Chiral States Research Articles

Topological defect states in mesoscopic superconducting squares with spin correlations

In the framework of the microscopic Bogoliubov-de Gennes theory, we study the topological defect states in mesoscopic superconducting square systems with spin correlations. The dominant spin-triplet -wave pairing symmetry of order parameters can be realized by choosing appropriate band parameters. At zero external magnetic field, the single-domain-wall state tends to emerge as the ground state of the system. When the magnetic field is applied, there exist field-driven phase transitions among three types of (anti)vortex patterns for the vortex-free ground state. With increasing field, a large number of coreless single-skyrmionic states with different topological charges can appear as the ground states. In particular, a novel chiral domain-wall ground state carrying fractional total flux quanta can take place, accompanied by an unclosed half-quantum-vortex chain in the phase difference profile. Several unique metastable states are also revealed in the strong flux range in the present system.

Modulation of circularly polarized luminescence through excited-state symmetry breaking and interbranched exciton coupling in helical push-pull organic systems.

π-Helical push-pull dyes were prepared and their (chir)optical properties were investigated both experimentally and computationally. Specific fluorescent behaviour of bis-substituted system was observed with unprecedented solvent effect on the intensity of circularly polarized luminescence (CPL, dissymmetry factor decreasing from 10-2 to 10-3 with an increase in solvent polarity) that was linked to a change in symmetry of chiral excited state and suppression of interbranched exciton coupling. The results highlight the potential of CPL spectroscopy to study and provide a deeper understanding of electronic photophysical processes in chiral π-conjugated molecules.

Dynamics of chiral state transitions and relaxations in an FeGe thin plate via in situ Lorentz microscopy.

Studying the magnetic transition between different topological spin textures in noncentrosymmetric magnets under external stimuli is an important topic in chiral magnetism. Here, using in situ Lorentz transmission electron microscopy (LTEM) we directly visualize the thermal-driven magnetic transitions and dynamic characteristics in FeGe thin plates. A novel protocol-dependent phase diagram of FeGe thin plates was obtained via pulsed laser excitation. Moreover, by setting the appropriate specimen temperature, the relaxation of chiral magnetic states in FeGe specimens was recorded and analyzed with an Arrhenius-type relaxation mechanism. We present the field-dependent activation energy barriers for chiral state transitions and the magnetic transition pathways of these spin textures for FeGe thin plates. Our results unveil the effects of thermal excitation on the topological spin texture transitions and provide useful information about magnetic dynamics of chiral magnetic state relaxation.

Topological superconductivity in Ni-based transition metal trichalcogenides

Based on a two-orbital honeycomb lattice model and random phase approximation, we investigate the pairing symmetry of the Ni-based transition-metal trichalcogenide. We find that an I-wave (A2g) state and a chiral d-wave state are dominant and nearly degenerate for typical electron and hole dopings. These two states carry nontrivial topological properties, which are manifested by the presence of chiral edge states in the d+id-wave state and dispersionless Andreev bound state at zero energy in the I-wave state. Ni-based transition-metal trichalcogenides provide us a new platform to study the exotic phenomena emerged from electron-electron correlation effects.

Higher-order topological insulators in a crisscross antiferromagnetic model

We present a $4'/m'$-respecting crisscross AFM model in 2D and 3D, both belonging to the $Z_2$ classification and exhibiting interesting magnetic high-order topological insulating (HOTI) phases. The topologically nontrivial phase in the 2D model is characterized by the fractional charge localized around the corners and the quantized charge quadrupole moment. Moreover, our 2D model also exhibits the quantized magnetic quadrupole moment, which is a unique feature compared with previous studies. The 3D system stacked from layers of the 2D model possesses the HOTI phase holding chiral 1D metallic states on the hinge, which corresponds to the Wannier center flow between the valence and conduction bands. The novel transport properties such as the half-quantum spin-flop pumping phenomena on the side surfaces of the HOTI phase is also discussed.

