Chiral Order Research Articles

Circular Dichroism of Emergent Chiral Stacking Orders in Quasi-One-Dimensional Charge Density Waves.

Chirality-driven optical properties in charge density waves are of fundamental and practical importance. Here, we investigate the interaction between circularly polarized light and emergent chiral stacking orders in quasi-one-dimensional (quasi-1D) charge-density waves (CDWs) with density-functional theory calculations. In our specific system, self-assembled In nanowires on a Si(111) surface, spontaneous mirror symmetry breaking leads to four symmetrically distinct degenerate quasi-1D CDW structures, which exhibit geometrical chirality. Such geometrical chirality may naturally induce optically active phenomena even when the quasi-1D CDW structures are stacked perpendicular to the CDW chain direction. Indeed, we find that left- and right-chiral stacking orders show distinct circular dichroism responses while a nonchiral stacking order has no circular dichroism. Such optical responses are attributed to the existence of glide mirror symmetry of the CDW stacking orders. Our findings suggest that the CDW chiral stacking orders can lead to diverse active optical phenomena such as chirality-dependent circular dichroism, which can be observed in scanning tunneling luminescence measurements with circularly polarized light.

Bayesian parameter estimation in chiral effective field theory using the Hamiltonian Monte Carlo method

The number of low-energy constants (LECs) in chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$) grows rapidly with increasing chiral order, necessitating the use of Markov chain Monte Carlo techniques for sampling their posterior probability density function. For this we introduce a Hamiltonian Monte Carlo (HMC) algorithm and sample the LEC posterior up to next-to-next-to-leading order (NNLO) in the two-nucleon sector of $\ensuremath{\chi}\mathrm{EFT}$. We find that the sampling efficiency of HMC is three to six times higher compared to an affine-invariant sampling algorithm. We analyze the empirical coverage probability and validate that the NNLO model yields predictions for two-nucleon scattering data with largely reliable credible intervals, provided that one ignores the leading-order EFT expansion parameter when inferring the variance of the truncation error. We also find that the NNLO truncation error dominates the error budget.

Simulation of ring-exchange models with projected entangled pair states

Algorithms to simulate ring-exchange models on a square lattice using projected entangled pair states (PEPSs) are developed. We generalize the imaginary time evolution (ITE) method to optimize PEPS wave functions for the models with ring-exchange interactions. We compare the effects of different approximations of the environment. To understand the numerical instability during optimization, we introduce the ``singularity'' of a PEPS and develop a regulation procedure that can effectively reduce the singularity of a PEPS. We benchmark our method with the toric code model and obtain extremely accurate ground-state energies and topological entanglement entropy. We also benchmark our method with the two-dimensional cyclic ring-exchange model, and find that the ground state has a strong vector chiral order. The algorithms can be a powerful tool to investigate the models with ring interactions. The methods developed in this work, e.g., the regularization process to reduce the singularity, can also be applied to other models.

Anomalous Thermal Hall Effect in Chiral Phases of $$^3$$He-Aerogel

We report theoretical results for heat transport by quasiparticle excitations in superfluid $^3$He infused into silica aerogel engineered with uniaxial anisotropy. For this system two distinct equal spin pairing (ESP) superfluid phases have been reported based on NMR spectroscopy. Theoretical analysis predicts the first ESP state to be the chiral A phase with chiral axis aligned along the strain axis, and the lower temperature phase to be a polar-distorted chiral phase with random transverse fluctuations in the orientation of the chiral axis. We report calculations of heat transport for the high temperature chiral phase, including an anomalous (zero field) thermal Hall current originating from branch conversion scattering of Bogoliubov quasiparticles by the chiral order parameter induced by potential scattering by the silica aerogel. Observation of an anomalous thermal Hall current would provide a direct signature of the underlying chirality and topology of the superfluid phase of $^3$He in "stretched" silica aerogels.

Prediction of two-dimensional monolayer C2O2Fe with chiral magnetic and ferroelectric orders.

