Chiral symmetry protected topological nodal superconducting phase and Majorana Fermi arc

With an external in-plane magnetic field, we show the emergence of a topological nodal superconducting phase of the two-dimensional topological surface states. This nodal superconducting phase is protected by the chiral symmetry with a non-zero magnetic field, and there are corresponding Majorana Fermi arcs(also known as flat band Andreev bound states) connecting the two Majorana nodes along the edges, similar to the case of Weyl semimetal. The topological nodal superconductor is an intermediate phase between two different chiral superconductors, and is stable against the effects of substrates. The two-dimensional effective theory of the nodal superconducting phase also captures the low energy behavior of a three-dimensional lattice model which describes the iron-based superconductor with a thin film geometry. The localizations of the Majorana nodes can be manipulated through external in-plane magnetic fields, which may introduce a non-trivial topological Berry phase between them.

Critical Behavior of Dynamical Chiral Symmetry Breaking with Gauge Boson Mass in QED3

Since the massless quantum electrodynamics in 2＋1 dimensions （QEDa） with nonzero gauge boson mass ζ can be used to explain some important traits of high-Tc superconductivity in planar cuprates, it is worthwhile to apply this model to analyze the nature of chiral phase transition at the critical value ζ. Based on the feature of chiral susceptibility, we show that the system at ζ exhibits a second-order phase transition which accords with the nature of appearance of the high-To superconductivity, and the estimated critical exponents around ζ are illustrated.

Chiral symmetry restoration and properties of Goldstone bosons at finite temperature

We study chiral symmetry restoration by analyzing thermal properties of QCD's(pseudo-)Goldstone bo-sons,especially the pion.The meson properties are obtained from the spectral densities of mesonic imaginary-time correlation functions.To obtain the correlation functions,we solve the Dyson-Schwinger equations and the inhomo-geneous Bethe-Salpeter equations in the leading symmetry-preserving rainbow-ladder approximation.In chiral limit,the pion and its partner sigma degenerate at the critical temperature T_(c).At T≥T_(c),it was found that the pion rapidly dissociates,which signals deconfinement phase transition.Beyond the chiral limit,the pion dissociation temperature can be used to define the pseudo-critical temperature of the chiral phase crossover,which is consistent with that ob-tained by the maximum point of chiral susceptibility.A parallel analysis for kaon and pseudoscalar ss suggests that heavymesons maysurviveabove T_(c).

Dynamical chiral symmetry breaking in NJL Model with a strong background magnetic field and Lorentz-violating extension of the Standard Model

The Eigenstate Method has been developed to deduce the fermion propagator with a constant external magnetic field. In general, we find its result is equivalent to other methods and this new method is more convenient,especially when one evaluates the contribution from the infinitesimal imaginary term of the fermion propagator. Using the Eigenstate Method we try to discuss whether the infinitesimal imaginary frequency of the fermion propagator in a strong magnetic field and Lorentz-violating extension of the minimal SU（3）×SU（2）×SU（1） Standard Model could have a significant influence on the dynamical mass. When the imaginary term of the fermion propagator in this model is not trivial（√（α-1）eB/3） 〈 σ 〈（√（α-1）2eB/3）, this model gives a correction to the dynamical mass.When one does not consider the influence from the imaginary term（σ 〉√（α-1）2eB/3）, there is another correction from the conventional term. Under both circumstances, chiral symmetry is broken.

Chiral symmetry restoration in excited hadrons and dense matter

We overview two interconnected topics： possible effective restoration of chiral symmetry in highly excited hadrons and possible existence of confined but chirally symmetric matter at low temperatures and high densities.

