Starting from a general sixth-order nonlinear wave equation, we present its multiple kink solutions, which are related to the famous Hirota form. We also investigate the restrictions on the coefficients of this wave equation for possessing multiple kink structures. By introducing the velocity resonance mechanism to the multiple kink solutions, we obtain the soliton molecule solution and the breather-soliton molecule solution of the sixth-order nonlinear wave equation with particular coefficients. The three-dimensional image and the density map of these soliton molecule solutions with certain choices of the involved free parameters are well exhibited. After matching the parametric restrictions of the sixth-order nonlinear wave equation for having three-kink solution with the coefficients of the integrable bidirectional Sawada–Kotera–Caudrey–Dodd–Gibbons (SKCDG) equation, the breather-soliton molecule solution for the bidirectional SKCDG equation is also illustrated.

An integrable non-Hermitian generalized Rabi model is constructed. A twist matrix is introduced to the construction of Hamiltonian and generates the non-Hermitian properties. The Yang–Baxter integrability of the system is proven. The exact energy spectrum and eigenstates are obtained using the Bethe ansatz. The method given in this study provides a general way to construct integrable spin-boson models.

The solutions of the problems related to open quantum systems have attracted considerable interest. We propose a variational quantum algorithm to find the steady state of open quantum systems. In this algorithm, we employ parameterized quantum circuits to prepare the purification of the steady state and define the cost function based on the Lindblad master equation, which can be efficiently evaluated with quantum circuits. We then optimize the parameters of the quantum circuit to find the steady state. Numerical simulations are performed on the one-dimensional transverse field Ising model with dissipative channels. The result shows that the fidelity between the optimal mixed state and the true steady state is over 99%. This algorithm is derived from the natural idea of expressing mixed states with purification and it provides a reference for the study of open quantum systems.

Understanding why the scale of emergent hadron mass is obvious in the proton but hidden in the pion may rest on mapping the distribution functions (DFs) of all partons within the pion and comparing them with those in the proton; and since glue provides binding in quantum chromodynamics, the glue DF could play a special role. Producing reliable predictions for the proton's DFs is difficult because the proton is a three-valence-body bound-state problem. As sketched herein, the situation for the pion, a two-valence-body problem, is much better, with continuum and lattice predictions for the valence-quark and glue DFs in agreement. This beginning of theory alignment is timely because experimental facilities now either in operation or planning promise to realize the longstanding goal of providing pion targets, thereby enabling precision experimental tests of rigorous theory predictions concerning Nature's most fundamental Nambu–Goldstone bosons.

We provide a concise review on recent theory advancements towards full-fledged (3+1)D dynamical descriptions of relativistic nuclear collisions at finite baryon density. Heavy-ion collisions at different collision energies produce strongly coupled matter and probe the QCD phase transition at the crossover, critical point, and first-order phase transition regions. Dynamical frameworks provide a quantitative tool to extract properties of hot QCD matter and map fireballs to the QCD phase diagram. Outstanding challenges are highlighted when confronting current theoretical frameworks with current and forthcoming experimental measurements from the RHIC beam energy scan programs.

We revisit the laser-intensity-dependent ionization and fragmentation yields of C$_{60}$ molecules irradiated by 25-fs, 798-nm laser pulses based on the approach in which photoions are measured via a velocity map imaging spectrometer working in a time-sliced mode. This approach dramatically improves the signal-to-background ratio compared to those using a simple (traditional) time-of-flight mode (spectrometer), and thus allows us to measure the laser-intensity dependences down to a previously untouched region, which is expected to provide new insights into the intense-field ionization and fragmentation of C$_{60}$. Indeed, we find that the saturation intensities for C$_{60}$ ionizations and the onset intensity for C$_{60}$ fragmentation are much lower than those reported in previous experiments. Furthermore, the derived saturation-intensity dependence on charge distribution demonstrates the validity of the over-the-barrier ionization using a conducting sphere model.

A photon source with high-dimensional entanglement is able to bring increasing capacity of information in quantum communication. The dimensionality is determined by the chosen degree of freedom of the photons and is limited by the complexity of the physical systems. Here we propose a new type of high-dimensional entangled photon source, generated via path-indistinguishable scheme from a two-dimensional atomic cloud, which is prepared in a magneto-optical trap. To verify the photon source, we demonstrate experimentally the quantum state of the single photons heralded by its partner photon, with homodyne tomographic technology.