Low-dimensional multiferroics are highly desired for applications and contain exotic physical properties. Here we predict a two-dimensional material, C2O2Fe monolayer, through Fe intercalation in the graphene oxide monolayer. The crystal stable texture, chiral spin order, and ferroelectric polarization of the C2O2Fe monolayer are theoretically studied by considering the electron on-site Coulomb interaction and spin orbit coupling, which also manifests the ferroelectric polarization and reversal barrier at 30% biaxial tensile strain comparable with the other two-dimensional ferroelectric materials, such as GeS and GeSe. Moreover, first-principles calculations show that the polarization flipping is accompanied by spin orientation reversal, when the ferroelectric polarization is upward to the plane, a clockwise chiral antiferromagnetic ground state is obtained, while when the polarization is downward, the monolayer shows the anticlockwise chiral antiferromagnetic structure. In this sense, a strong electrically controlled magnetism exists in the designed C2O2Fe monolayer film.

Magnetovolume effects and thermal expansion in chiral helical ferromagnets Fe-=SUB=-1-x-=/SUB=-Co-=SUB=-x-=/SUB=-Si

Within the framework of the theory of band magnetism and the Heine model for the volume dependence of the electronic spectrum, an approach is being developed to study magneto-volume effects in chiral helical ferromagnets. Using Fe1-xCoxSi as an example, it was found that in the range of long-range order (at temperature T<Tc) the magnetovolume effect is determined by the amplitude of helicoidal spin spirals and leads to the experimentally observed negative volume thermal expansion coefficient. In the region of phase transitions of the first order (from Tc to Ts) prolonged in temperature, a new mechanism of the magnetovolume effect is established due to the spatial fluctuations of spin spirals arising due to the difference in the Hubbard potentials of iron and cobalt. It is shown that the considered volume effects lead not only to the experimentally observed negative volume thermal expansion coefficient (VCTE) in the chiral spin short-range order phase, but also to a noticeable increase in the transition temperature to the paramagnetic state (T>Ts). Keywords: helicoidal ferromagnetism, chirality, spin fluctuations, electronic and crystal structure, thermal expansion.

Магнитообъемные эффекты и тепловое расширение в киральных геликоидальных ферромагнетиках Fe-=SUB=-1-x-=/SUB=-Co-=SUB=-x-=/SUB=-Si

Within the framework of the theory of band magnetism and the Heine model for the volume dependence of the electronic spectrum, an approach is being developed to study magneto-volume effects in chiral helical ferromagnets. Using Fe1-хCoxSi as an example, it was found that in the range of long-range order (at temperature Т<Tc) the magnetovolume effect is determined by the amplitude of helicoidal spin spirals and leads to the experimentally observed negative volume thermal expansion coefficient. In the region of phase transitions of the first order (from Тс to Тs) prolonged in temperature, a new mechanism of the magnetovolume effect is established due to the spatial fluctuations of spin spirals arising due to the difference in the Hubbard potentials of iron and cobalt. It is shown that the considered volume effects lead not only to the experimentally observed negative volume thermal expansion coefficient (VCTE) in the chiral spin short-range order phase, but also to a noticeable increase in the transition temperature to the paramagnetic state (Т>Ts).

Directional scrambling of quantum information in helical multiferroics

Local excitations as carriers of quantum information spread out in the system in ways governed by the underlying interaction and symmetry. Understanding this phenomenon, also called quantum scrambling, is a prerequisite for employing interacting systems for quantum information processing. The character and direction dependence of quantum scrambling can be inferred from the out-of-time-ordered commutators (OTOCs) containing information on correlation buildup and entanglement spreading. Employing OTOC, we study and quantify the directionality of quantum information propagation in oxide-based helical spin systems hosting a spin-driven ferroelectric order. In these systems, magnetoelectricity permits the spin dynamics and associated information content to be controlled by an electric field coupled to the emergent ferroelectric order. We show that topologically nontrivial quantum phases, such as chiral or helical spin ordering, allow for electric-field controlled anisotropic scrambling and a direction-dependent buildup of quantum correlations. Based on general symmetry considerations, we find that starting from a pure state (e.g., the ground state) or a finite temperature state is essential for observing directional asymmetry in scrambling. In the systematic numerical studies of OTOC on finite-size helical multiferroic chains, we quantify the directional asymmetry of the scrambling and verify the conjectured form of the OTOC around the ballistic wavefront. The obtained direction-dependent butterfly velocity ${v}_{\mathrm{B}}(\mathbf{n})$ provides information on the speed of the ballistic wavefront. In general, our calculations show an early time power-law behavior of OTOC, as expected from an analytic expansion for small times. The long-time behavior of OTOC reveals the importance of (non)integrability of the underlying Hamiltonian as well as the implications of conserved quantities such as the $z$ projection of the total spin. The results point to the potential of spin-driven ferroelectric materials for the use in solid-state-based quantum information processing.

