A special case of PEMC circular reflector is also discussed.

The Chirality Parameter for Chiral Chemical Solutions

The frequency dependent chirality parameter of a chiral chemical solution is derived as a function of the specific rotation and molar ellipticity analytically by solving Maxwell’s equations for a dispersive chiral medium. The specific rotations found by measurements in a wide range of frequencies for d-glucose solution is used to find the Condon model parameters for this important chiral chemical solution. The Cotton effect is analyzed with adequate accuracy in this Condon modulation as a summation term. The frequency dependent behaviors of the real and imaginary parts of the Condon model for chiral chemical solutions are similar to the measured data for the specific rotation and circular dichroism, respectively.

Characteristics of surface plasmon polaritons in a dielectrically chiral-metal-chiral waveguiding structure.

We demonstrate theoretically the characteristics of surface plasmon polaritons (SPPs) with an asymmetric chiral-metal-chiral (CMC) waveguide structure, under realistic frequency dependencies of the permittivity and chirality parameters. Generalized dispersion relations are derived which can be applied to the nonchiral SPPs. We find that the existence of cutoffs in different modes for the CMC structures may facilitate the design of mode-selective surface plasmon waveguides. CMC-SPPs also exhibit an interesting dependence of the polarization on the chiral strength. These novel characteristics of CMC-SPPs provide new possibilities for the design of more compact nanophotonic devices.

Asymptotic method based on Maslov’s theory for the focusing of 3D elliptical lens placed in chiral medium

The high-frequency field expressions for the refracted waves from the dielectric 3D elliptical lens embedded in homogeneous and reciprocal chiral medium around the focal region are derived using an asymptotic method based on Maslov’s theory. Ray-based Geometric Optics (GO) technique was initially used to derive the expressions for the electrical field intensities for both left circular polarized and right circular polarized waves which are inherited in the chiral medium. However, GO method is not applicable at the focal points due to the shrinking of ray volume at these points which causes unreal singularities. Therefore, an asymptotic method based on Maslov’s theory is applied to derive the fields at the focal points. Moreover, the effect of chirality parameter on the behavior of focal points electric field intensities are indicated using the line plots obtained from the numerical solution of the derived equations using MATLAB software. A special case of the dielectric 3D elliptical lens placed in achiral medium is also discussed using the expressions.

Coriolis effect and spin Hall effect of light in an inhomogeneous chiral medium.

We theoretically investigate the spin Hall effect of spinning light in an inhomogeneous chiral medium. The Hamiltonian equations of the photon are analytically obtained within eikonal approximation in the noninertial orthogonal frame. Besides the usual spin curvature coupling, the chiral parameter enters the Hamiltonian as a spin-torsion-like interaction. We reveal that both terms have parallel geometric origins as the Coriolis terms of Maxwell's equations in nontrivial frames.

Dileptons and Chiral Symmetry Restoration

We report on recent work relating the medium effects observed in dilepton spectra in heavy-ion collisions to potential signals of chiral symmetry restoration. The key connection remains the approach to spectral function degeneracy between the vector-isovector channel with its chiral partner, the axialvector-isovector channel. Several approaches are discussed to elaborate this connection, namely QCD and Weinberg sum rules with input for chiral order parameters from lattice QCD, and chiral hadronic theory to directly evaluate the medium effects of the axialvector channel and the pertinent pion decay constant as function of temperature. A pattern emerges where the chiral mass splitting between ρ and a1 burns off and is accompanied by a strong broadening of the spectral distributions.

Broadband asymmetric transmission and polarization conversion of a linearly polarized wave based on chiral metamaterial in terahertz region

A novel chiral metamaterial consisting of double L resonators on two sides of the dielectric substrate is proposed in this paper. The structure can realize broadband asymmetric transmission and polarization conversion of a linearly polarized wave in the terahertz band. The polarization conversion ratio of the linearly polarized wave is more than 80% across a wide frequency range from 2.65 THz to 5.58 THz. Furthermore, the structure realizes three bands polarization angle independent 90° polarization rotator. In addition, optical activity and chirality parameter changing with frequency are studied in detail. The physical mechanism of the polarization conversion is also analyzed by the electric field distributions.

