Chiral Order Parameter Research Articles

New interpretation of the chiral phase transition: Violation of the trilemma in QCD

We find that the chiral phase transition (chiral crossover) in QCD at physical point is triggered by big imbalance among three fundamental quantities essential for the QCD vacuum structure: susceptibility functions for the chiral symmetry, axial symmetry, and the topological charge. The balance, dobbed the QCD trilemma, is unavoidably violated when one of the magnitudes among them is highly dominated, or suppressed. Based on a three-flavor Nambu-Jona-Lasinio model, we explicitly evaluate the amount of violation of the QCD trilemma at physical point, and show that the violation takes place not only at vacuum, but even in a whole temperature regime including the chiral crossover epoch. This work confirms and extends the suggestion recently reported from lattice QCD with 2 flavors on dominance of the axial and topological susceptibilities left in the chiral susceptibility at high temperatures. It turns out that the imbalance is essentially due to the flavor symmetry violation of the lightest three flavors, and the flavor breaking specifically brings enhancement of the axial anomaly contribution in the chiral order parameter, while the the strength of the axial breaking and the transition rate of the topological charge are fairly insensitive to the flavor symmetry. The violation of QCD trilemma and its flavor dependence can be tested by lattice simulations with 2 + 1 flavors in the future, and would also give a new guiding principle to explore the flavor dependence of the chiral phase transition, such as the Columbia plot, including possible extension with external fields.

Cumulants of the chiral order parameter at lower RHIC energies

We study cumulants of the chiral order parameter as function of beam energy as a possible signal for the presence of a critical end point and first-order phase transition in the QCD phase diagram. We model the expansion of a heavy-ion collision by a fluid dynamic expansion coupled to the explicit propagation of the chiral order parameter sigma via a Langevin equation. We evolve the medium until a parametrized freeze-out condition is met where we calculate event-by-event fluctuations and cumulants of sigma which are expected to follow the trend of net-proton number cumulants. We emphasize the role of a nonequilibrium first-order phase transition: The presence of an unstable phase causes the well-known bending of the trajectories in the space of temperature and baryochemical potential. For these cases at lower beam energies, the system crosses the freeze-out line more than once, allowing us to calculate a range of cumulants for each initial condition which are overall enhanced for the second hit of the freeze-out line. We thus find not only the critical end point but also the phase transition of the underlying model clearly reflected in the cumulants. The impact of volume fluctuations is demonstrated to play a measurable role for fluid dynamical evolutions that last significantly long.

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.

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).

Nematicity Arising from a Chiral Superconducting Ground State in Magic-Angle Twisted Bilayer Graphene under In-Plane Magnetic Fields.

Recent measurements of the resistivity in magic-angle twisted bilayer graphene near the superconducting transition temperature show twofold anisotropy, or nematicity, when changing the direction of an in-plane magnetic field [Cao etal., Science 372, 264 (2021)SCIEAS0036-807510.1126/science.abc2836]. This was interpreted as strong evidence for exotic nematic superconductivity instead of the widely proposed chiral superconductivity. Counterintuitively, we demonstrate that in two-dimensional chiral superconductors the in-plane magnetic field can hybridize the two chiral superconducting order parameters to induce a phase that shows nematicity in the transport response. Its paraconductivity is modulated as cos(2θ_{B}), with θ_{B} being the direction of the in-plane magnetic field, consistent with experiment in twisted bilayer graphene. We therefore suggest that the nematic response reported by Cao etal. does not rule out a chiral superconducting ground state.

Chiral phase structure and critical end point in QCD

We map out the QCD phase structure at finite temperature and chemical potential for 2-flavour and 2+1-flavour QCD. This is done within a generalised functional approach to QCD put forward in [1]. Specifically we compute the quark propagator and the finite-temperature and density fluctuations of the gluon propagator and the quark-gluon vertex on the basis of precision data for vacuum correlation functions. The novel ingredient is the direct self-consistent computation of the DSEs for the three dominant dressings of the quark-gluon vertex, in contrast to the common use of STI-inspired vertices.For small densities the results for the chiral order parameter agree with the respective lattice and functional renormalisation group results, for large densities the present results are in a quantitative agreement with the latter, including the location of the critical end point.

