Chiral Charge Research Articles

Global caustic and phase chirality reversal of the focused vortex beam.

We predict the reversal of the phase chirality before and after the focal plane during propagation based on ray tracing. The interference patterns of a focused vortex beam (FVB) and a plane beam during propagation verify the fact of phase chirality reversal through diffraction theoretical simulations and experiments. Also, we deduce an analytical expression for the caustic based on the ray equation, which effectively represents the change of the hollow light field during propagation. Simulation and experimental results demonstrate the effectiveness of the caustic in describing the variation of the global hollow dark spot radius. Furthermore, based on the caustic results at the focal plane, we customize FVBs with the same dark spot radii but different topological charges. Our research results reveal the characteristics of the light field and phase distribution of the FVB during propagation, which will expand our understanding of the properties of the FVB and provide a reference value for applications such as chiral particle manipulation and topological charge recognition.

Fermionic defects of topological phases and logical gates

We discuss the codimension-1 defects of (2+1)D bosonic topological phases, where the defects can support fermionic degrees of freedom. We refer to such defects as fermionic defects, and introduce a certain subclass of invertible fermionic defects called “gauged Gu-Wen SPT defects” that can shift self-statistics of anyons. We derive a canonical form of a general fermionic invertible defect, in terms of the fusion of a gauged Gu-Wen SPT defect and a bosonic invertible defect decoupled from fermions on the defect. We then derive the fusion rule of generic invertible fermionic defects. The gauged Gu-Wen SPT defects give rise to interesting logical gates of stabilizer codes in the presence of additional ancilla fermions. For example, we find a realization of the CZ logical gate on the (2+1)D \mathbb{Z}_2ℤ2 toric code stacked with a (2+1)D ancilla trivial atomic insulator. We also investigate a gapped fermionic interface between (2+1)D bosonic topological phases realized on the boundary of the (3+1)D Walker-Wang model. In that case, the gapped interface can shift the chiral central charge of the (2+1)D phase. Among these fermionic interfaces, we study an interesting example where the (3+1)D phase has a spatial reflection symmetry, and the fermionic interface is supported on a reflection plane that interpolates a (2+1)D surface topological order and its orientation-reversal. We construct a (3+1)D exactly solvable Hamiltonian realizing this setup, and find that the model generates the \mathbb{Z}_8ℤ8 classification of the (3+1)D invertible phase with spatial reflection symmetry and fermion parity on the reflection plane. We make contact with an effective field theory, known in literature as the exotic invertible phase with spacetime higher-group symmetry.

Recipe for single-pair-Weyl-points phonons carrying the same chiral charges

Recipe for single-pair-Weyl-points phonons carrying the same chiral charges

Intrinsic Triple Degeneracy Point Bounded by Nodal Surfaces in Chiral Photonic Crystal.

In periodic systems, band degeneracies are typically protected and classified by spatial symmetries. However, in photonic systems, the Γ point at zero frequency is an intrinsic degeneracy due to the polarization degree of freedom of electromagnetic waves. For chiral photonic crystals, such an intrinsic degeneracy carries ±2 chiral topological charge while having linear band dispersions, different from the general perception of charge-2 nodes being associated with quadratic dispersions. Here, we show that these topological characters originate from the spin-1 Weyl point at zero frequency node of triple degeneracy, due to the existence of an electrostatic flat band. Such a topological charge at zero frequency is usually buried in bulk band projections and has never been experimentally observed. To address this challenge, we introduce space-group screw symmetries in the design of chiral photonic crystal, which makes the Brillouin zone boundary an oppositely charged nodal surface enclosing the Γ point. As a result, the emergent Fermi arcs are forced to connect the projections of these topological singularities, enabling their experimental observation. The number of Fermi arcs then directly reveals the embedded topological charge at zero frequency.

Low Detection Limit Circularly Polarized Light Detection Realized by Constructing Chiral Perovskite/Si Heterostructures.

Chiral perovskites have been demonstrated as promising candidates for direct circularly polarized light (CPL) detection due to their intrinsic chirality and excellent charge transport ability. However, chiral perovskite-based CPL detectors with both high distinguishability of left- and right-handed optical signals and low detection limit remain unexplored. Here, a heterostructure, (R-MPA)2 MAPb2 I7 /Si (MPA = methylphenethylamine, MA = methylammonium) is constructed, to achieve high-sensitive and low-limit CPL detection. The heterostructures with high crystalline quality and sharp interface exhibit a strong built-in electric field and a suppressed dark current, not only improving the separation and transport of the photogenerated carriers but also laying a foundation for weak CPL signals detection. Consequently, the heterostructure-based CPL detector obtains a high anisotropy factor up to 0.34 with a remarkably low CPL detection limit of 890nWcm-2 under the self-driven mode. As a pioneering study, this work paves the way for designing high-sensitive CPL detectors that simultaneously have great distinguishing capability and low detection limit of CPL.