Elliptical reflector in strong chiral medium supporting PPV and NPV simultaneously

The high-frequency electromagnetic waves reflected from a perfect electric conductor (PEC) elliptical surface placed in homogeneous, reciprocal, and isotropic medium with high value of chirality parameter are analyzed. Negative phase velocity (NPV) and positive phase velocity (PPV) can be obtained by properly adjusting the value of chirality parameter. For the value of only PPV can propagate in the elliptical reflector and out of this range both PPV and NPV are supported by the elliptical reflector in chiral medium. The line plots are given which illustrate the reflected waves at different values of chirality parameter .

Analysis of 3D elliptical reflector antenna coated with chiral layer under normal incident electromagnetic wave

In this paper, a 3D elliptical reflector coated with chiral medium has been analyzed to find the field in the vicinity of focal region using geometrical optics (GO) and Maslov's method. As the GO approximation does not work at the focal points due to unreal singularities occur at these points. Therefore, Maslov's theory has been applied to derive the expressions which are also valid at focal points. These focal points usually are of great importance in all practical applications. The effects of thickness (d) of the coated medium, chirality parameter (β) of the coated medium and permittivity (ɛ) of the medium on the focal region fields are illustrated. A special case of elliptical reflector coated with conventional medium has also been evaluated. The derived fields expressions are plotted using MATLAB software.

Effects on the focusing of 3D elliptical reflector with strong chiral background supporting both PPV and NPV modes

The reflected electromagnetic waves from a perfect electric conductor (PEC) 3D elliptical reflector with chiral background with high value of chirality parameter kβ are discussed. The chiral medium supports both negative phase velocity (NPV) and positive phase velocity (PPV) simultaneously by increasing the concentration of chiral objects in the host medium, i.e., with strong chiral medium. For the value of −1<kβ<1 only PPV can propagate in the chiral medium with 3D elliptical reflector and out of this range both PPV and NPV are supported by the chiral medium with 3D elliptical reflector embedded in chiral medium. The derived high frequency field expressions with the help of geometrical optics (GO) and Maslov's method are simulated using MATLAB software with different values of chirality parameter kβ greater than one.

A novel chiral nano structure for optical activities and negative refractive index

In this paper, we present a chiral hollowed-out split ring resonators nano structure. This novel chiral nano structure can form multiple electric dipoles and magnetic dipoles in infrared and visible regions. And the interaction of these dipoles caused optical activities and multi-band negative refractive index. The appropriate geometric parameters are obtained through optimization and analysis of this structure. Circular dichroism, polarization azimuthal rotation angle, ellipticity, refractive index and chiral parameter are calculated using S-parameter retrieval method, and these optical properties can be tunable by the geometric parameters of the chiral structure. This chiral structure metamaterial would offer electromagnetic applications in the infrared and visible regions, for fields like imaging, invisibility cloak and perfect lensing.

Propagation of Airy-Gaussian beams in a chiral medium

We have expressed and investigated the propagation of Airy-Gaussian beams (AiGBs) in a chiral medium analytically. It is shown that AiGBs split into two components, i.e., the left circularly polarized (LCP) beams and the right circularly polarized (RCP) beams, which have a different propagation trajectory and are affected by the chiral parameter γ and the distribution factor χ 0. It is found that the LCP beams accelerate faster than the RCP beams during propagation, and are influenced by the chiral parameter. With an increase in the chiral parameter, the acceleration of the LCP beams increases, but that of the RCP beams decreases. So, it is significant that we can control the self-acceleration of AiGBs by varying the chiral parameter and the distribution factor.

Electroweak chiral Lagrangian with a light Higgs and γγ → ZLZL, [formula omitted] scattering at one loop

In these proceedings we provide a brief summary of the findings of a previous article where we have studied the photon-photon scattering into longitudinal weak bosons within the context of the electroweak chiral Lagrangian with a light Higgs, a low-energy effective field theory including a Higgs-like scalar singlet and where the electroweak would-be Goldstone bosons are non-linearly realized. We consider the relevant Lagrangian up to next-to-leading order in the chiral counting, which is explained in some detail here. We find that these amplitudes are ultraviolet finite and the relevant combinations of next-to-leading parameters (cγ and a1−a2+a3) do not get renormalized. We propose the joined analysis of γγ–scattering and other photon related observables (Γ(h→γγ), S–parameter and the γ⁎→WL+WL− and γ⁎→hγ electromagnetic form-factors) in order to separate and determine each chiral parameter. Moreover, the correlations between observables provided by the NLO computations would lead to more stringent bounds on the new physics that is parametrized by means of this effective Lagrangian. We also show an explicit computation of the γγ–scattering up to next-to-leading order in the SO(5)/SO(4) minimally composite Higgs model.