K1/K⁎ enhancement as a signature of chiral symmetry restoration in heavy ion collisions

Based on the fact that the mass difference between the chiral partners is an order parameter of chiral phase transition and that the chiral order parameter reduces substantially at the chemical freeze-out point in ultra-relativistic heavy ion collisions, we argue that the production ratio of K1 over K⁎ in such collisions should be substantially larger than that predicted in the statistical hadronization model. We further show that while the enhancement effect might be contaminated by the relatively larger decrease of K1 meson than K⁎ meson during the hadronic phase, the signal will be visible through a systematic study on centrality as the kinetic freeze-out temperature is higher and the hadronic life time shorter in peripheral collisions than in central collisions.

Optical manipulation of domains in chiral topological superconductors

Optical control of chirality in chiral superconductors bears potential for future topological quantum computing applications. When a chiral domain is written and erased by a laser spot, the Majorana modes around the domain can be manipulated on ultrafast time scales. Here we study topological superconductors with two chiral order parameters coupled via light fields by a time-dependent real-space Ginzburg-Landau approach. Continuous optical driving, or the application of supercurrent, hybridizes the two chiral order parameters, allowing one to induce and control the superconducting state beyond what is possible in equilibrium. We show that superconductivity can even be enhanced if the mutual coupling between two order parameters is sufficiently strong. Furthermore, we demonstrate that short optical pulses with spot size larger than a critical one can overcome a counteracting diffusion effect and write, erase, or move chiral domains. Surprisingly, these domains are found to be stable, which might enable optically programmable quantum computers in the future.

Inducing and controlling superconductivity in the Hubbard honeycomb model using an electromagnetic drive

The recent successful experimental observation of quantum anomalous Hall effect in graphene under laser irradiation demonstrates the feasibility of controlling single-particle band structure by lasers. Here we study superconductivity in a Hubbard honeycomb model in the presence of an electromagnetic drive. We start with Hubbard honeycomb model in the presence of an electromagnetic field drive, both circularly and linearly polarized light and map it onto a Floquet $t\ensuremath{-}J$ model. We explore conditions on the drive under which one can induce superconductivity (SC) in the system. We study the Floquet $t\ensuremath{-}J$ model within the mean-field theory in the singlet pairing channel and explore superconductivity for small doping in the system using the Bogoliubov--de Gennes approach. We uncover several superconducting phases, which break lattice or time-reversal symmetries in addition to the standard U(1) symmetry. We show that the unconventional chiral SC order parameter ($d\ifmmode\pm\else\textpm\fi{}id$) can be driven to a nematic SC order parameter ($s+d$) in the presence of a circularly polarized light. The $d+id$ SC order parameter breaks time-reversal symmetry and is topologically nontrivial and supports chiral edge modes. We further show that the threefold nematic degeneracy can be lifted using linearly polarized light. Our work, therefore, provides a generic framework for inducing and controlling SC in the Hubbard honeycomb model, with possible application to graphene and other two-dimensional materials.

Universal Scaling Properties of QCD Close to the Chiral Limit

We present a lattice QCD based determination of the chiral phase transition temperature in QCD with two massless (up and down) and one strange quark having its physical mass. We propose and calculate two novel estimators for the chiral transition temperature for several values of the light quark masses, corresponding to Goldstone pion masses in the range of $58~{\rm MeV}\lesssim m_\pi\lesssim 163~{\rm MeV}$. The chiral phase transition temperature is determined by extrapolating to vanishing pion mass using universal scaling relations. After thermodynamic, continuum and chiral extrapolations we find the chiral phase transition temperature $T_c^0=132^{+3}_{-6}$ MeV. We also show some preliminary calculations that use the conventional estimator for the pseudo-critical temperature and compare with the new estimators for $T_c^0$. Furthermore, we show results for the ratio of the chiral order parameter and its susceptibility and argue that this ratio can be used to differentiate between $O(N)$ and $Z_2$ universality classes in a non-parametric manner.

Competing interactions and spin-vector chirality in spin chains

Studies of competing orders in 1D magnetic chains have attracted considerable attention in recent years, as the presence of long-range Heisenberg interactions is found to allow interesting quantum phase transitions. We investigate here the role of spin-orbit effects by considering spin-1/2 chains in the presence of both collinear and non-collinear long-range interactions. By employing exact diagonalization and density matrix renormalization group calculations we investigate the rich phase diagram of this system. We find transitions from collinear to transverse magnetic correlated order as the strength of the non-collinear coupling increases, accompanied by a jump in the vector spin chirality order parameter of the system. This shows that tuning long-range interactions allows control of the onset of sizable vector spin chirality in a system, which may be used to transmit information down the chain. We investigate the characteristic structure of the distinct phases and explore their possible physical implementation in different materials systems.