Chiral symmetry restoration and deconfinement in the contact interaction model of quarks with parallel electric and magnetic fields

We study the impact of steady,homogeneous,and external parallel electric and magnetic field strengths(eE||eB)on the chiral symmetry breaking-restoration and confinement-deconfinement phase transition.We also sketch the phase diagram of quantum chromodynamics(QCD)at a finite temperature T and in the presence of background fields.The unified formalism for this study is based on the Schwinger-Dyson equations,symmetry preserving vector-vector contact interaction model of quarks,and an optimal time regularization scheme.At T=0,in the purely magnetic case(i.e.,eE→0),we observe the well-known magnetic catalysis effect.However,in a pure electric field background(eB→0),the electric field tends to restore the chiral symmetry and deconfinement above the pseudo-critical electric field eE^(x,C)_(c).In the presence of both eE and eB,we determine the magnetic catalysis effect in the particular region where eB dominates over eE,whereas we observe the chiral inhibition(or electric chiral rotation)effect when eE overshadows eB.At finite T,in the pure electric field case,the phenomenon of inverse electric catalysis appears to exist in the proposed model.Conversely,for a pure magnetic field background,we observe the magnetic catalysis effect in the mean-field approximation and inverse magnetic catalysis with eB-dependent coupling.The combined effects of eE and eB on the pseudo-critical T^(x,C)_(c)yields an inverse electromagnetic catalysis,with and without an eB-dependent effective coupling of the model.The findings of this study agree well with the already predicted results obtained via lattice simulations and other reliable effective models of QCD.

Dark matter with chiral symmetry admixed with hadronic matterin compact stars

Using the two-fluid Tolman-Oppenheimer-Volkoff equation,the properties of dark matter(DM)admixed neutron stars(DANSs)have been investigated.In contrast to previous studies,we find that an increase in the maximum mass and a decrease in the radius of 1.4 M_(⊙)NSs can occur simultaneously in DANSs.This stems from the ability of the equation of state(EOS)for DM to be very soft at low density but very stiff at high density.It is well known that the IU-FSU and XS models are unable to produce a neutron star(NS)with a maximum mass greater than 2.0 M_(⊙).However,by considering the IU-FSU and XS models for DANSs,there are interactions with DM that can produce a maximum mass greater than 2.0 M_(⊙)and a radius of 1.4 M_(⊙)NSs below 13.7 km.When considering a DANS,the difference between DM with chiral symmetry(DMC)and DM with meson exchange(DMM)becomes obvious when the central energy density of DM is greater than that of nuclear matter(NM).In this case,the DMC model with a DM mass of 1000 MeV can still produce a maximum mass greater than 2.0 M_(⊙)and a radius of a 1.4 M_(⊙)NS below 13.7 km.Additionally,although the maximum mass of the DANS using the DMM model is greater than 2.0 M_(⊙),the radius of a 1.4 M_(⊙)NS can surpass 13.7 km.In the two-fluid system,the maximum mass of a DANS can be larger than 3.0 M_(⊙).Consequently,the dimensionless tidal deformabilityΛCP of a DANS with 1.4 M_(⊙),which increases with increasing maximum mass,may be larger than 800 when the radius of the 1.4 M_(⊙)DANS is approximately 13.0 km.

Viscosities in chiral symmetry breaking phase

In the chiral symmetry breaking phase described by the NJL model at quark level,along with the chiral symmetry restoration the ratio of shear viscosity to entropy density η/s drops down monotonously and reaches the minimum at the critical point,while the ratio of bulk viscosity to entropy density ζ/s behaves oppositely.

Transport properties of a ladder with two random dimer chains

We investigate the transport properties of a ladder with two random dimer （RD） chains. It is found that there are two extended states in the ladder with identical RD chains and a critical state regarded as an extended state in the ladder with pairing RD chains. Such a critical state is caused by the chiral symmetry. The ladder with identical RD chains can be decoupled into two isolated RD chains and the ladder with pairing RD chains can not. The analytic expressions of the extended states are presented for the ladder with identical RD chains.