AbInitio Calculation of the Contact Operator Contribution in the Standard Mechanism for Neutrinoless Double Beta Decay.

Starting from chiral nuclear interactions, we evaluate the contribution of the leading-order contact transition operator to the nuclear matrix element (NME) of neutrinoless double-beta decay, assuming a light Majorana neutrino-exchange mechanism. The corresponding low-energy constant (LEC) is determined by fitting the transition amplitude of the nn→ppe^{-}e^{-} process to a recently proposed synthetic datum. We examine the dependence of the amplitude on similarity renormalization group scale and chiral expansion order of the nuclear interaction, finding that both dependences can be compensated to a large extent by readjusting the LEC. We evaluate the contribution of both the leading-order contact operator and standard long-range operator to the neutrinoless double-beta decays in the light nuclei ^{6,8}He and the candidate nucleus ^{48}Ca. Our results provide the first clear demonstration that the contact term enhances the NME in calculations with commonly used chiral two- plus three-nucleon interactions. In the case of ^{48}Ca, for example, the NME obtained with the EM(1.8/2.0) interaction is enhanced from 0.61 to 0.87(4), where the uncertainty is propagated from the synthetic datum.

Monolithic Chiral Nematic Organization of Cellulose Nanocrystals under Capillary Confinement.

We demonstrate bioenabled crack-free chiral nematic films prepared via a unidirectional flow of cellulose nanocrystals (CNCs) in the capillary confinement. To facilitate the uniform long-range nanocrystal organization during drying, we utilized tunicate-inspired hydrogen-bonding-rich 3,4,5-trihydroxyphenethylamine hydrochloride (TOPA) for physical cross-linking of nanocrystals with enhanced hydrogen bonding and polyethylene glycol (PEG) as a relaxer of internal stresses in the vicinity of the capillary surface. The CNC/TOPA/PEG film is organized as a left-handed chiral structure parallel to flat walls, and the inner volume of the films displayed transitional herringbone organization across the interfacial region. The resulting thin films also exhibit high mechanical performance compared to brittle films with multiple cracks commonly observed for capillary-formed pure CNC films. The chiral nematic ordering of modified TOPA-PEG-CNC material propagates through the entire thickness of robust monolithic films and across centimeter-sized surface areas, facilitating consistent, vivid iridescence, and enhanced circular polarization. The best performance that prevents the cracks was achieved for a CNC/TOPA/PEG film with a minimal, 3% amount of TOPA. Overall, we suggest that intercalation of small highly adhesive molecules to cellulose nanocrystal-polymer matrices can facilitate uniform flow of liquid crystal phase and drying inside the capillary, resulting in improvement of the ultimate tensile strength and toughness (77% and 100% increase, respectively) with controlled uniform optical reflection and enhanced circular polarization unachievable during regular drying conditions.

Analysis of Charge Order in the Kagome Metal AV_{3}Sb_{5} (A=K,Rb,Cs).

Motivated by the recent discovery of unconventional charge order, we develop a theory of electronically mediated charge density wave formation in the family of kagome metals AV_{3}Sb_{5} (A=K,Rb,Cs). The intertwining of van Hove filling and sublattice interference suggests a three-fold charge density wave instability at T_{CDW}. From there, the charge order forming below T_{CDW} can unfold into a variety of phases capable of exhibiting orbital currents and nematicity. We develop a Ginzburg Landau formalism to stake out the parameter space of kagome charge order. We find a nematic chiral charge order to be energetically preferred, which shows tentative agreement with experimental evidence.