We propose a controllable exponential-Cosine Gaussian vortex (ECGV) beam, which can evolve into the different beam profiles with three parameters: distance modulation factor (DMF), split modulation factor (SMF) and rotation modulation factor (RMF). When SMF is 0, the ECGV beam appears as a perfect single-ring vortex beam and the ring radius can be adjusted by the DMF. We deduce from mathematics and give the reason for the single-ring characteristics. When SMF is not 0, the beam splits symmetrically. DMF, SMF and RMF control the number, distance and rotation angle of the split, respectively. Our experiments verify the correctness of the theory.

It is well known that spatial symmetry in a photonic crystal (PhC) slab is capable of creating bound states in the continuum (BICs), which can be characterized by topological charges of polarization vortices. Here, we show that when a PT-symmetric perturbation is introduced into the PhC slab, a new type of BICs ($pt$-BICs) will arise from each ordinary BIC together with the creation of rings of lasing threshold modes with $pt$-BICs embedded in these rings. Different from ordinary BICs, the $Q$-factor divergence rate of a $pt$-BIC is reduced and anisotropic in momentum space. Also, $pt$-BICs can even appear at off-high symmetry lines of the Brillouin zone. The $pt$-BICs also carry topological charges and can be created or annihilated with the total charge conserved. A unified picture on $pt$-BICs and the associated lasing threshold modes is given based on the temporal coupled mode theory. Our findings reveal the new physics arising from the interplay between PT symmetry and BIC in PhC slabs.

We theoretically study the Casimir interaction between Weyl semimetals. When the distance $a$ between semi-infinite Weyl semimetals is in the micrometer regime, the Casimir attraction can be enhanced by the chiral anomaly. The Casimir attraction depends sensitively on the relative orientations between the separations ($\boldsymbol{b}_1$, $\boldsymbol{b}_2$) of Weyl nodes in the Brillouin zone and show anisotropic behavior for the relative orientation of these separations ($\boldsymbol{b}_1$, $\boldsymbol{b}_2$) when they orient parallel to the interface. This anisotropy is quite larger than that in conventional birefringent materials. The Casimir force can be repulsive in the micrometer regime if the Weyl semimetal slabs are sufficiently thin and the direction of Weyl nodes separations ($\boldsymbol{b}_1$, $\boldsymbol{b}_2$) is perpendicular to the interface. The Casimir attraction between Weyl semimetal slabs decays slower than $1/a^4$ when the Weyl nodes separations $\boldsymbol{b}_1$ and $\boldsymbol{b}_2$ are both parallel to the interface.

The excitation condition of reversed shear Alfvén eigenmodes (RSAEs) has been investigated during sawtooth-like oscillation in the EAST tokamak. The sawtooth-like phenomena can be reproduced in the configuration of reversed magnetic shear, and the threshold gradient of electron temperature is formed accordingly, together with the increasing of the confinement of thermal particles. The distribution function of energetic ions density is altered dramatically when the neutral beam is switched from NBI1L (tangent) to NBI1R (perpendicular), which can be captured by the measurement of radial neutron camera. The RSAEs are excited easily in the vicinity of $q_{\min}$ (1.99 m $\leq R \leq 2.06$ m) for the injection of neutral beam with perpendicular direction, which should be excited by the steep gradient of energetic ions density. Furthermore, the excitation of RSAEs and the formation of threshold gradient of electron temperature can take place concurrently, which means that the neutral beam with perpendicular injection is beneficial for the establishment of internal transport barrier.

The kinetic effects of thermal particles and fast ions on internal kink (IK) mode are numerically investigated by the MHD-kinetic hybrid code MARS-K. It is shown that either thermal particles or fast ions have stabilizing influence on IK. However, the former can not fully stabilize IK, and the later can suppress the IK. In addition, the synergistic effect from thermal particles and fast ions induces more stronger damping on IK. The kinetic effects from particles significantly raise the critical value of poloidal beta ($\beta_{\rm p}^{\rm crit}$) for driving IK in the toroidal plasma. This implies a method of controlling IK or sawtooth in the high-$\beta_{\rm p}$ discharge scenario of tokamak. It is noted that, at the $q=1$ rational surface, mode structure becomes more sharp due to the self-consistent modification by particles' kinetic effect.

Semiconductivity and superconductivity are remarkable quantum phenomena that have immense impact on science and technology, and materials that can be tuned, usually by pressure or doping, to host both types of quantum states are of great fundamental and practical significance. Here we show by first-principles calculations a distinct route for tuning semiconductors into superconductors by diverse large-range elastic shear strains, as demonstrated in exemplary cases of silicon and silicon carbide. Analysis of strain driven evolution of bonding structure, electronic states, lattice vibration, and electron-phonon coupling unveils robust pervading deformation induced mechanisms auspicious for modulating semiconducting and superconducting states under versatile material conditions. This finding opens vast untapped structural configurations for rational exploration of tunable emergence and transition of these intricate quantum phenomena in a broad range of materials.

