Chiral Order Research Articles

The chiral Lagrangian with three flavors and large-N_c sum rules

We reconsider the chiral Lagrangian with three-flavor baryon fields. A systematic analysis of all low-energy constants (LEC) that contribute to the axial-vector and pseudoscalar currents in the baryon octet and decuplet fields at next-to-leading order in the inverse number of colors (1/N_c) of QCD is performed. We study the correlation function consisting of axial-vector and scalar currents as well. While there are 4 LEC relevant at leading chiral order, the number of relevant LEC at subleading order is 23. For those a leading order large-N_c analysis predicts 3 and 18 sum rules respectively. At the next accuracy level the number of sum rules is reduced to 2 and 8. Our results are illustrated by a tree-level analysis of available axial-vector coupling constants and strong decay widths of the baryon decuplet states.

Anionic nickel and nitrogen effects in the chiral antiferromagnetic antiperovskite Mn3NiN.

Magnetic antiperovskites, having chiral noncollinear antiferromagnetic ordering, have shown remarkable properties that range from negative thermal expansion to anomalous Hall effects. Nevertheless, details on the electronic structure, related to the oxidation states and the octahedral center's site effects, are still scarce. Here, we show a theoretical study, based on first-principles calculations in the framework of density-functional theory (DFT), on the electronic properties associated with the nitrogen site effects on the structural, electronic, magnetic, and topological degrees of freedom. Thus, we show that the nitrogen vacancy increases the value of the anomalous Hall conductivity and retains the chiral Γ4g antiferromagnetic ordering. Moreover, we reveal, based on the Bader charges and the electronic structure analysis, the negative and positive oxidation states of the Ni- and Mn-sites, respectively. This is in agreement with the expected A3α+Bβ-Xδ- oxidation states to satisfy charge neutrality in antiperovskites, but the negative charge is rare for transition metals. Finally, we extrapolate our findings on the oxidation states to several Mn3BN compounds, showing that the antiperovskite structure is an ideal platform to encounter negative oxidation states for metals sitting at the corner B-sites.

Measurement as a Shortcut to Long-Range Entangled Quantum Matter

The preparation of long-range entangled states using unitary circuits is limited by Lieb-Robinson bounds, but circuits with projective measurements and feedback (``adaptive circuits'') can evade such restrictions. We introduce three classes of local adaptive circuits that enable low-depth preparation of long-range entangled quantum matter characterized by gapped topological orders and conformal field theories (CFTs). The three classes are inspired by distinct physical insights, including tensor-network constructions, multiscale entanglement renormalization ansatz (MERA), and parton constructions. A large class of topological orders, including chiral topological order, can be prepared in constant depth or time, and one-dimensional CFT states and non-abelian topological orders with both solvable and non-solvable groups can be prepared in depth scaling logarithmically with system size. We also build on a recently discovered correspondence between symmetry-protected topological phases and long-range entanglement to derive efficient protocols for preparing symmetry-enriched topological order and arbitrary CSS (Calderbank-Shor-Steane) codes. Our work illustrates the practical and conceptual versatility of measurement for state preparation.

A visible multi-response electrochemical sensor based on cellulose nanocrystals

Cellulose nanocrystals (CNCs), a renewable material extracted from plants, algae, and bacteria, form iridescent films with chiral nematic order. Here, we report stimuli-responsive CNC / polyaniline (PANI) composite films for use in optical and electrochemical sensing. CNC-PANI and CNC-glucose-PANI films with bright structural color were obtained by an optimized self-assembly process. The films responded to humidity, pH and organic solvents with a change in the reflection wavelength, change in visible structural color, and changes in conductivity. A two-layer, conductive CNC-PANI film was prepared and incorporated into a circuit, where it could respond to stimuli with a change in color and increased conductivity. Moreover, a PANI electrochromic device (ECD) with CNC films was fabricated for information encryption. With voltages up to 1.5 V, the color of the ECD changed from green to blue within 1 s, and the CNC pattern hidden inside appeared with good cyclability. The ECD can also be used for anti-counterfeiting due to the chiral nematic CNC pattern. This novel iridescent CNC-PANI film demonstrates the potential of visible electrochemical multi-sensing using natural, sustainable materials.