Anisotropic microwave propagation in a reconfigurable chiral spin soliton lattice

We investigated microwave propagation in the chiral spin soliton lattice (CSL) phase of micrometer-sized crystals of the monoaxial chiral helimagnet ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$. An advantage of the CSL is that its periodicity can be reconfigured over a macroscopic length scale by means of an external magnetic field. Using a two-antenna microwave spectroscopy technique, we measured the anisotropic response of the transmitted microwaves via the spin dynamics of the CSL. When propagating along the direction parallel to the helical axis, the microwave amplitude increased up to a factor of twenty with decreasing the number of chiral soliton kinks. When the propagation direction was rotated by ${90}^{\ensuremath{\circ}}$ with regards to the helical axis, the microwave amplitude increased by one order of magnitude upon formation of the chiral helimagnetic order in the vicinity of zero magnetic field, exceeding that of the ferromagnetic phase above the critical field. Our findings open a novel route for controlling the characteristics of microwave propagation using noncollinear spin textures.

Chiral order and multiferroic domain relaxation in NaFeGe2O6

Controlling chiral magnetic domains in a multiferroic material is promising for applications in spintronics or data storage devices. The authors study the electric-field driven relaxation of multiferroic domains in NaFeGe${}_{2}$O${}_{6}$ as a function of temperature and electric field over several decades in time. An astonishingly simple combination of an Arrhenius-like temperature dependence with a Merz law for the electric-field dependence describes the relaxation times with only two parameters, indicating that multiferroic relaxation is essentially determined by domain-wall motion.

Monte Carlo studies on shape deformation and stability of 3D skyrmions under mechanical stresses

We study the stability/instability of skyrmions under mechanical stresses by Monte Carlo simulations in a 3D disk composed of tetrahedrons. Skyrmions emerge in chiral magnetic materials, such as FeGe and MnSi, under the competition of ferromagnetic interaction (FMI) and Dzyaloshinskii-Moriya interaction (DMI) and are stabilized by the external magnetic field. Recent experimental studies show that skyrmions are also stabilized/destabilized by uniaxial compressive stress perpendicular to or along the magnetic field direction. These phenomena are studied by using a 3D Finsler geometry (FG) model. In this 3D FG model, the DMI coefficient is automatically anisotropic by a geometrically implemented coupling of strains and electronic spins. We find that skyrmions are stabilized (destabilized) by extension (compression) stress along the direction of the applied magnetic field consistent with reported experimental data. This consistency implies that the 3D FG model successfully implements the magnetostrictive or magneto-elastic effect of external mechanical stresses on chiral magnetic orders, including the skyrmion configuration.

Low-energy effective theory and symmetry classification of flux phases on the kagome lattice

Motivated by recent experiments on AV$_3$Sb$_5$ (A=K,Rb,Cs), the chiral flux phase has been proposed to explain time-reversal symmetry breaking. To fully understand the physics behind the chiral flux phase, we construct a low-energy effective theory based on the van-Hove points around the Fermi surface. The possible symmetry-breaking states and their classifications of the low-energy effective theory are completely studied, especially the flux phases on Kagome lattice. In addition, we discuss the relations between the low-energy symmetry breaking orders, the chiral flux and charge bond orders. We find all possible 183 flux phases on Kagome lattice within 2*2 unit cell by brute-force approach and classify them by point group symmetry. Among the 183 phases, we find 3 classes in 1*1 unit cell, 8 classes in 1*2 unit cell and 18 classes in 2*2 unit cell, respectively. These results provide a full picture of the time-reversal symmetry breaking in Kagome lattices.

Competing phases and critical behaviour in three coupled spinless Luttinger liquids

We study electronic phase competition in a strongly correlated system of three coupled spinless Luttinger liquids—one of the simplest models where topologically nontrivial chiral orders may be realized. We study the problem as a coupled sine-Gordon model, using a perturbative renormalization group (RG) approach. In contrast with counterparts with fewer fermionic species, here the scaling procedure generates off-diagonal contributions to the phase stiffness matrix, which require both rescaling as well as large rotations of the bosonic fields. These rotations, generally non-abelian in nature, introduce a coupling between different interaction channels even at the tree-level order in the coupling constant scaling equations. We study competing phases in this system, taking into account the aforementioned rotations, and determine its critical behaviour in a variety of interaction parameter regimes where perturbative RG is possible. The phase boundaries are found to be of the Berezinskii–Kosterlitz–Thouless type, and we specify the parameter regimes where symmetry breaking between the three flavours of bosonic fields, orders involving different flavours, and chiral orders may be observed. Our approach and findings may be relevant for understanding phases and transitions at high magnetic fields in semimetals such as bismuth featuring three Fermi pockets.