Spectroscopic visualization and phase manipulation of chiral charge density waves in 1T-TaS2

The chiral charge density wave is a many-body collective phenomenon in condensed matter that may play a role in unconventional superconductivity and topological physics. Two-dimensional chiral charge density waves provide the building blocks for the fabrication of various stacking structures and chiral homostructures, in which physical properties such as chiral currents and the anomalous Hall effect may emerge. Here, we demonstrate the phase manipulation of two-dimensional chiral charge density waves and the design of in-plane chiral homostructures in 1T-TaS2. We use chiral Raman spectroscopy to directly monitor the chirality switching of the charge density wave—revealing a temperature-mediated reversible chirality switching. We find that interlayer stacking favours homochirality configurations, which is confirmed by first-principles calculations. By exploiting the interlayer chirality-locking effect, we realise in-plane chiral homostructures in 1T-TaS2. Our results provide a versatile way to manipulate chiral collective phases by interlayer coupling in layered van der Waals semiconductors.

Nonperturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1) dimensions

In (1+1)D topological phases, unpaired Majorana zero modes (MZMs) can arise only if the internal symmetry group $G_f$ of the ground state splits as $G_f = G_b \times \mathbb{Z}_2^f$, where $\mathbb{Z}_2^f$ is generated by fermion parity, $(-1)^F$. In contrast, (2+1)D topological superconductors (TSC) can host unpaired MZMs at defects even when $G_f$ is not of the form $G_b \times \mathbb{Z}_2^f$. In this paper we study how $G_f$ together with the chiral central charge $c_-$ strongly constrain the existence of unpaired MZMs and the quantum numbers of symmetry defects. Our results utilize a recent algebraic characterization of (2+1)D invertible fermionic topological states, which provides a non-perturbative approach based on topological quantum field theory, beyond free fermions. We study physically relevant groups such as $\mathrm{U}(1)^f\rtimes H,\mathrm{SU}(2)^f \times H, \mathrm{U}(2)^f\rtimes H $, generic Abelian groups, as well as more general compact Lie groups, antiunitary symmetries and crystalline symmetries. We present an algebraic formula for the fermionic crystalline equivalence principle, which gives an equivalence between states with crystalline and internal symmetries. In light of our theory, we discuss several previously proposed realizations of unpaired MZMs in TSC materials such as Sr$_2$RuO$_4$, transition metal dichalcogenides and iron superconductors, in which crystalline symmetries are often important; in some cases we present additional predictions for the properties of these models.

Magneto-responsive optics in a chiral crystal with thermally triggered reversible phase transitions between chiral space groups.

Herein, a chiral charge transfer crystal that exhibits reversible phase transition between chiral space groups has been fabricated. When the phase switches from left-handed to right-handed chiral space group, more pronounced orbital angular momentum effects will be generated, where magneto-responsive optics are the opposite for chiral enantiomers. Moreover, circularly polarized light could enhance the chiral orbit of the crystal with the same spiral orientation to let spin have a better ability to resist external magnetic field. Thus, the magnetic field dependence of transmission and photoluminescence of chiral crystals are strongly dependent on the polarized state of incident light. Furthermore, by studying the coupling among spin, orbit, and circular photon, we obtained that the chiral orbit plays a key role in the coupling between the spin and circular photon. It is expected that this work could promote further exploration of organic chiral magneto-optical crystals in potential applications of sensing.

Decoupling intranode and internode scattering in Weyl fermions

A series of recent papers claimed that intranode scattering alone can contribute to positive longitudinal magnetoconductance (LMC) due to the chiral anomaly (CA) in Weyl semimetals (WSMs) in the quasiclassical limit. We revisit the problem of CA-induced LMC in WSMs in the quasiclassical limit and show that intranode scattering, by itself, does not result in enhancement of LMC. In the limit of zero internode scattering, chiral charge must remain conserved, which is shown to actually decrease LMC. Only in the presence of a finite nonzero internode scattering does one obtain a positive LMC due to nonconservation of the chiral charge. Even weak internode scattering suffices in generating positive LMC since it redistributes charges across both the nodes, although on a timescale larger than that of the intranode scattering. Our work is fundamental to correctly interpret the recent experiments on magnetoconductance in Weyl semimetals that claim to have observed chiral anomaly. Furthermore, our calculations reveal that, in contrast to recent works, in inhomogeneous WSMs strain-induced axial magnetic field ${B}_{5}$, by itself, leads to negative longitudinal magnetoconductance and a negative planar Hall conductance.

Fermiology of Chiral Cadmium Diarsenide CdAs2, a Candidate for Hosting Kramers-Weyl Fermions.