Orbital-Hybridization-Driven Charge Density Wave Transition in CsV3 Sb5 Kagome Superconductor.

Owing to its inherent non-trivial geometry, the unique structural motif of the recently discovered kagome topological superconductor AV3 Sb5 (A = K, Rb, Cs) is an ideal host of diverse topologically non-trivial phenomena, including giant anomalous Hall conductivity, topological charge order, charge density wave (CDW), and unconventional superconductivity. Despite possessing a normal-state CDW order in the form of topological chiral charge order and diverse superconducting gaps structures, it remains unclear how fundamental atomic-level properties and many-body effects including Fermi surface nesting, electron-phonon coupling, and orbital hybridization contribute to these symmetry-breaking phenomena. Here, the direct participation of the V3d-Sb5p orbital hybridization in mediating the CDW phase transition in CsV3 Sb5 is reported. The combination of temperature-dependent X-ray absorption and first-principles studies clearly indicates the inverse Star-of-David structure as the preferred reconstruction in the low-temperature CDW phase. The results highlight the critical role that Sb orbitals play and establish orbital hybridization as the direct mediator of the CDW states and structural transition dynamics in kagome unconventional superconductors. This is a significant step toward the fundamental understanding and control of the emerging correlated phases from the kagome lattice through the orbital interactions and provides promising approaches to novel regimes in unconventional orders and topology.

Ab initio nucleon-nucleus elastic scattering with chiral effective field theory uncertainties

Background: Effective interactions for nucleon-nucleus elastic scattering from first principles require the use of the same nucleon-nucleon interaction in the structure and reaction calculations and a consistent treatment of the relevant operators at each order.Purpose: Systematic investigations of the effect of truncation uncertainties of chiral nucleon-nucleon ($NN$) forces have been carried out for scattering observables in the two- and three-nucleons system as well as for bound-state properties of light nuclei. Here we extend this type of study to proton and neutron elastic scattering for $^{16}\mathrm{O}$ and $^{12}\mathrm{C}$.Methods: Using the frameworks of the spectator expansion of multiple scattering theory as well as the no-core shell model, we employ one specific chiral interaction from the LENPIC collaboration and consistently calculate the leading-order effective nucleon-nucleus interaction up to the third chiral order, from which we extract elastic scattering observables. Then we apply pointwise as well as correlated uncertainty quantification for the estimation of the chiral truncation error.Results: We calculate and analyze proton elastic scattering observables for $^{16}\mathrm{O}$ and $^{12}\mathrm{C}$ as well as neutron elastic scattering observables for $^{12}\mathrm{C}$ between 65 and 185 MeV projectile kinetic energy. We find in all cases qualitatively similar results for the chiral truncation uncertainties as in few-body systems and assess them using similar diagnostic tools. The order-by-order convergence of the scattering observables for $^{16}\mathrm{O}$ and $^{12}\mathrm{C}$ is very reasonable around 100 MeV, while for higher energies the chiral expansion parameter becomes too large for convergence. Comparing proton and neutron differential cross sections reveals that their description is comparable up to around 100 MeV. We also find a nearly perfect correlation between the differential cross section for neutron scattering and the $NN$ Wolfenstein amplitudes for small momentum transfers.Conclusions: The diagnostic tools for studying order-by-order convergence in observables in few-body systems can be employed for observables in nucleon-nucleus scattering with only minor modifications provided the momentum scale in the problems is not too large. We also find that the chiral $NN$ interaction on which our study is based gives a very good description of differential cross sections for $^{16}\mathrm{O}$ and $^{12}\mathrm{C}$ as low as 65-MeV projectile energy, particularly in the forward direction. In addition, the very forward direction of the neutron differential cross section mirrors the behavior of the $NN$ interaction amazingly well.

