Chiral Order Parameter Research Articles

Variational MonteCarlo Study of the 1/9-Magnetization Plateau in Kagome Antiferromagnets.

Motivated by very recent experimental observations of the 1/9-magnetization plateaus in YCu_{3}(OH)_{6+x}Br_{3-x} and YCu_{3}(OD)_{6+x}Br_{3-x}, our study delves into the magnetic-field-induced phase transitions in the nearest-neighbor antiferromagnetic Heisenberg model on the kagome lattice using the variational MonteCarlo technique. We uncover a phase transition from a zero-field Dirac spin liquid to a field-induced magnetically disordered phase that exhibits the 1/9-magnetization plateau. Through a comprehensive analysis encompassing the magnetization distribution, spin correlations, chiral order parameter, topological entanglement entropy, ground-state degeneracy, Chern number, and excitation spectrum, we pinpoint the phase associated with this magnetization plateau as a chiral Z_{3} topological quantum spin liquid and elucidate its diverse physical properties.

Baryogenesis via QCD preheating with nonadiabatic baryon chemical potential

The chiral phase transition in QCD can be supercooled in the thermal history of the universe to be instantaneously out-of equilibrium, if QCD is coupled to a dark QCD sector exhibiting the dark chiral phase transition of the first order. In that case the QCD sigma meson field (as the chiral order parameter, or the light quark condensate) starts to roll in a nonadiabatic way down to the true QCD vacuum. Meanwhile a dynamic baryonic chemical potential can be generated solely within QCD, which is governed by the dynamic motion of the QCD sigma meson field, analogously to the spontaneous baryogenesis or the leptogenesis via the Higgs or axionlike relaxation scenario. When QCD is further allowed to communicate with a dark fermion with mass of order of 1 GeV and the baryon number violating coupling to neutron, the nonadiabatic QCD sigma motion along with the nonadiabatic baryon chemical potential can trigger the preheating and produce the baryon number asymmetry. We discuss this scenario in details to find that the QCD-induced dynamic baryon chemical potential plays a significant role for the QCD preheating and the baryogenesis, which yields the desired amount of the asymmetry today consistently with current astrophysical, cosmological, and terrestrial experimental constraints. Cosmological and phenomenological consequences characteristic to the present scenario are also addressed.

Anomalous Hall effects in chiral superconductors

We report theoretical results for the electronic contribution to thermal and electrical transport for chiral superconductors belonging to even or odd-parity E1 and E2 representations of the tetragonal and hexagonal point groups. Chiral superconductors exhibit novel properties that depend on the topology of the order parameter and Fermi surface, and—as we highlight—the structure of the impurity potential. An anomalous thermal Hall effect is predicted and shown to be sensitive to the winding number, ν, of the chiral order parameter via Andreev scattering that transfers angular momentum from the chiral condensate to excitations that scatter off the random potential. For heat transport in a chiral superconductor with isotropic impurity scattering, i.e., point-like impurities, a transverse heat current is obtained for ν = ±1, but vanishes for |ν| > 1. This is not a universal result. For finite-size impurities with radii of order or greater than the Fermi wavelength, R ≥ ℏ/pf, the thermal Hall conductivity is finite for chiral order with |ν|≥ 2, and determined by a specific Fermi-surface average of the differential cross-section for electron-impurity scattering. Our results also provide quantitative formulae for analyzing and interpreting thermal transport measurements for superconductors predicted to exhibit broken time-reversal and mirror symmetries.

Critical Opalescence and Its Impact on the Jet Quenching Parameter q^

Jet quenching parameter q^ is essential for characterizing the interaction strength between jet partons and nuclear matter. Based on the quark-meson model, we develop a new framework for calculating q^ at finite chemical potentials, in which q^ is related to the spectral function of the chiral order parameter. A mean field perturbative calculation up to the one-loop order indicates that the momentum broadening of jets is enhanced at both high temperature and high chemical potential, and approximately proportional to the parton number density in the partonic phase. We further investigate the behavior of q^ in the vicinity of the critical endpoint (CEP) by coupling our calculation with a recently developed equation of state that includes a CEP in the universality class of the Ising model, from which we discover the partonic critical opalescence, i.e., the divergence of scattering rate of jets and their momentum broadening at the CEP, contributed by scatterings via the σ exchange process. Hence, for the first time, jet quenching is connected with the search of CEP.