Mass of heavy-light mesons in a constituent quark picture with partially restored chiral symmetry

We probe effects of the partial chiral symmetry restoration to the mass of heavy-light mesons in a constituent quark model by changing the constituent quark mass of the light quark. Due to the competing effect between the quark mass and the linearly rising potential, whose contribution to the energy increases as the quark mass decreases, the heavy-light meson mass has a minimum value near the constituent quark mass typically used in the vacuum. Hence, the meson mass increases as one decreases the constituent quark mass consistent with recent QCD sum rule analyses, which show an increasing $D$ meson mass as the chiral order parameter decreases.

Simultaneous amplification and attenuation in isotropic chiral materials

The electromagnetic field phasors in an isotropic chiral material (ICM) are superpositions of two Beltrami fields of different handedness. Application of the Bruggeman homogenization formalism to two-component composite materials delivers ICMs wherein Beltrami fields of one handedness attenuate whereas Beltrami fields of the other handedness amplify. One component material is a dissipative ICM, the other an active dielectric material. The range of the volume fraction of the active component material for which simultaneous amplification and attenuation is exhibited decreases—but does not vanish—as the ICM component becomes more dissipative and as its chirality parameter reduces in magnitude.

Power flux distribution in chiroplasma‐filled perfect electromagnetic conductor circular waveguides

AbstractTheoretical analysis of the electromagnetic wave propagation in circular waveguides with a chiroplasma core coated with a perfect electromagnetic conductor (PEMC) is presented. The presented formulations and analysis are general for any perfect electric, perfect magnetic, or perfect electromagnetic conductor (PEMC) waveguides filled with any general anisotropic/isotropic metamaterial including plasma. The characteristic equation for the modes in this waveguide is obtained, and the behavior of the dispersion curves and the power flux are examined and evaluated numerically. The results demonstrate that the behavior of the power flux transported in the guide, in magnitude and orientation, is highly determined by the chirality parameter and the plasma and cyclotron frequencies. The mode cutoff frequencies are sensitive to the variations in the filling material and chirality parameters and likewise affected by the variations in the PEMC admittance parameter.

Structure of vortex-bound states in spin-singlet chiral superconductors

We investigate the structure of vortex-bound states in spin-singlet chiral superconductors with ($d_{x^2-y^2} \pm i d_{xy}$)-wave and ($d_{xz} \pm id_{yz}$)-wave pairing symmetries. It is found that vortices in the ($d_{xz} \pm id_{yz}$)-wave state bind zero-energy states which are dispersionless along the vortex line, forming a doubly degenerate Majorana flat band. Vortex-bound states of ($d_{x^2-y^2} \pm i d_{xy}$)-wave superconductors, on the other hand, exist only at finite energy. Using exact diagonalization and analytical solutions of tight-binding Bogoliubov-de Gennes Hamiltonians, we compute the energy spectrum of the vortex-bound states and the local density of states around the vortex and antivortex cores. We find that the tunneling conductance peak of the vortex is considerably broader than that of the antivortex. This difference can be used as a direct signature of the chiral order parameter symmetry.

Tunable multi-band chiral metamaterials based on double-layered asymmetric split ring resonators

We have numerically demonstrated chiral metamaterials based on double-layered asymmetric Au film with hollow out design of split ring resonators on either side of the polyimide. Multiple electric dipoles and magnetic dipoles resulted from parallel and antiparallel currents between the eight split ring resonators. Multi-band circular dichroism is found in the visible frequency regime by studying the transmission properties. Huge optical activity and the induced multi-band negative refractive index are obtained at resonance by calculating the optical activity and ellipticity of the transmitted E-fields. Chirality parameter and effective refractive index are retrieved to illustrate the tunable optical properties of the metamaterials. The underlying mechanisms for the observed circular dichroism are analyzed. These metamaterials would offer flexible electromagnetic applications in the infrared and visible regime.