Extension of Noether's theorem in PT-symmetry systems and its experimental demonstration in an optical setup

Noether’s theorem is one of the fundamental laws in physics,relating the symmetry of a physical system to its constant of motion and conservation law.On the other hand,there exist a variety of non-Hermitian parity-time(PT)-symmetric systems,which exhibit novel quantum properties and have attracted increasing interest.In this work,we extend Noether’s theorem to a class of significant PT-symmetry systems for which the eigenvalues of the PT-symmetry Hamiltonian HPTchange from purely real numbers to purely imaginary numbers,and introduce a generalized expectation value of an operator based on biorthogonal quantum mechanics.We find that the generalized expectation value of a time-independent operator is a constant of motion when the operator presents a standard symmetry in the PT-symmetry unbroken regime,or a chiral symmetry in the PT-symmetry broken regime.In addition,we experimentally investigate the extended Noether’s theorem in PT-symmetry single-qubit and two-qubit systems using an optical setup.Our experiment demonstrates the existence of the constant of motion and reveals how this constant of motion can be used to judge whether the PT-symmetry of a system is broken.Furthermore,a novel phenomenon of masking quantum information is first observed in a PT-symmetry two-qubit system.This study not only contributes to full understanding of the relation between symmetry and conservation law in PT-symmetry physics,but also has potential applications in quantum information theory and quantum communication protocols.

Extending the Truncated Dyson-Schwinger Equation to Finite Temperatures

In view of the properties of mesons in hot strongly interacting matter, the properties of the solutions of the truncated Dyson-Schwinger equation for the quark propagator at finite temperatures within the rainbow-ladder approximation are analysed in some detail. In Euclidean space within the Matsubara imaginary time formalism, the quark propagator is not longer a O(4) symmetric function and possesses a discrete spectrum of the fourth component of the momentum. This makes the treatment of the Dyson-Schwinger and Bethe-Salpeter equations conceptually different from the vacuum and technically much more involved. The question whether the interaction kernel known from vacuum calculations can be applied at finite temperatures remains still open. We find that, at low temperatures, the model interaction with vacuum parameters provides a reasonable description of the quark propagator, while at temperatures higher than a certain critical value Tc the interaction requires stringent modifications. The general properties of the quark propagator at finite temperatures can be inferred from lattice QCD (LQCD) calculations. We argue that, to achieve a reasonable agreement of the model calculations with that from LQCD, the kernel is to be modified in such a way as to screen the infra-red part of the interaction at temperatures larger than Tc . For this, we analyse the solutions of the truncated Dyson-Schwinger equation with existing interaction kernels in a large temperature range with particular attention on high temperatures in order to find hints to an adequate temperature dependence of the interaction kernel to be further implemented in the Bethe-Salpeter equation for mesons. This will allow investigating the possible in medium modifications of the meson properties as well as the conditions of quark deconfinement in hot matter.

A Universal Binding Mechanism in Molecular Covalent Bonding and Nucleon-Nucleon Interaction

In the hydrogen molecular ion, the kinetic energy lowering of the electron is associated with its delocalization due to electron exchange between the two protons of the molecule. This decrease in the kinetic energy of the exchanged electron in the hydrogen molecular ion and the decrease in the dynamical mass of the two exchanged pions in the nucleon-nucleon interaction are at the origin of the attraction mechanism in the molecular covalent bonding and in the nuclear interaction. Based on this unitary approach of the attraction mechanism, the formulas of molecular potential and central nucleon-nucleon potential were derived. The decrease in the mass of the exchanged pions in the nucleon-nucleon bound state, actually means the decrease in the mass of the nucleons. This nucleon mass decrease could be a manifestation of the partial chiral symmetry restoration in nuclear matter.