Phase structure of the on-shell parametrized 2+1 flavor Polyakov quark-meson model

Augmenting the improved chiral effective potential of the on-shell renormalized 2+1 flavor quark-meson (RQM) model with the Polyakov-loop potential that accounts for the deconfinement transition, we get the quantum chromodynamics (QCD)-like framework of the renormalized Polyakov quark-meson (RPQM) model. When the divergent quark one-loop vacuum term is included in the effective potential of the quark-meson (QM) model, its tree-level parameters, or the parameters fixed by the use of meson curvature masses, become inconsistent as the curvature masses involve the self-energy evaluations at zero momentum. Using the modified minimal subtraction method, the consistent chiral effective potential for the RQM model has been calculated after relating the counterterms in the on-shell scheme to those in the MS¯ scheme and finding the relations between the renormalized parameters of both the schemes where the physical (pole) masses of the π, K, η, and η′ pseudoscalar mesons and the scalar σ meson, the pion and kaon decay constants, have been put into the relation of the running couplings and mass parameter. Using the RPQM model and the PQM model with different forms for the Polyakov-loop potentials in the presence or the absence of the quark backreaction, we have computed and compared the effect of the consistent quark one-loop correction and the quark backreaction on the scaled chiral order parameter, the QCD phase diagrams, and the different thermodynamic quantities. The results have been compared with the 2+1 flavor lattice QCD data from the Wuppertal-Budapest Collaboration [ 73, ] and the HotQCD Collaboration []. Published by the American Physical Society 2024

Two-component nematic superconductivity in 4Hb-TaS2

Most superconductors have an isotropic, single component order parameter and are well described by the standard (BCS) theory for superconductivity. Unconventional, multiple-component superconductors are exceptionally rare and are much less understood. Here, we combine scanning tunneling microscopy and angle-resolved macroscopic transport for studying the candidate chiral superconductor, 4Hb-TaS2. We reveal quasi-periodic one-dimensional modulations in the tunneling conductance accompanied by two-fold symmetric superconducting critical field. The strong modulation of the in-plane critical field, Hc2, points to a nematic, unconventional order parameter. However, the imaged vortex core is isotropic at low temperatures. We suggest a model that reconciles this apparent discrepancy and takes into account previously observed spontaneous time-reversal symmetry breaking at low temperatures. The model describes a competition between a dominating chiral superconducting order parameter and a nematic one. The latter emerges close to the normal phase. Our results strongly support the existence of two-component superconductivity in 4Hb-TaS2 and can provide valuable insights into other systems with coexistent charge order and superconductivity.

Drastic magnetic-field-induced chiral current order and emergent current-bond-field interplay in kagome metals.

In kagome metals, the chiral current order parameter [Formula: see text] with time-reversal-symmetry-breaking is the source of various exotic electronic states, while the method of controlling the current order and its interplay with the star-of-David bond order [Formula: see text] are still unsolved. Here, we reveal that tiny uniform orbital magnetization [Formula: see text] is induced by the chiral current order, and its magnitude is prominently enlarged under the presence of the bond order. Importantly, we derive the magnetic-field ([Formula: see text])-induced Ginzburg-Landau (GL) free energy expression [Formula: see text], which enables us to elucidate the field-induced current-bond phase transitions in kagome metals. The emergent current-bond-[Formula: see text] trilinear coupling term in the free energy, [Formula: see text], naturally explains the characteristic magnetic-field sensitive electronic states in kagome metals, such as the field-induced current order and the strong interplay between the bond and current orders. The GL coefficients of [Formula: see text] derived from the realistic multiorbital model are appropriate to explain various experiments. Furthermore, we discuss the field-induced loop current orders in the square lattice models that have been studied in cuprate superconductors.

Transport phenomena in time-reversal symmetry-breaking Kagome superconductors

Recent studies have found that all three materials within the vanadium-based Kagome superconductors (<i>A</i>V<sub>3</sub>Sb<sub>5</sub>, <i>A</i> = K, Cs, Rb) exhibit time-reversal symmetry-breaking behaviors in the superconducting states. Among the three, the Josephson junctions structured Nb/K<sub>1–<i>x</i></sub>V<sub>3</sub>Sb<sub>5</sub>/Nb and RbV<sub>3</sub>Sb<sub>5</sub> show magnetic hysteresis below the superconducting transition temperature. In CsV<sub>3</sub>Sb<sub>5</sub>, there exists a zero-field superconducting diode effect, meaning the magnitude of the positive and negative superconducting critical current are different. We first discuss the similarities and differences among the three above-mentioned experiments. Then, we discuss the possible mechanisms responsible for the unconventional superconducting transport phenomena: such as chiral superconducting order parameter (d+id or p+ip), and chiral pair density waves arising from the coupling of the charge density waves and conventional superconducting states.