Entropy-Driven Unconventional Crystallization of Spherical Colloidal Nanocrystals Confined in Wide Cylinders.

The densest packings of identical spherical colloidal nanocrystals in a thin cylinder generally give rise to confinement-induced chiral ordering. Here, we demonstrate that entropy can invalidate Pauling's packing rules for the nanocrystals confined in wide cylinders and novel ordered phases, where chiral ordering is broken, emerge. The nucleation and growth of spherical colloidal nanocrystals in the wide cylinders exhibit unique mechanisms which are distinctly different from that of thin ones. Furthermore, theoretical models which capture the essential physics of the ordering transitions are developed to reproduce the achiral ordering and reveal that the ordered phases are thermodynamically stable and stabilized through confinement-mediated entropic effect. These findings demonstrate that entropy arising from thermal motion can invalidate Pauling's packing rules of spherical colloidal nanocrystals confined in cylinders, which provides new insights into confinement physics of colloidal particles and might inspire nonintuitive design rules for the fabrication of novel ordered phases through confinement.

Spin Vortex Crystal Order in Organic Triangular Lattice Compound.

Organic salts represent an ideal experimental playground for studying the interplay between magnetic and charge degrees of freedom, which has culminated in the discovery of several spin-liquid candidates such as κ-(ET)_{2}Cu_{2}(CN)_{3} (κ-Cu). Recent theoretical studies indicate the possibility of chiral spin liquidsstabilized by ring exchange, but the parent states with chiral magnetic order have not been observed in this material family. In this Letter, we discuss the properties of the recently synthesized κ-(BETS)_{2}Mn[N(CN)_{2}]_{3} (κ-Mn). Based on analysis of specific heat, magnetic torque, and NMR measurements combined with abinitio calculations, we identify a spin-vortex crystal order. These observations definitively confirm the importance of ring exchange in these materials and support the proposed chiral spin-liquid scenario for triangular lattice organics.

Magnetotransport properties of chiral helimagnet Cr1/3NbS2 near phase transition

Many interesting physical phenomena emerge in the vicinity of phase transition temperature (Tc) for magnetic materials. However, it remains a big challenge to elucidate the near-Tc behaviors of chiral helimagnets, owing to their diversified magnetic interactions and complicated phase transitions. Here, we have systematically studied the near-Tc properties of a chiral helimagnet Cr1/3NbS2 by magnetotransport measurements with fine tuning of temperature and magnetic field. An anomalous positive magnetoresistance (MR) appears around the critical field (Hc) in a narrow temperature range (~ 128–132 K), which can be attributed to the competing scattering effects on electrons between the chiral magnetic order and thermal fluctuation near critical point. Moreover, the negative MR continues to increase even above Hc, and this behavior becomes more pronounced near Tc. Based on the MR results, a near-Tc magnetic phase diagram of Cr1/3NbS2 is presented, with a particular emphasis on the determination of internal phase boundary of chiral soliton lattice (CSL). This work gains an insight on the near-Tc behaviors of chiral magnetic materials and sheds light on the related electronic and spintronic applications.

Locating the critical endpoint of QCD: Mesonic backcoupling effects

We study the effects of pion and sigma meson backcoupling on the chiral order parameters and the QCD phase diagram and determine their effect on the location of the chiral critical endpoint. To this end, we solve a coupled set of truncated Dyson-Schwinger equations for Landau gauge quark and gluon propagators with ${N}_{\mathrm{f}}=2+1$ dynamical quark flavors and explicitly backcoupled mesons. The corresponding meson bound-state properties and the quark-meson Bethe-Salpeter vertices are obtained from their homogeneous Bethe-Salpeter equation. We find chiral-restoration effects of the pion and/or sigma meson backcoupling and observe a (small) shift of the critical endpoint towards smaller chemical potentials. The curvature of the chiral crossover line decreases. Our results indicate that the location of the critical endpoint in the phase diagram is mainly determined by the microscopic degrees of freedom of QCD (in contrast to its critical properties).