Effects of asymmetric geometry and surface defects on vortical configurations in mesoscopic superconducting loops

In the framework of the microscopic Bogoliubov–de Gennes theory, we investigate the vortical patterns of dominant chiral p-wave orders in mesoscopic asymmetric superconducting loops. For the case of rectangular samples with a small ratio of length to height Ny/Nx, a coreless skyrmionic-like mode containing separated one-component vortices can be obtained. With further increasing Ny/Nx, such a spatial structure is broken due to the aspect-radio effect, and singular vortices with point-like cores tend to appear. In addition, when an indentation defect is introduced at the outer boundary of a mesoscopic square or rectangular loop, the order modulations are strongly affected by the locations of the surface defect, and several peculiar vortical configurations inside the sample can be presented.

Omnidirectional flat bands in chiral magnonic crystals

The magnonic band structure of two-dimensional chiral magnonic crystals is theoretically investigated. The proposed metamaterial involves a three-dimensional architecture, where a thin ferromagnetic layer is in contact with a two-dimensional periodic array of heavy-metal square islands. When these two materials are in contact, an anti-symmetric exchange coupling known as the Dzyaloshinskii–Moriya interaction (DMI) arises, which generates nonreciprocal spin waves and chiral magnetic order. The Landau–Lifshitz equation and the plane-wave method are employed to study the dynamic magnetic behavior. A systematic variation of geometric parameters, the DMI constant, and the filling fraction allows the examination of spin-wave propagation features, such as the spatial profiles of the dynamic magnetization, the isofrequency contours, and group velocities. In this study, it is found that omnidirectional flat magnonic bands are induced by a sufficiently strong Dzyaloshinskii–Moriya interaction underneath the heavy-metal islands, where the spin excitations are active. The theoretical results were substantiated by micromagnetic simulations. These findings are relevant for envisioning applications associated with spin-wave-based logic devices, where the nonreciprocity and channeling of the spin waves are of fundamental and practical scientific interest.

Simulating Chiral Spin Liquids with Projected Entangled-Pair States.

Doubts have been raised on the representation of chiral spin liquids exhibiting topological order in terms of projected entangled pair states (PEPSs). Here, starting from a simple spin-1/2 chiral frustrated Heisenberg model, we show that a faithful representation of the chiral spin liquid phase is in fact possible in terms of a generic PEPS upon variational optimization. We find a perfectly chiral gapless edge mode and a rapid decay of correlation functions at short distances consistent with a bulk gap, concomitant with a gossamer long-range tail originating from a PEPS bulk-edge correspondence. For increasing bond dimension, (i)the rapid decrease of spurious features-SU(2) symmetry breaking and long-range tails in correlations-together with (ii)a faster convergence of the ground state energy as compared to state-of-the-art cylinder matrix-product state simulations involving far more variational parameters, prove the fundamental relevance of the PEPS ansatz for simulating systems with chiral topological order.

Collective excitations of fractional quantum Hall states in monolayer graphene

We study the collective excitations of fractional quantum Hall states in graphene. We focus on states which allow for chiral symmetry breaking orders, specifically antiferromagnetism and charge density wave order. We investigate numerically how the collective excitation spectra depend on filling and the flux attachment scheme for two classes of variational states, the T\"oke-Jain sequence and the Modak-Mandal-Sengupta sequence.

Schwinger boson theory of the J1, J2=J3 kagome antiferromagnet

We study the kagome antiferromagnet for quantum spin-1/2 with first J1, second J2 and third J3 neighbour exchanges, along the J2 = J3 = J line. We use Schwinger-boson mean-field theory for the precise determination of the phase diagram, and two different rewritings of the Hamiltonian to build an intuition about the origin of the transitions. The spin liquid obtained at J = 0 remains essentially stable over a large window, up to J = 1/3, because it is only weakly frustrated by the J term. Then at J = 1/2, the intermediate Z2 spin liquid condenses into a long-range chiral order because of the change of nature of local magnetic fluctuations. As a side benefit, our Hamiltonian rewriting offers an exact solution for the ground state of our model on a Husimi cactus.

Visualization of Chiral Electronic Structure and Anomalous Optical Response in a Material with Chiral Charge Density Waves.