The heavy fermion ferromagnet CeRh$_6$Ge$_4$ is the first example of a clean stoichiometric system where the ferromagnetic transition can be continuously suppressed by hydrostatic pressure to a quantum critical point. In order to reveal the outcome when the magnetic lattice of CeRh$_6$Ge$_4$ is diluted with non-magnetic atoms, this study reports comprehensive measurements of the physical properties of both single crystal and polycrystalline samples of La$_x$Ce$_{1-x}$Rh$_6$Ge$_4$. With increasing $x$, the Curie temperature decreases, and no transition is observed for $x > 0.25$, while the system evolves from exhibiting coherent Kondo lattice behaviors at low $x$ to the Kondo impurity scenario at large $x$. Moreover, non-Fermi liquid behavior is observed over a wide doping range, which agrees well with the disordered Kondo model for $0.52 \leq x \leq 0.66$, while strange metal behavior is revealed in the vicinity of $x_{\rm c} = 0.26$.

The competition between the RKKY interaction and the Kondo effect leads to a magnetic phase transition, which occurs ubiquitously in heavy fermion materials. However, there are more and more experimental evidences indicating that the valence fluctuation plays an essential role in the Ce- and Y-based compounds. We study an extended periodic Anderson model (EPAM) which includes the onsite Coulomb repulsion $U_{cf}$ between the localized electrons and conduction electrons. By employing the density matrix embedding theory, we investigate the EPAM in the symmetric case at half filling. By fixing the onsite Coulomb repulsion $U$ of the localized electrons to an intermediate value, the interplay between the RKKY interaction, the Kondo effect and the Coulomb repulsion $U_{cf}$ brings rich physics. We find three different phases, the antiferromagnetic phase, the charge order phase and paramagnetic phase. When the hybridization strength $V$ between the localized orbital and the conduction orbital is small, the Kondo effect is weak so that the AF phase and the CO phase are present. The phase transition between the two long-range ordered phase is of first order. We also find a coexistence region between the two phases. As $V$ increases, the Kondo effect becomes stronger, and the paramagnetic phase appears between the other two phases.

Enhancing the dopability of semiconductors via strain engineering is critical to improving their functionalities, which is, however, largely hindered by the lack of basic rules. In this study, for the first time, we develop a universal theory to understand the total energy changes of point defects (or dopants) with different charge states under strains, which can exhibit either parabolic or superlinear behaviors, determined by the size of defect-induced local volume change ($\Delta V$). In general, $\Delta V$ increases (decreases) when an electron is added (removed) to (from) the defect site. Consequently, in terms of this universal theory, three basic rules can be obtained to further understand or predict the diverse strain-dependent doping behaviors, i.e., defect formation energies, charge-state transition levels, and Fermi pinning levels, in semiconductors. These three basic rules could be generally applied to improve the doping performance or overcome the doping bottlenecks in various semiconductors.

Depositing magnetic insulators on graphene has been a promising route to introduce magnetism via exchange proximity interaction in graphene for future spintronics applications. Molecule-based magnets may offer unique opportunities because of their synthesis versatility. Here, we investigate the magnetic proximity effect of epitaxial iron phthalocyanine (FePc) molecules on high-quality monolayer and bilayer graphene devices on hexagonal boron nitride substrates by probing the local and nonlocal transport. Although the FePc molecules introduce large hole doping effects combined with mobility degradation, the magnetic proximity gives rise to a canted antiferromagnetic state under a magnetic field in the monolayer graphene. On bilayer graphene and FePc heterostructure devices, the nonlocal transport reveals a pronounced Zeeman spin-Hall effect. Further analysis of the scattering mechanism in the bilayer shows a dominated long-range scattering. Our findings in graphene/organic magnetic insulator heterostructure provide a new insight for use of molecule-based magnets in two-dimensional spintronic devices.