Surface chiral superconductivity in odd-parity nematic superconductors with magnetic impurities

We study odd-parity nematic superconductivity in doped topological insulators in presence of surface magnetic impurities. The peculiar surface subgap spectrum, characterized by a Majorana flatband, nodal cones and the surface states of the parent topological insulator, gives rise to an overall ferromagnetic RKKY interactions between the surface impurities. An additional coupling between the impurities and a preemptive chiral order parameter promote a surface time-reversal symmetry breaking solution at the surface of the system. We discuss the relevant scenarios and suggest to engineer surface chiral superconductivity by properly choosing magnetic adatoms with highly anisotropic exchange coupling.

A molecular dynamics study of epitaxy-induced chain orientation and ordering of isotactic polypropylene

Phase selective nucleation of single chain isotactic polypropylene (iPP) into specific crystalline polymorphs is enabled by heterogeneous nucleating agents. Molecular dynamics simulations were used to investigate the ordering of isolated iPP chains over ideal (α-iPP and β-iPP) and commercial (triphenodithiazine, TPDT) heterogeneous nucleating surfaces during the early stages of nucleation. The ordering of an iPP chain during nucleation is analyzed by following the evolution of helix conformations, chiral order parameter, chain orientation and radius of gyration. The results show that α-iPP and β-iPP have a greater tendency to select chirality. However, TPDT is the most efficient in orienting the chain because of bulky phenyl groups on its surface. Based on helix evolution and segment orientation, early-stage ordering of iPP on crystalline surfaces is proposed to proceed by two different routes; (i) CTEH (coil-to-extended helix) where helix formation and segment orientation occur simultaneously, and (ii) CTEC (coil-to-extended coil) where segment orientation occurs without helix formation, thus indicating multistage nucleation through an intermediate mesomorphic phase. Whereas, CTEC is the predominant ordering route on TPDT, both CTEC and CTEH occur simultaneously on α-iPP and β-iPP, emphasizing the important role of epitaxy in early-stage ordering during crystallization.

The effects of KSEA interaction on the ground-state properties of spin chains in a transverse field

The effects of symmetric helical interaction which is called the Kaplan, Shekhtman, Entin-Wohlman, and Aharony (KSEA) interaction on the ground-state properties of three kinds of spin chains in a transverse field have been studied by means of correlation functions and chiral order parameter. We find that the anisotropic transition of $XY$ chain in a transverse field ($XY$TF) disappears because of the KSEA interaction. For the other two chains, we find that the regions of gapless chiral phases in the parameter space induced by the DM or $XZY-YZX$ type of three-site interaction are decreased gradually with increase of the strength of KSEA interaction. When it is larger than the coefficient of DM or $XZY-YZX$ type of three-site interaction, the gapless chiral phases also disappear.

Impurity-Induced Anomalous Thermal Hall Effect in Chiral Superconductors.

Chiral superconductors exhibit novel transport properties that depend on the topology of the order parameter, topology of the Fermi surface, the spectrum of bulk and edge Fermionic excitations, and the structure of the impurity potential. In the case of electronic heat transport, impurities induce an anomalous (zero-field) thermal Hall conductivity that is easily orders of magnitude larger than the quantized edge contribution. The effect originates from branch-conversion scattering of Bogoliubov quasiparticles by the chiral order parameter, induced by potential scattering. The former transfers angular momentum between the condensate and the excitations that transport heat. The anomalous thermal Hall conductivity is shown to depend to the structure of the electron-impurity potential, as well as the winding number ν of the chiral order parameter Δ(p)=|Δ(p)|e^{iνϕ_{p[over ^]}}. The results provide quantitative formulas for interpreting heat transport experiments seeking to identify broken T and P symmetries, as well as the topology of the order parameter for chiral superconductors.

Spontaneous emergence of Josephson junctions in homogeneous rings of single-crystal Sr2RuO4

The chiral p-wave order parameter in Sr2RuO4 would make it a special case amongst the unconventional superconductors. A consequence of this symmetry is the possible existence of superconducting domains of opposite chirality. At the boundary of such domains, the locally suppressed condensate can produce an intrinsic Josephson junction. Here, we provide evidence of such junctions using mesoscopic rings, structured from Sr2RuO4 single crystals. Our order parameter simulations predict such rings to host stable domain walls across their arms. This is verified with transport experiments on loops, with a sharp transition at 1.5 K, which show distinct critical current oscillations with periodicity corresponding to the flux quantum. In contrast, loops with broadened transitions at around 3 K are void of such junctions and show standard Little–Parks oscillations. Our analysis demonstrates the junctions are of intrinsic origin and makes a compelling case for the existence of superconducting domains.