Chiral materials have attracted significant research interests as they exhibit intriguing physical properties, such as chiral optical response, spin-momentum locking, and chiral induced spin selectivity. Recently, layered transition metal dichalcogenide 1T-TaS_{2} has been found to host a chiral charge density wave (CDW) order. Nevertheless, the physical consequences of the chiral order, for example, in electronic structures and the optical properties, are yet to be explored. Here, we report the spectroscopic visualization of an emergent chiral electronic band structure in the CDW phase, characterized by windmill-shaped Fermi surfaces. We uncover a remarkable chirality-dependent circularly polarized Raman response due to the salient in-plane chiral symmetry of CDW, although the ordinary circular dichroism vanishes. Chiral Fermi surfaces and anomalous Raman responses coincide with the CDW transition, proving their lattice origin. Our Letter paves a path to manipulate the chiral electronic and optical properties in two-dimensional materials and explore applications in polarization optics and spintronics.

Two types of charge order with distinct interplay with superconductivity in the kagome material CsV3Sb5

The kagome metals of the family AV3Sb5, featuring a unique structural motif, harbor an array of intriguing phenomena such as chiral charge order and superconductivity. CsV3Sb5 is of particular interest because it displays a double superconducting dome in the region of the temperature-pressure phase diagram where charge order is still present. However, the microscopic origin of such an unusual behavior remains an unsolved issue. Here, to address it, we combine high-pressure, low-temperature muon spin relaxation/rotation with first-principles calculations. We observe a pressure-induced threefold enhancement of the superfluid density, which also displays a double-peak feature, similar to the superconducting critical temperature. This leads to three distinct regions in the phase diagram, each of which features distinct slopes of the linear relation between superfluid density and the critical temperature. These results are attributed to a possible evolution of the charge order pattern from the superimposed tri-hexagonal Star-of-David phase at low pressures (within the first dome) to the staggered tri-hexagonal phase at intermediate pressures (between the first and second domes). Our findings suggest a change in the nature of the charge-ordered state across the phase diagram of CsV3Sb5, with varying degrees of competition with superconductivity.

Relations for low-energy coupling constants in baryon chiral perturbation theory derived from the chiral quark model

The quark model symmetry can be adopted to establish relations between the low-energy constants (LECs) in the baryon chiral perturbation theory ($\chi PT$) if one assumes that a baryon-baryon-meson coupling is described equivalently by a quark-quark-meson coupling at the quark level. Through the correspondence between the $SU(2)$ description and the $SU(3)$ description for the same coupling vertex at the quark level, we find some relations between the LECs in $SU(2)_{\chi PT}$ and $SU(3)_{\chi PT}$ up to the third chiral order. The $SU(3)_{\chi PT}$ LEC relations at the same order are also obtained. The numerical analysis roughly supports these relations. In the situation that the available experimental data are not enough, one may employ such constraints to reduce the number of LECs.

Quantum spin liquid with emergent chiral order in the triangular-lattice Hubbard model

The interplay between spin frustration and charge fluctuation gives rise to an exotic quantum state in the intermediate-interaction regime of the half-filled triangular-lattice Hubbard model, while the nature of the state is under debate. Using the density matrix renormalization group with SU(2)$_{\rm{spin}} \otimes $U(1)$_{\rm{charge}}$ symmetries implemented, we study the triangular-lattice Hubbard model defined on the long cylinder geometry up to circumference $W=6$. A gapped quantum spin liquid, with on-site interaction $9 \lesssim U / t \lesssim 10.75$, is identified between the metallic and the antiferromagnetic Mott insulating phases. In particular, we find that this spin liquid develops a robust long-range spin scalar-chiral correlation as the system length $L$ increases, which unambiguously unveils the spontaneous time-reversal symmetry breaking. In addition, the degeneracy of the entanglement spectrum supports symmetry fractionalization and spinon edge modes in the obtained ground state. The possible origin of chiral order in this intermediate spin liquid and its relation to the rotonlike excitations have also been discussed.