Nonmagnetic chiral crystals are a new class of systems hosting Kramers-Weyl Fermions, arising from the combination of structural chirality, spin-orbit coupling (SOC), and time-reversal symmetry. These materials exhibit nontrivial Fermi surfaces with SOC-induced Chern gaps over a wide energy range, leading to exotic transport and optical properties. In this study, we investigate the electronic structure and transport properties of CdAs2, a newly reported chiral material. We use synchrotron-based angle-resolved photoelectron spectroscopy (ARPES) and density functional theory (DFT) to determine the Fermiology of the (110)-terminated CdAs2 crystal. Our results, together with complementary magnetotransport measurements, suggest that CdAs2 is a promising candidate for novel topological properties protected by the structural chirality of the system. Our work sheds light on the details of the Fermi surface and topology for this chiral quantum material, providing useful information for engineering novel spintronic and optical devices based on quantized chiral charges, negative longitudinal magnetoresistance, and nontrivial Chern numbers.

Impact of the orbital current order on the superconducting properties of the kagome superconductors

Motivated by recent experimental evidences signalling the chiral charge order in the vanadium-based kagome superconductors, we theoretically investigate the impact of the chiral flux charge order over the experimental outcomes for the normal and the SC properties. It is revealed that the spectral weight on the Fermi surface (FS) is partially gaped by the chiral flux charge order with the reservation of the spectral weight on the $M$ points and the midpoint between the two adjacent $M$ points, resulting in the momentum-dependent energy gap being consistent with the recent experimental observations. More importantly, by considering the influence of the chiral flux charge order, we find that a conventional fully gapped SC pairing state evolves into a nodal gap feature for the spectral weight due to the spectral gap modulations on the FS. As a result, the U-shaped density of states (DOS) deforms to the V-shaped one along with the residual DOS near the Fermi energy. These results bear some resemblance to the experimental observations, and may serve as a promising proposal to mediate the divergent or seemingly contradictory experimental outcomes about the SC pairing symmetry.

Electrically controlled superconductor-to-failed insulator transition and giant anomalous Hall effect in kagome metal CsV3Sb5 nanoflakes

The electronic correlations (e.g. unconventional superconductivity (SC), chiral charge order and nematic order) and giant anomalous Hall effect (AHE) in topological kagome metals AV3Sb5 (A = K, Rb, and Cs) have attracted great interest. Electrical control of those correlated electronic states and AHE allows us to resolve their own nature and origin and to discover new quantum phenomena. Here, we show that electrically controlled proton intercalation has significant impacts on striking quantum phenomena in CsV3Sb5 nanodevices mainly through inducing disorders in thinner nanoflakes and carrier density modulation in thicker ones. Specifically, in disordered thin nanoflakes (below 25 nm), we achieve a quantum phase transition from a superconductor to a “failed insulator” with a large saturated sheet resistance for T → 0 K. Meanwhile, the carrier density modulation in thicker nanoflakes shifts the Fermi level across the charge density wave (CDW) gap and gives rise to an extrinsic-intrinsic transition of AHE. With the first-principles calculations, the extrinsic skew scattering of holes in the nearly flat bands with finite Berry curvature by multiple impurities would account for the giant AHE. Our work uncovers a distinct disorder-driven bosonic superconductor-insulator transition (SIT), outlines a global picture of the giant AHE and reveals its correlation with the unconventional CDW in the AV3Sb5 family.

Vortical effects in Dirac fluids with vector, chiral and helical charges

Helicity of free massless Dirac fermions is a conserved, Lorentz-invariant quantity at the level of the classical equations of motion. For a generic ensemble consisting of particles and antiparticles, the helical and chiral charges are different conserved quantities. The flow of helicity can be modelled by the helicity current, which is again conserved in the absence of interactions. Similar to the axial vortical effect which generates an axial (chiral) current, the helicity current is induced by vorticity in a finite temperature medium with vector (electrical) charge imbalance via the helical vortical effects, leading to new nondissipative transport phenomena. These phenomena lead to the appearance of a new hydrodynamic excitation, the helical vortical wave. Our results suggest the existence of a new type of triangle anomalies in QED which involve the helicity currents in addition to the standard vector and axial currents. Further exploiting the conservation of the helical current, we show that a finite helical chemical potential may be used to characterise thermodynamic ensembles of fermions similarly to, but independently of, the vector charge and chirality. We derive the pressure P for fermions at finite vector, axial and helical chemical potentials and show that the quantities arising in anomalous transport, including various vortical and circular conductivities and the shear-stress coefficients, can be obtained by differentiation of P with respect to the appropriate chemical potentials. Finally, we calculate the helicity relaxation time in the quark-gluon plasma above the crossover and show that it is similar to that for the axial charge.