Parity-dependent unidirectional and chiral photon transfer in reversed-dissipation cavity optomechanics

Nonreciprocal elements,such as isolators and circulators,play an important role in classical and quantum information processing.Recently,strong nonreciprocal effects have been experimentally demonstrated in cavity optomechanical systems.In these approaches,the bandwidth of the nonreciprocal photon transmission is limited by the mechanical resonator linewidth,which is arguably much smaller than the linewidths of the cavity modes in most electromechanical or optomechanical devices.In this work,we demonstrate broadband nonreciprocal photon transmission in the reversed-dissipation regime,where the mechanical mode with a large decay rate can be adiabatically eliminated while mediating anti-PT-symmetric dissipative coupling with two kinds of phase factors.Adjusting the relative phases allows the observation of periodic Riemann-sheet structures with distributed exceptional points(Eps).At the Eps,destructive quantum interference breaks both theT-andP-inversion symmetry,resulting in unidirectional and chiral photon transmissions.In the reversed-dissipation regime,the nonreciprocal bandwidth is no longer limited by the mechanical mode linewidth but is improved to the linewidth of the cavity resonance.Furthermore,we find that the direction of the unidirectional and chiral energy transfer could be reversed by changing the parity of the Eps.Extending non-Hermitian couplings to a three-cavity model,the broken anti-PT-symmetry allows us to observe high-order Eps,at which a parity-dependent chiral circulator is demonstrated.The driving-phase controlled periodical Riemann sheets allow observation of the parity-dependent unidirectional and chiral energy transfer and thus provide a useful cell for building up nonreciprocal array and realizing topological,e.g.,isolators,circulators,or amplifiers.

声波超材料中D类拓扑的观测

Topological materials and metamaterials opened new paradigms to create and manipulate phases of matter with unconventional properties.Topological D-class phases(TDPs)are archetypes of the ten-fold classification of topological phases with particle-hole symmetry.In two dimensions,TDPs support propagating topological edge modes that simulate the elusive Majorana elementary particles.Furthermore,a piercing ofπ-flux Dirac-solenoids in TDPs stabilizes localized Majorana excitations that can be braided for the purpose of topological quantum computation.Such two-dimensional(2D)TDPs have been a focus in the research frontier,but their experimental realizations are still under debate.Here,with a novel design scheme,we realize 2D TDPs in an acoustic crystal by synthesizing both the particle-hole and fermion-like time reversal symmetries for a wide range of frequencies.The design scheme leverages an enriched unit cell structure with real-valued couplings that emulate the targeted Hamiltonian of TDPs with complex hoppings:A technique that could unlock the realization of all topological classes with passive metamaterials.In our experiments,we realize a pair of TDPs with opposite Chern numbers in two independent sectors that are connected by an intrinsic fermion-like timereversal symmetry built in the system.We measure the acoustic Majorana-like helical edge modes and visualize their robust topological transport,thus revealing the unprecedented D and DIII class topologies with direct evidence.Our study opens up a new pathway for the experimental realization of two fundamental classes of topological phases and may offer new insights in fundamental physics,materials science,and phononic information processing.

Extension/Compression-Controlled Complete Band Gaps in 2D Chiral Square-Lattice-Like Structures

Achieving tunable band gaps in a structure by external stimuli is of great importance in acoustic applications. This paper aims to investigate the tunability of band gaps in square-lattice-like elastic periodic structures that are usually not featured with notable band gaps. Endowed with chirality, the periodic structures here are able to undergo imperfection-insensitive large deformation under extension or compression. The influences of geometric parameters on band gaps are discussed via the nonlinear finite element method. It is shown that the band gaps in such structures with curved beams can be very rich and, more importantly, can be efficiently and robustly tuned by applying appropriate mechanical loadings without inducing buckling. As expected, geometry plays a more significant role than material nonlinearity does in the evolution of band gaps. The dynamic tunability of band gaps through mechanical loading is further studied. Results show that closing, opening, and shifting of band gaps can be realized by exerting real-time global extension or compression on the structure. The proposed periodic structure with well-designed chiral symmetry can be useful in the design of particular acoustic devices.