Microscopic origin of criticality at macroscale in QCD chiral phase transition

We reveal that the criticality of the chiral phase transition in QCD at the macroscale arises from the microscopic energy levels of its fundamental constituents, the quarks. We establish a novel relation between cumulants of the chiral order parameter (i.e., chiral condensate) and correlations among the energy levels of quarks (i.e., eigenspectra of the massless Dirac operator), which naturally leads to a generalization of the Banks-Casher relation. Based on this novel relation and through (2+1)-flavor lattice QCD calculations using the HISQ action with varying light quark masses in the vicinity of the chiral phase transition, we demonstrate that the correlations among the infrared part of the Dirac eigenspectra exhibit same universal scaling behaviors as expected of the cumulants of the chiral condensate. We find that these universal scaling behaviors extend up to the physical values of the up and down quark masses.

Optically Induced Symmetry Breaking Due to Nonequilibrium Steady State Formation in Charge Density Wave Material 1T-TiSe2.

The strongly correlated charge density wave (CDW) phase of 1T-TiSe2 is of interest to verify the claims of a chiral order parameter. Characterization of the symmetries of 1T-TiSe2 is critical to understand the origin of its intriguing properties. Here we use very low-power, continuous wave laser excitation to probe the symmetries of 1T-TiSe2 by using the circular photogalvanic effect. We observe that the ground state of the CDW phase (D3d) is achiral. However, laser excitation above a threshold intensity transforms 1T-TiSe2 into a nonequilibrium chiral phase (C3), which changes the electronic correlations in the material. The inherent sensitivity of the photogalvanic technique to structural symmetries provides evidence of the different optically driven phase of 1T-TiSe2, which allows us to assign symmetry groups to these states. Our work demonstrates that optically induced phase change can occur at extremely low optical intensities in strongly correlated materials, providing a pathway to engineer new phases using light.

Probing the QCD phase transition with hadron multiplicity ratios

We investigate the impact of a first-order chiral phase transition and critical point on hadron multiplicity ratios. We model the dynamical expansion of the hot and dense matter created in a heavy ion collision with a Bjorken hydrodynamics expansion coupled to the explicit evolution of the chiral order parameter at center-of-mass energies from 2 to 7 GeV. Hereby, the chiral dynamics is implemented using a Langevin equation including dissipation and noise. We find a strong enhancement of the entropy-per-baryon S/A at lowest energies which is created at the non-equilibrium first-order phase transition. By mapping the initial and final S/A to a hadron resonance gas, we can quantify the shift of hadron multiplicity ratios.

Chiral superconductivity in the doped triangular-lattice Fermi-Hubbard model in two dimensions

The triangular-lattice Fermi-Hubbard model has been extensively investigated in the literature due to its connection to chiral spin states and unconventional superconductivity. Previous simulations of the ground state of the doped system rely on quasi-one-dimensional lattices where true long-range order is forbidden. Here we simulate two-dimensional and quasi-one-dimensional triangular lattices using state-of-the-art Auxiliary-Field Quantum Monte Carlo. Upon doping a non-magnetic chiral spin state, we observe evidence of chiral superconductivity supported by long-range order in Cooper-pair correlation and a finite value of the chiral order parameter. With this aim, we first locate the transition from the metallic to the non-magnetic insulating phase and the onset of magnetic order. Our results pave the way towards a better understanding of strongly correlated lattice systems with magnetic frustration.

Chiral symmetry breaking and entropy production in Dean vortices

In toroidal pipes, the secondary flow in cross section is a mirror symmetric pair of counter-rotating axially oriented Dean vortices. This mirror symmetry is broken in helical pipes. We investigate in detail the mirror symmetry breaking in these secondary flows in going from toroidal to helical geometries. We quantify the degree of mirror symmetry breaking in helical flows by calculating both an (i) order-parameter − 1 ≤ χ ≤ 1 that measures the net integrated chirality of vortices in section and (ii) the entropy production due to both viscous shear forces and convection for Dean vortices as the Dean number and pitch of the helix are varied. We prove that the entropy production due to convective processes is always greater than that due to viscous shear, for stationary incompressible flows in the absence of body forces. For the same pipe radius and pipe curvature, fluid density, viscosity, and entrance flows, the vortex entropy production in the stationary state is minimized for helical conduits (for a given Dean number) with respect to that of toroidal pipes (zero pitch). The dissipation in the fluid flow due to Dean vortices decreases in going from a toroidal to a helical geometry, while the chiral order parameter tends to χ = ± 1 for finite values of the pitch as the Dean number is decreased.