Dynamical conductivity in the multiply degenerate point-nodal semimetal CoSi

We investigate the dynamical conductivity in multiply-degenerate point-nodal semimetal CoSi. In the semimetal, the band structure holds point nodes at the $\Gamma$ and R points in the Brillouin zone and more than three bands touch at the nodes. Around the nodes, electronic states are predicted to be described as the multifold chiral fermion, a new class of fermion. We show that the dynamical conductivity exhibits a characteristic spectrum corresponding to the band structure and the chiral fermionic states. The dynamical conductivity of CoSi is calculated as a function of photon energy by using the first-principles band calculation and linear response theory. We show that a dip structure in the low photon-energy region is attributed to not only the band structure but also the chirality of electronic states. The chirality leads to the prohibition of transition between the lower and upper bands of threefold chiral fermion and thus the transition between the middle and lower bands is relevant to the dynamical conductivity. This transition property is different from the Dirac and Weyl semimetals, the other point-nodal semimetals, where the excitation between the upper and lower bands is relevant to the dynamical conductivity. We discuss the relation between the prohibition and the dip structure by using an effective Hamiltonian describing threefold chiral fermion.

Optomechanics of Chiral Dielectric Metasurfaces

AbstractThe coupling between electromagnetic fields and mechanical motion in micro‐ and nanostructured materials has recently produced intriguing fundamental physics, such as the observation of mesoscopic optomechanical phenomena in objects operating in the quantum regime. It is also yielding innovative device applications, for instance in the manipulation of the optical response of photonic elements. Following this concept, here it is shown that combining a nanostructured chiral metasurface with a semiconductor suspended micromembrane can open new scenarios where the mechanical motion affects the polarization state of a light beam, and vice versa. Optical characterization of the fabricated samples, assisted by theory and numerical modeling, reveals that the interaction is mediated via moving‐boundary and thermoelastic effects, triggered by intracavity photons. This work represents a first example of “Polarization Optomechanics,” which can give access to new forms of polarization nonlinearities and control. It can also lead to wide applications in fast polarimetric devices, polarization modulators, and dynamically tunable chiral state generators and detectors.

Photonic emulation of two-dimensional materials with antiferromagnetic order

We introduce an electromagnetic metamaterial - a spin-valley photonic topological insulator (SV-PTI) - that emulates a wide class of theoretically predicted gapped two-dimensional materials with antiferromagnetic order coupled to the valley degree of freedom. First-principles electromagnetic simulations and an analytic model reveal that a single parameter controls the propagation properties of the chiral states at the domain wall between two SV-PTIs: their group velocity, polarization, and the existence/absence of topological protection. The latter is determined by the geometry of the line of the least frequency separation between the bandgap-forming propagation bands. Topologically-protected compression of electromagnetic energy via group velocity control is enabled by SV-PTIs.

Quantization in Chiral Higher Order Topological Insulators: Circular Dichroism and Local Chern Marker.

The robust quantization of observables in units of universal constants is a hallmark of topological phases. We show that chiral higher order topological insulators (HOTIs), bulk insulators with chiral hinge states, present two unusual features related to quantization. First, we show that circular dichroism is quantized to an integer or zero depending on the orientation of the sample. This probe locates the hinge states, and can be used to distinguish different types of chiral HOTIs. Second, we find that the average of the local Chern marker over a single surface, an observable related to the surface Hall conductivity known to be quantized in the infinite slab geometry, is nonuniversal for a finite surface. This is due to a nonuniversal contribution of the hinge states, previously unaccounted for, that distinguishes surfaces of chiral HOTIs from Chern insulators. Our findings are relevant to establish higher order topology in systems such as the axion insulator candidate EuIn_{2}As_{2}, and cold atomic realizations.

Chiral vortices and pseudoscalar condensation due to rotation

We investigate the influence of rotation on the dynamical chiral symmetry breaking in strongly interacting matter. We develop a self-consistent Bogoliubov-de Gennes-like theoretical framework to study the inhomogeneous chiral condensate and the possible chiral vortex state in rotating finite-size matter in four-fermion interacting theories. We show that for sufficiently rapid rotation in $2+1$ dimensions, the ground state can be a chiral vortex state, a type of topological defect in analogy to superfluids and superconductors. The vortex state exhibits pion condensation, providing a new mechanism to realize pseudoscalar condensation in strongly interacting matter.

Second-order topological phases protected by chiral symmetry

We study second-order topological insulators and semimetals characterized by chiral symmetry. We investigate topological phase transitions of a model for construction of the two-dimensional second-order topological insulators protected only by chiral symmetry. By the theory of the phase transitions, we propose a second-order topological semimetal and insulators with flat hinge bands in chiral-symmetric three-dimensional systems. The three-dimensional second-order topological phases can be obtained from the stacked two-dimensional second-order topological insulators with chiral symmetry. Moreover, we show that broken chiral symmetry in the three-dimensional second-order topological phase allows a second-order topological insulator with chiral hinge states. We also demonstrate the second-order topological phases by using a lattice model.