Gapless Chiral Superconducting (d + id)-Wave Phase in Strongly Correlated Layered Material with a Triangular Lattice

It is shown that interlayer electron tunneling in the quasi-two-dimensional ensemble of Hubbard fermions leads to the realization of the gapless superconducting phase with the chiral (d + id)-wave order parameter symmetry, not for a single value of sodium ion concentration, but in a wide range of concentrations. Precisely this situation corresponds to experimental data on the layered sodium cobaltite intercalated by water (NaxCoO2 ⋅ yH2O). Intra-atomic electron repulsion that determines the strong electron correlation regime leads to the representation of Hubbard fermions, the interaction of which ensures Cooper instability. Intersite intralayer interactions between fermions considerably affect the positions of nodal points of the chiral order parameter and change the critical concentration at which a topological transition occurs in the 2D system of Hubbard fermions.

Chiral two-dimensional p -wave superfluid from s -wave pairing in the Bose-Einstein-condensate regime

Twodimensional spin-orbit-coupled Fermi gases subject to s-wave pairing can be driven into a topological phase by increasing the Zeeman spin splitting beyond a critical value. In the topological phase, the system exhibits the hallmarks of chiral p-wave superfluidity, including exotic Majorana excitations. Previous theoretical studies of this realization of a twodimensional topological Fermi superfluid have focused on the BCS regime where the s-wave Cooper pairs are only weakly bound and, hence, the induced chiral p-wave order parameter has a small magnitude. Motivated by the goal to identify potential new ways for the experimental realization of robust topological superfluids in ultra-cold atom gases, we study the BCS-to-BEC crossover driven by increasing the Cooper-pair binding energy for this system. In particular, we obtain phase diagrams in the parameter space of two-particle bound-state energy and Zeeman spin-splitting energy. Ordinary characteristics of the BCS-to-BEC crossover, in particular the shrinking and eventual disappearance of the Fermi surface, are observed in the nontopological phase. In contrast, the topological phase retains all features of chiral p-wave superfluidity, including a well-defined underlying Fermi surface, even for large s-wave pair-binding energies. Compared to the BCS limit, the topological superfluid in the BEC regime turns out to be better realizable even for only moderate magnitude of spin-orbit coupling because the chiral p-wave order parameter is generally larger and remnants of s-wave pairing are suppressed. We identify optimal parameter ranges that can aid further experimental investigations and elucidate the underlying physical reason for the persistence of the chiral p-wave superfluid.

Properties of the H−T phase diagram of the 3−K phase in eutectic Sr2RuO4 -Ru: Evidence for chiral superconductivity

We use the Ginzburg-Landau theory for a chiral $p$-wave superconductor to describe the filamentary superconducting phase nucleating at temperatures higher than the bulk transition temperature near the interfaces between Ru metal and ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ in eutectic ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$-Ru. The peculiar phase diagram of magnetic field versus temperature shows very distinct properties for different directions of the magnetic field. A clear feature of the magnetic fields in the basal plane of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, perpendicular to the chiral axis ($c$ axis), is the occurrence of a second superconducting transition with a new order parameter visible as a zero-bias anomaly in tunneling spectroscopy. For the field along the $c$ axis of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, two transitions merge, indicating that the field drives the second-order parameter through the paramagnetic coupling to a chiral supercurrent. The resulting phenomenology shows that the assumption of a chiral superconducting order parameter in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ yields an image reproducing the qualitative properties observed in the experiment. This discussion is qualitatively analogous to the corresponding chiral even- and odd-parity channels.

Phase-field crystal for an antiferromagnet with elastic interactions.

We introduce a model which contains the essential elements to formulate and study antiferromagnetism, using the phase-field crystal framework. We focus on the question of how magneto-elastic coupling could lift the frustration in the two-dimensional hexagonal antiferromagnetic phase. Using simulations we observe a rich variety of different phases stable in this model. To characterize different phases we calculate the chiral order parameter and identify the scaling behavior of this order parameter. Furthermore, we observe that vortices appear and are stable close to the nonmagnetic defects. Finally, we studied the ferrimagnetic and spin-flop phase transition in the presence of an external magnetic field.