Quantifying the chiral magnetic effect from anomalous-viscous fluid dynamics

The Chiral Magnetic Effect（CME） is a macroscopic manifestation of fundamental chiral anomaly in a many-body system of chiral fermions, and emerges as an anomalous transport current in the fluid dynamics framework. Experimental observation of the CME is of great interest and has been reported in Dirac and Weyl semimetals. Significant efforts have also been made to look for the CME in heavy ion collisions. Critically needed for such a search is the theoretical prediction for the CME signal. In this paper we report a first quantitative modeling framework, Anomalous Viscous Fluid Dynamics（AVFD）, which computes the evolution of fermion currents on top of realistic bulk evolution in heavy ion collisions and simultaneously accounts for both anomalous and normal viscous transport effects. AVFD allows a quantitative understanding of the generation and evolution of CME-induced charge separation during the hydrodynamic stage, as well as its dependence on theoretical ingredients. With reasonable estimates of key parameters, the AVFD simulations provide the first phenomenologically successful explanation of the measured signal in 200 AGe V Au Au collisions.

Transition magnetic moments of J^P=3/2^+ decuplet to J^P=1/2^+ octet baryons in the chiral constituent quark model

In light of the developments of the chiral constituent quark model（χ^（CQM）） in studying low energy hadronic matrix elements of the ground-state baryons, we extend this model to investigate their transition properties.The magnetic moments of transitions from the J^P=3/2~＋ decuplet to J^P=1/2~＋ octet baryons are calculated with explicit valence quark spin, sea quark spin and sea quark orbital angular momentum contributions. Since the experimental data is available for only a few transitions, we compare our results with the results of other available models. The implications of other complicated effects such as chiral symmetry breaking and SU（3） symmetry breaking arising due to confinement of quarks are also discussed.

Restriction on the form of the quark anomalous magnetic moment from lattice QCD results

The quark anomalous magnetic moment(AMM)is dynamically generated through spontaneous chiral symmetry breaking.It has been revealed that,even though its exact form is still unknown,the quark AMM is essential to exploring quark matter properties and QCD phase structure under external magnetic fields.In this study,we take three different forms of the quark AMM and investigate its influence on the chiral phase transition under a magnetic field.In general,a negative(positive)quark AMM acts as a magnetic-catalyzer(magnetic-inhibitor)for chiral symmetry breaking.It is found that a constant quark AMM drives an unexpected 1st order chiral phase transition,a quark AMM proportional to the chiral condensate flips the sign on the chiral condensate,and a quark AMM proportional to the square of the chiral condensate suppresses the magnetic enhancement in the chiral condensate at finite temperatures while retaining the chiral crossover phase transition.We also evaluate the intrinsic temperature dependence of the effective AMM form by fitting the effective model result of the chiral condensate to lattice QCD data,which may have a nontrivial correlation with the chiral phase transition.

A semiclassical perspective on nuclear chirality

The application of the semiclassical description to a particle-core system with imbued chiral symmetry is presented.The classical features of the chiral geometry in atomic nuclei and the associated dynamics are investigated for various core deformations and single-particle alignments.Distinct dynamical characteristics are identified in specific angular momentum ranges,triaxiality and alignment conditions.Quantum observables will be extracted from the classical picture for a quantitative description of experimental data provided as numerical examples of the model’s performance.

Exploring the light-quark interaction

Two basic motivations for an upgraded JLab facility are the needs： to determine the essential nature of light-quark confinement and dynamical chiral symmetry breaking （DCSB）; and to understand nucleon structure and spectroscopy in terms of QCD＇s elementary degrees of freedom. During the next ten years a programme of experiment and theory will be conducted that can address these questions. We present a Dyson- Schwinger equation perspective on this effort with numerous illustrations, amongst them： an interpretation of string^breaking; a symmetry-preserving truncation for mesons; the nucleon＇s strangeness σ-term; and the neutron＇s charge distribution.