Chiral Higgs Mode in Nematic Superconductors.

Nematic superconductivity with spontaneously broken rotation symmetry has recently been reported in doped topological insulators, M_{x}Bi_{2}Se_{3} (M=Cu, Sr, Nb). Here we show that the electromagnetic (EM) response of these compounds provides a spectroscopy for bosonic excitations that reflect the pairing channel and the broken symmetries of the ground state. Using quasiclassical Keldysh theory, we find two characteristic bosonic modes in nematic superconductors: the nematicity mode and the chiral Higgs mode. The former corresponds to the vibrations of the nematic order parameter associated with broken crystal symmetry, while the latter represents the excitation of chiral Cooper pairs. The chiral Higgs mode softens at a critical doping, signaling a dynamical instability of the nematic state towards a new chiral ground state with broken time reversal and mirror symmetry. Evolution of the bosonic spectrum is directly captured by EM power absorption spectra. We also discuss contributions to the bosonic spectrum from subdominant pairing channels to the EM response.

Inverse-perovskites A3BO (A = Sr, Ca, Eu/B = Pb, Sn): A platform for control of Dirac and Weyl Fermions

Bulk Dirac electron systems have attracted strong interest for their unique magnetoelectric properties as well as their close relation to topological (crystalline) insulators. Recently, the focus has been shifting toward the role of magnetism in stabilizing Weyl fermions as well as chiral surface states in such materials. While a number of nonmagnetic systems are well known, experimental realizations of magnetic analogs are a key focus of current studies. Here, we report on the physical properties of a large family of inverse perovskites A3BO (A = Sr, Ca, Eu/B = Pb, Sn) in which we are able to not only stabilize 3D Dirac electrons at the Fermi energy but also chemically control their properties. In particular, it is possible to introduce a controllable Dirac gap, change the Fermi velocity, tune the anisotropy of the Dirac dispersion, and—crucially—introduce complex magnetism into the system. This family of compounds therefore opens up unique possibilities for the chemical control and systematic investigation of the fascinating properties of such topological semimetals.

Signatures of a Charge Density Wave Phase and the Chiral Anomaly in the Fermionic Material Cobalt Monosilicide CoSi

AbstractMaterials with topological electronic states have emerged as one of the most exciting discoveries of condensed quantum matter, hosting quasiparticles with extremely low effective mass and high mobility. Weyl materials contain such topological states in the bulk and additionally have a non‐trivial chiral charge. However, despite known quantum effects caused by these chiral states, the interplay between chiral states, and a charge density wave phase, an ordering of the electrons to a correlated phase is not experimentally explored. Indications for the formation of a charge density wave phase in the Weyl material cobalt monosilicide CoSi are observed. Furthermore, the typical signatures of the charge density wave phase together with typical signatures of Weyl fermions in magnetic field dependent electrical transport characterization are investigated. The charge density wave and the chiral contribution to the electrical magneto‐transport are separated as well as a suppression of the charge density wave phase is observed in magnetic fields.

Dynamical conductivity of the Fermi arc and the Volkov-Pankratov states on the surface of Weyl semimetals

Weyl semimetals are known to host massless surface states called Fermi arcs. These Fermi arcs are the manifestation of the bulk-edge correspondence in topological matter and thus are analogous to the topological chiral surface states of topological insulators. It has been shown that the latter, depending on the smoothness of the surface, host massive Volkov-Pankratov(VP) states that coexist with the chiral ones. Here, we investigate these VP states in the framework of Weyl semimetals, namely their density of states and magneto-optical response. We find the selection rules corresponding to optical transitions which lead to anisotropic responses to external fields. In the presence of a magnetic field parallel to the interface, the selection rules and hence the poles of the response functions are mixed.

Topological states on fractal lattices

We investigate the fate of topological states on fractal lattices. Focusing on a spinless chiral p-wave paired superconductor, we find that this model supports two qualitatively distinct phases when defined on a Sierpinski gasket. While the trivial phase is characterized by a self-similar spectrum with infinitely many gaps and extended eigenstates, the novel "topological" phase has a gapless spectrum and hosts chiral states propagating along edges of the graph. Besides employing theoretical probes such as the real-space Chern number, inverse participation ratio, and energy-level statistics in the presence of disorder, we develop a simple physical picture capturing the essential features of the model on the gasket. Extending this picture to other fractal lattices and topological states, we show that the p+ip state admits a gapped topological phase on the Sierpinski carpet and that a higher-order topological insulator placed on this lattice hosts gapless modes localized on corners.