Bulk evidence of anisotropic s-wave pairing with no sign change in the kagome superconductor CsV3Sb5

The recently discovered kagome superconductors AV3Sb5 (A = K, Rb, Cs) exhibit unusual charge-density-wave (CDW) orders with time-reversal and rotational symmetry breaking. One of the most crucial unresolved issues is identifying the symmetry of the superconductivity that develops inside the CDW phase. Theory predicts a variety of unconventional superconducting symmetries with sign-changing and chiral order parameters. Experimentally, however, superconducting phase information in AV3Sb5 is still lacking. Here we report the impurity effects in CsV3Sb5 using electron irradiation as a phase-sensitive probe of superconductivity. Our magnetic penetration depth measurements reveal that with increasing impurities, an anisotropic fully-gapped state changes to an isotropic full-gap state without passing through a nodal state. Furthermore, transport measurements under pressure show that the double superconducting dome in the pressure-temperature phase diagram survives against sufficient impurities. These results support that CsV3Sb5 is a non-chiral, anisotropic s-wave superconductor with no sign change both at ambient and under pressure.

The equilibrium and dynamical cumulants of QCD chiral order parameter with parametric Landau free energy

By linearly parameterizing the QCD Landau free energy near the critical point in the baryon chemical potential and temperature plane, we study the fluctuations of the QCD chiral order parameter field (the sigma field) in the equilibrium case and dynamical phase transition, respectively. By setting the system size to the typical size of the QGP fireball (approx 10^3 fm^3), we show that in the equilibrium case, the discontinuity of the order parameter in the first order phase transition region is replaced by smooth crossover, and the corresponding fluctuations are broadened. Meanwhile, the quartic cumulant kappa _4 of the sigma field is generally negative near the phase transition line. We further derive the dynamical evolution of the QCD Landau free energy in the Fokker–Plank framework, based on which we deduce the dynamical cumulants of the sigma field. Assuming the temperature decreases as a known function of time, we numerically evaluate the dynamical cumulants and confirm that the cumulants present clear memory effects. Moreover, the memory effects on the first order phase transition side is stronger than that on the crossover side, and the dynamical cumulants at the hypothetical freeze-out line present rich non-monotonic structures.

Stability of line-node semimetals with strong Coulomb interactions and properties of the symmetry-broken state

We study the stability and phenomenology of line-node semimetals in the presence of Coulomb interactions. Our results indicate a phase transition to a chiral insulating state that occurs at a finite interaction threshold, which we determine. We also compute the Landau levels for out-of-plane and in-plane magnetic fields in the symmetric and symmetry-broken phases. We find that the magnetic field couples to the chiral order parameter, implying that this degree of freedom can be manipulated in situ in experiments. Finally, we check the existence of edge states in the symmetry-broken phase. On the system's boundary, we note that the metallic ``drum-head'' states that exist in the symmetric phase are gapped out. However, the symmetry-broken phase permits topological defects in the macroscopic order parameter in the form of domain walls, which host metallic ``interface states.'' These consist of linelike gap-closings that occur on the two-dimensional interfaces.

Evidence for chiral superconductivity on a silicon surface

Tin adatoms on a Si(111) substrate with a one-third monolayer coverage form a two-dimensional triangular lattice with one unpaired electron per site. These electrons order into an antiferromagnetic Mott-insulating state, but doping the Sn layer with holes creates a two-dimensional conductor that becomes superconducting at low temperatures. Although the pairing symmetry of the superconducting state is currently unknown, the combination of repulsive interactions and frustration inherent in the triangular adatom lattice opens up the possibility of a chiral order parameter. Here we study the superconducting state of Sn/Si(111) using scanning tunnelling microscopy, scanning tunnelling spectroscopy and quasiparticle interference imaging. We find evidence for a doping-dependent superconducting critical temperature with a fully gapped order parameter, the presence of time-reversal symmetry breaking and a strong enhancement in zero-bias conductance near the edges of the superconducting domains. Although each individual piece of evidence could have a more mundane interpretation, our combined results suggest the possibility that Sn/Si(111) is an unconventional chiral d-wave superconductor.

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.

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.

Chiral superconductivity in UTe2 via emergent C4 symmetry and spin-orbit coupling

A lot of attention has been drawn to superconductivity in UTe$_2$, with suggestions of time-reversal symmetry breaking triplet chiral superconducting order parameter. The chirality of the order parameter has been attributed to an accidental near degeneracy of two superconducting components belonging to 1D irreps $B_{2u}$ and $B_{3u}$ of the relevant $D_{2h}$ point group, and it has been argued that the chiral $B_{2u}+iB_{3u}$ combination is selected by ferromagnetic fluctuations. In this work we present a possible explanation of the near-degeneracy as a result of an accidental $C_4$ symmetry of the band structure, with the superconducting order parameter belonging the 2D $E_u$ irrep of $D_{4h}$ that uniquely descends to the sought after $B_{2u}+iB_{3u}$ combination. We show that the $C_4$ symmetry is emergent at the level of the interactions using a renormalization group calculation and argue that the chiral combination of the order parameter is favored when spin-orbit coupling is added to the model.