Effect of nonequilibrium order parameter on the optical response of superconductor Sr2RuO4

The breaking of time reversal symmetry of the superconducting pairings is expected to manifest itself through characteristic transport properties such as a non-zero Kerr angle which provides fingerprint of the quantum anomalous Hall state. In this work, we theoretically study the Kerr effect or the Hall-type response and also consider how this response is modified by the nonequilibrium shape of order parameter of the superconducting state due to the influence of the electromagnetic radiation for the most favorable candidates of chiral superconducting order parameters and of the non-chiral states in strontium ruthenate (Sr2RuO4). The unique sensitivity of the Hall-type response introduced above to different types of pairings can be used to identify the most favored pairing which is a serious doubt on the superconducting state of this material.

Discovery of charge density wave in a kagome lattice antiferromagnet.

A hallmark of strongly correlated quantum materials is the rich phase diagram resulting from competing and intertwined phases with nearly degenerate ground-state energies1,2. A well-known example is the copper oxides, in which a charge density wave (CDW) is ordered well above and strongly coupled to the magnetic order to form spin-charge-separated stripes that compete with superconductivity1,2. Recently, such rich phase diagrams have also been shown in correlated topological materials. In 2D kagome lattice metals consisting of corner-sharing triangles, the geometry of the lattice can produce flat bands with localized electrons3,4, non-trivial topology5-7, chiral magnetic order8,9, superconductivity and CDW order10-15. Although CDW has been found in weakly electron-correlated non-magnetic AV3Sb5 (A = K, Rb, Cs)10-15, it has not yet been observed in correlated magnetic-ordered kagome lattice metals4,16-21. Here we report the discovery of CDW in the antiferromagnetic (AFM) ordered phase of kagome lattice FeGe (refs. 16-19). The CDW in FeGe occurs at wavevectors identical to that of AV3Sb5 (refs. 10-15), enhances the AFM ordered moment and induces an emergent anomalous Hall effect22,23. Our findings suggest that CDW in FeGe arises from the combination of electron-correlations-driven AFM order and van Hove singularities (vHSs)-driven instability possibly associated with a chiral flux phase24-28, in stark contrast to strongly correlated copper oxides1,2 and nickelates29-31, in which the CDW precedes or accompanies the magnetic order.

Three-Dimensional Quantum Cellular Automata from Chiral Semion Surface Topological Order and beyond

We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (characterized by $U(1)_2$ Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on ${2^n}$-dimensional qudits that feature surface anyons described by $U(1)_{2^n}$ Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.

Net-proton number cumulant ratios as a function of beam energy from an expanding nonequilibrium chiral fluid

The beam energy scan program at RHIC provides data on net-proton number fluctuations with the goal to detect the QCD critical end point and first-order phase transition. Interpreting these experimental signals requires a vital understanding of the interplay of critical phenomena and the nonequilibrium dynamics of the rapidly expanding fireball. We study these aspects with a fluid dynamic expansion coupled to the explicit propagation of the chiral order parameter sigma via a Langevin equation. Assuming a sigma-proton coupling through an effective proton mass, we relate cumulants of the order parameter and the net-proton number at freeze-out and obtain observable cumulant ratios as a function of beam energy. We emphasize the role of the nonequilibrium first-order phase transition where a mixed phase with gradual freeze-out can significantly alter the cumulants. We find that the presence of a critical end point is clearly visible in the cumulant ratios for a relatively wide range of center-of-mass energies.

Cluster quantum Monte Carlo study of two-dimensional weakly coupled frustrated trimer antiferromagnets

We report results from spin trimer-based cluster quantum Monte Carlo simulations for the thermodynamic properties of two-dimensional frustrated quantum antiferromagnets that are composed of weakly-coupled three-spin (trimer) clusters. In particular, we consider the spin-1/2 kagome lattice with a strong breathing distortion, and the triangle-square lattice model proposed previously for the cuprate La${}_4$Cu${}_3$MoO${}_{12}$. For both cases, we demonstrate that an appropriately chosen trimer-based computational basis allows us to significantly reduce the quantum Monte Carlo sign problem down to the low-temperature regime. Besides exploring the thermodynamic behavior for the triangle-square lattice model we also assess a mean field theory-based prediction for the onset of chiral order. For the breathing distorted kagome lattice model, we observe a robust two-peak structure in the specific heat, both in the quantum spin liquid and the lattice-nematic regimes.