Chiral broken symmetry descendants of the kagome lattice chiral spin liquid

The breaking of chiral and time-reversal symmetries provides a pathway to exotic quantum phenomena and topological phases. Recent work has extensively explored the resulting emergence of chiral charge orders and chiral spin liquids (CSLs) on the kagome lattice. Such CSLs are closely tied to bosonic fractional quantum Hall states with anyonic quasiparticles; however, their connection to nearby ordered states has remained a mystery. Here, we use spin-wave theory, parton Gutzwiller wave functions, and exact diagonalization to show that two distinct magnetic orders with uniform scalar chirality---the XYZ umbrella state and the octahedral spin crystal--emerge as competing orders in close proximity to the CSL. In this letter, we highlight the intimate link between a topologically ordered liquid and broken symmetry states with nontrivial real-space topology.

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.

From Entanglement Generated Dynamics to the Gravitational Anomaly and Chiral Central Charge.

We apply modular flow-entanglement generated dynamics-to characterize quantum orders of ground state wave functions. In particular, we study the linear response of the entanglement entropy of a simply connected region with respect to modular flow. First, we apply it to (1+1)D conformal field theories and demonstrate its relationship to the chiral central charge-or, equivalently, the perturbative gravitational anomaly-which is shown to vanish. Next, we apply it to (2+1)D gapped ground states where it reduces to a recently proposed formula by Kim etal. that is conjectured to compute the edge chiral central charge. Modular flow provides an intuitive picture for this conjecture based on bulk-edge correspondence. We also provide numerics on free-fermion models that lend support to our picture.

Modular Commutators in Conformal Field Theory.

The modular commutator is a recently discovered entanglement quantity that quantifies the chirality of the underlying many-body quantum state. In this Letter, we derive a universal expression for the modular commutator in conformal field theories in 1+1 dimensions and discuss its salient features. We show that the modular commutator depends only on the chiral central charge and the conformal cross ratio. We test this formula for a gapped (2+1)-dimensional system with a chiral edge, i.e., the quantum Hall state, and observe excellent agreement with numerical simulations. Furthermore, we propose a geometric dual for the modular commutator in certain preferred states of the AdS/CFT correspondence. For these states, we argue that the modular commutator can be obtained from a set of crossing angles between intersecting Ryu-Takayanagi surfaces.

Chirality-induced intrinsic charge rectification in a tellurium-based field-effect transistor

Chiral conductors exhibit spin-related charge rectification but its controllability is largely unexplored. Here, the authors combine chiral charge rectification with a field-effect transistor of tellurium. They demonstrate a gate-variable hundredfold enhancement of the rectification efficiency and enable quantitative comparison with theoretical calculations which considered chiral spin-momentum locking alongside the Zeeman effect. With this comparison across a wide range of temperature, an unexpected deviation from the conventional theory is revealed, which hints at the relevance of chirality-induced spin selectivity at higher temperatures.

Discovery of a maximally charged Weyl point

The hypothetical Weyl particles in high-energy physics have been discovered in three-dimensional crystals as collective quasiparticle excitations near two-fold degenerate Weyl points. Such momentum-space Weyl particles carry quantised chiral charges, which can be measured by counting the number of Fermi arcs emanating from the corresponding Weyl points. It is known that merging unit-charged Weyl particles can create new ones with more charges. However, only very recently has it been realised that there is an upper limit — the maximal charge number that a two-fold Weyl point can host is four — achievable only in crystals without spin-orbit coupling. Here, we report the experimental realisation of such a maximally charged Weyl point in a three-dimensional photonic crystal. The four charges support quadruple-helicoid Fermi arcs, forming an unprecedented topology of two non-contractible loops in the surface Brillouin zone. The helicoid Fermi arcs also exhibit the long-pursued type-II van Hove singularities that can reside at arbitrary momenta. This discovery reveals a type of maximally charged Weyl particles beyond conventional topological particles in crystals.

Single pair of multi-Weyl points in nonmagnetic crystals

Topological semimetal states having the minimal number, i.e., only a single pair, of Weyl points are desirable for the study of effects associated with chiral topological charges. So far, the search for such states is focused on magnetic spinful systems. Here, we find that nonmagnetic spinless systems can host a class of single-pair-Weyl-point (SP-WP) states, where the two Weyl points are located at two high-symmetry time-reversal-invariant momenta. We identify 32 candidate space groups that host such states, and we show that the chiral charge of each Weyl point in the SP-WP state must be an even integer. Besides achieving the minimal number, Weyl points in SP-WP states are far separated in momentum space, making the physics of each individual point better exposed. The large separation combined with the even topological charge lead to extended surface Fermi loops with a non-contractible winding topology on the surface Brillouin zone torus, distinct from conventional Weyl semimetals. We confirm our proposal in the phonon spectra of two concrete materials TlBO$_2$ and KNiIO$_6$. Our finding applies to a wide range of systems, including electronic, phononic, and various artificial systems. It offers a new direction for the search of ideal platforms to study chiral particles.