The angular-dependent magnetoresistance (AMR) of the $ab$ plane is measured on the single crystals of iron-chalcogenide FeSe$_{1-x}$S$_{x}$ ($x = 0$, 0.07, 0.13 and 1) and FeSe$_{1-y}$Te$_{y}$ ($y = 0.06$, 0.61 and 1) at various temperatures under fields up to 9 T. A pronounced twofold-anisotropic carrier-scattering effect is identified by AMR, and attributed to a magnetic-field-induced spin nematicity that emerges from the tetragonal normal-state regime below a characteristic temperature $T_{\rm sn}$. This magnetically polarized spin nematicity is found to be ubiquitous in the isoelectronic FeSe$_{1-x}$S$_{x}$ and FeSe$_{1-y}$Te$_{y}$ systems, no matter whether the sample shows an electronic nematic order at $T_{\rm s} \lesssim T_{\rm sn}$, or an antiferromagnetic order at $T_{\rm N} < T_{\rm sn}$, or neither order. Importantly, we find that the induced spin nematicity shows a very different response to sulfur substitution from the spontaneous electronic nematicity: The spin-nematic $T_{\rm sn}$ is not suppressed but even enhanced by the substitution, whereas the electronic-nematic $T_{\rm s}$ is rapidly suppressed, in the FeSe$_{1-x}$S$_{x}$ system. Furthermore, we find that the superconductivity is significantly suppressed with the enhancement of the induced spin nematicity in both FeSe$_{1-x}$S$_{x}$ and FeSe$_{1-y}$Te$_{y}$ samples.

Compounds with the A15 structure have attracted extensive attention due to their superconductivity and nontrivial topological band structures. We have successfully grown Nb$_3$Sb single crystals with the A15 structure and systematically measured the longitudinal resistivity, Hall resistivity and quantum oscillations in magnetization. Similar to other topological trivial/nontrivial semimetals, Nb$_3$Sb exhibits large magnetoresistance (MR) at low temperatures (717$\%$, 2 K and 9 T), unsaturating quadratic field dependence of MR and up-turn behavior in $\rho_{xx}(T)$ curves under magnetic field, which is considered to result from a perfect hole-electron compensation, as evidenced by the Hall resistivity measurements. The nonzero Berry phase obtained from the de-Hass van Alphen (dHvA) oscillations demonstrates that Nb$_3$Sb is topologically nontrivial. These results indicate that Nb$_{3}$Sb superconductor is also a semimetal with large MR and nontrivial Berry phase. This indicates that Nb$_{3}$Sb may be another platform to search for the Majorana zero-energy mode.

Interface engineering is an effective and feasible method to regulate the magnetic anisotropy of films by altering interfacial states between films. Using the technique of pulsed laser deposition, we prepared La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ (LSMO) and La$_{0.67}$Sr$_{0.33}$MnO$_{3}$/SrCoO$_{2.5}$ (LSMO/SCO) films on (110)-oriented La$_{0.3}$Sr$_{0.7}$Al$_{0.65}$Ta$_{0.35}$O$_{3}$ substrates. By covering the SCO film above the LSMO film, we transformed the easy magnetization axis of LSMO from the [001] axis to the [1$\bar{1}$0] axis in the film plane. Based on statistical analyses, we find that the corresponding Mn–Mn ionic distances are different in the two types of LSMO films, causing different distortions of Mn–O octahedron in LSMO. In addition, it also induces diverse electronic occupation states in Mn$^{3+}$ ions. The $e_{\rm g}$ electron of Mn$^{3+}$ occupies 3$z^{2}-r^{2}$ and $x^{2}-y^{2}$ orbitals in the LSMO and LSMO/SCO, respectively. We conclude that the electronic spin reorientation leads to the transformation of the easy magnetization axis in the LSMO films.

Ferroelectric materials are spontaneous symmetry breaking systems that are characterized by ordered electric polarizations. Similar to its ferromagnetic counterpart, a ferroelectric domain wall can be regarded as a soft interface separating two different ferroelectric domains. Here we show that two bound state excitations of electric polarization (polar wave), or the vibration and breathing modes, can be hosted and propagate within the ferroelectric domain wall. In particular, the vibration polar wave has zero frequency gap, thus is constricted deeply inside ferroelectric domain wall, and can even propagate in the presence of local pinnings. The ferroelectric domain wall waveguide as demonstrated here offers a new paradigm in developing ferroelectric information processing units.

The persistent spin helix (PSH) system is considered to have promising applications in energy-conservation spintronics because it supports an extraordinarily long spin lifetime of carriers. Here, we predict that the existence of PSH state in two-dimensional (2D) ferroelectric NbOI$_{2}$ monolayers. Our first-principles calculation results show that there exists Dresselhaus-type spin-orbit coupling (SOC) band splitting near the conduction-band minimum (CBM) of the NbOI$_{2}$ monolayer. It is revealed that the spin splitting near CBM merely refers to out-of-plane spin configuration in the wave vector space, which gives rise to a long-lived PSH state that can be controlled by reversible ferroelectric polarization. We believe that the coupling characteristics of ferroelectric polarization and spin texture in NbOI$_{2}$ provide a platform for the realization of fully electric controlled spintronic devices.