Chiral asymmetry detected in a 2D array of permalloy square nanomagnets using circularly polarized x-ray resonant magnetic scattering

The sensitivity of circularly polarized x-ray resonant magnetic scattering (CXRMS) to chiral asymmetry has been demonstrated. The study was performed on a 2D array of Permalloy (Py) square nanomagnets of 700 nm lateral size arranged in a chess pattern, in a square lattice of 1000 nm lattice parameter. Previous x-ray magnetic circular dichroism photoemission electron microscopy (XMCD-PEEM) images on this sample showed the formation of vortices at remanence and a preference in their chiral state. The magnetic hysteresis loops of the array along the diagonal axis of the squares indicate a non-negligible and anisotropic interaction between vortices. The intensity of the magnetic scattering using circularly polarized light along one of the diagonal axes of the square magnets becomes asymmetric in intensity in the direction transversal to the incident plane at fields where the vortex states are formed. The asymmetry sign is inverted when the direction of the applied magnetic field is inverted. The result is the expected in the presence of an unbalanced chiral distribution. The effect is observed by CXRMS due to the interference between the charge scattering and the magnetic scattering.

Raman Scattering in Chiral-Pure and Racemic Phases of Tryptophan and Tyrosine Polycrystals

Raman spectra of tryptophan and tyrosine polycrystals have been analyzed in a wide spectral range by fiber-optic spectroscopy. The Raman spectra have been recorded with a BWS465-785H spectrometer in the spectral range of 0–2700 cm–1 using a 785-nm cw laser as an excitation source. Parameters of the Raman spectra are compared for three crystalline phase modifications of aromatic amino acids: left-handed, right-handed, and racemic phase. The presence of strong Raman satellites, the characteristics of which change depending on the type of the chiral phase state of amino acid, is found in the low-frequency Raman spectra of tryptophan and tyrosine amino acid lattices. The results obtained can be used for monitoring the chiral purity of bioactive preparations containing amino acids.

Topological phononic crystals

Valley phononic crystals (VPCs) and Weyl phononic crystals (WPCs) are two typical types of topological phononic crystals. The valleys are the pair of energy extrema at two inequivalent corners of the reduced Brillouin zone of the 2-D hexagonal materials. The valley pseudospin, as new degree of freedom in addition to charge and spin, may provide a great alternative to be used in information encoding and processing. VPCs are 2-D acoustic or elastic artificial materials with valleys, and chiral valley states and robust valley edge transport, can be exhibited in either the acoustic or elastic VPCs. Weyl semimetals are materials in which the electrons have linear dispersions in all directions while are doubly degenerate at single points, called the Weyl points, near the Fermi surface in 3-D momentum space. Weyl points also exist in 3-D phononic crystals for acoustic or elastic waves, referred to as WPCs. The surface arc states in the WPC, not only manifest the normal refraction, but also the negative refraction when turning from one surface to another. In either case, they are immune against reflection. Topological phononic crystals extend topological physics from microscopic scales to macroscopic scales, which may accelerate the practical application of the topological physics.

Chiral Optical Tamm States at the Interface between an All-Dielectric Polarization-Preserving Anisotropic Mirror and a Cholesteric Liquid Crystal

As a new localized state of light, the chiral optical Tamm state exists at the interface between a polarization-retaining anisotropic mirror and a substance with optical activity. Considering a hybrid structure comprising a metal-free polarization-preserving mirror and a cholesteric liquid crystal, we highlight the high Q factor arising from the all-dielectric framework. The intensity of localized light decreases exponentially with increasing distance from the interface. The penetration of the field into the cholesteric liquid crystal is essentially prohibited for wavelengths lying in the photonic bandgap and close to the cholesteric pitch length. The dielectric mirror has its own photonic bandgap. The energy transfer along the interface can be effectively switched off by setting the tangential wave vector to zero. The spectral behavior of the chiral optical Tamm state is observed both as reflection and transmission resonance. This Fano resonance is analogous to the Kopp–Genack effect. Our analytics are well in line with precise calculations, which may pave a new route for the future development of intelligent design for laser and sensing applications.