The organic-inorganic hybrid perovskite CH$_{3}$NH$_{3}$PbI$_{3}$ has been a good candidate for many optoelectronic applications such as light-emitting diodes due to its unique properties. Optimizing the optical properties of the CH$_{3}$NH$_{3}$PbI$_{3}$ material to improve the device performance is a hot topic. Herein, a new strategy is proposed to enhance the light emission of CH$_{3}$NH$_{3}$PbI$_{3}$ phosphor effectively. By adding the reactant CH$_{3}$NH$_{3}$I powder in an appropriate proportion and simply grinding, the emission intensity of CH$_{3}$NH$_{3}$PbI$_{3}$ is greatly improved. The advantages of the proposed method are swiftness, simplicity and reproducibility, and no requirement for a complex organic ligand. The mechanism of this phenomenon is revealed by x-ray diffraction, scanning electron microscopy, energy dispersive spectroscopy, photoluminescence, and temperature-dependent photoluminescence. This study offers a unique insight for optimizing the optical properties of halide perovskite materials.

Lithium-excess cation disordered rock-salt materials have received much attention because of their high-capacity as a candidate for cathodes for lithium-ion batteries. The ultra-high specific capacity comes from the coordinated charge compensation of both transition metal and lattice oxygen. However, the oxygen redox at high voltage usually leads to irreversible oxygen release, thereby degrading the structure stability and electrochemical performance. Lithium-excess Li$_{1.14}$Ni$_{0.57+0.5 x}$Ti$_{0.19-0.5 x}$Mo$_{0.10}$O$_{2-x}$F$_{x}$ ($x=0$, 0.05, 0.10, 0.15, and 0.20) with different amounts of fluorine substitution were synthesized. Among them, Li$_{1.14}$Ni$_{0.620}$Ti$_{0.140}$Mo$_{0.10}$O$_{1.85}$F$_{0.15}$ exhibits a lower capacity decline, better rate performance, and lower structure damage. The effects of fluorine substitution on the electrochemical property and structural stability were systematic studied by x-ray photoelectron spectroscopy and in situ XRD etc. Results show that fluorine substitution reduces the average valence of the anion, allowing a larger proportion of low-valent redox active transition metals, increasing the transition metal redox capacity, inhibiting irreversible oxygen release and side reaction. Fluorine substitution further improves the structural stability and suppresses lattice deformation of the material.

We show that the Coulomb interaction between two circuits separated by an insulating layer leads to unconventional thermoelectric effects, such as the cooling by thermal current effect, the transverse thermoelectric effect and Maxwell's demon effect. The first refers to cooling in one circuit induced by the thermal current in the other circuit. The middle represents electric power generation in one circuit by the temperature gradient in the other circuit. The physical picture of Coulomb drag between the two circuits is first demonstrated for the case with one quantum dot in each circuit and it is then elaborated for the case with two quantum dots in each circuit. In the latter case, the heat exchange between the two circuits can vanish. Finally, we also show that the Maxwell's demon effect can be realized in the four-terminal quantum dot thermoelectric system, in which the quantum system absorbs the heat from the high-temperature heat bath and releases the same heat to the low-temperature heat bath without any energy exchange with the two heat baths. Our study reveals the role of Coulomb interaction in non-local four-terminal thermoelectric transport.

Iron oxide is one of the most important components in the Earth's mantle. The recent discovery of the stable presence of Fe$_{5}$O$_{6}$ in the Earth's mantle environment has stimulated significant interests in understanding of this new category of iron oxides. We report the electronic structure and magnetic properties of Fe$_{5}$O$_{6}$ calculated by the density functional theory plus dynamic mean field theory (DFT + DMFT) approach. Our calculations indicate that Fe$_{5}$O$_{6}$ is a conductor at ambient pressure with dominant Fe-$3d$ density of states at the Fermi level. The magnetic moments of iron atoms at three non-equivalent crystallographic sites in Fe$_{5}$O$_{6}$ collapse at significantly different rates under pressure. This site-selective collapse of magnetic moments originates from the shifting of energy levels and the consequent charge transfer among the Fe-$3d$ orbits when Fe$_{5}$O$_{6}$ is being compressed. Our simulations suggest that there could be high conductivity and volume contraction in Fe$_{5}$O$_{6}$ at high pressure, which may induce anomalous features in seismic velocity, energy exchange, and mass distribution in the deep interior of the Earth.