A complete scalar classification for dark Sharma–Tasso–Olver's (STO's) equations is derived by requiring the existence of higher order differential polynomial symmetries. There are some free parameters for every class of dark STO systems, thus some special equations including symmetry equation and dual symmetry equation are obtained by selecting a free parameter. Furthermore, the recursion operators of STO equation and dark STO systems are constructed by a direct assumption method.

Motivated by the recent experiment [Nature 530 (2016) 194] in which a stable droplet in a dipolar quantum gas has been created by the interaction-induced instability, we focus on the modulation instability of an optically-trapped dipolar Bose–Einstein condensate with three-body interaction. Within the mean-field level, we analytically solve the discrete cubic-quintic Gross–Pitaevskii equation with dipole–dipole interaction loaded into a deep optical lattice and show how combined effects of the three-body interaction and dipole–dipole interaction on the condition of modulational instability. Our results show that the interplay of the three-body interaction and dipole–dipole interaction can dramatically change the modulation instability condition compared with the ordinary Gross–Pitaevskii equation. We believe that the predicted results in this work can be useful for the future possible experiment of loading a Bose–Einstein condensate of $^{164}$Dy atoms with strong magnetic dipole–dipole interaction into an optical lattice.

The Jaynes–Cummings model is solved with the raising and lowering (shift) operators using the matrix-diagonalizing technique. Bell nonlocality is also found to be present ubiquitously in the excitation states of the model.

The quasinormal modes (QNMs) of massless scalar field perturbation in a noncommutative-geometry-inspired Schwarzschild black hole spacetime are studied using the third-order Wentzel–Kramers–Brillouin approximative approach. The result shows that the noncommutative parameter plays an important role for the quasinormal (QNM) frequencies.

Based on the quark model the cross section for the $e^+e^-\to Z^0/\gamma^*\to{\it \Omega}_{ccc}^{++}\bar{\it \Omega}_{ccc}^{--}$ exclusive process is investigated at the tree level. Compared with the $ Z^0\to{\it \Omega}^{-}\bar{\it \Omega}^{+}$ decay, our result shows that the $Z^0$ boson favors decaying into charmed baryon pairs. The results are also compared with the calculation of inclusively charmed baryon production.

We describe high-level ab initio calculations on the BH$_{2}$, HBF, HBCl and HBBr radicals. Molecular structure, vibrational frequencies and potential energy curves of the ground state and the first excited state, which are two Renner–Teller components for a $^2{\it \Pi}$ state at linearity, are studied using the basis sets aug-cc-pVTZ and icMRCI+Q technique. On the basis of the potential energy curves, a reliable potential energy barrier to dissociation HB+$X$ ($X$=F, Cl, Br) fragments and to linearity are given. The ab initio results will add some understanding on the spectrum and the photo-dissociation dynamics of the series of radicals.

Fine control of the dynamics of a quantum system is the key element to perform quantum information processing and coherent manipulations for atomic and molecular systems. We propose a control protocol using a tangent-pulse driven model and demonstrate that it indicates a desirable design, i.e., of being both fast and accurate for population transfer. As opposed to other existing strategies, a remarkable character of the present scheme is that high velocity of the nonadiabatic evolution itself not only will not lead to unwanted transitions but also can suppress the error caused by the truncation of the driving pulse.

We study theoretically the optical response for perfect zigzag-edge silicene nanoribbons with $N$ silicon atoms of the A and B sublattices ($N$-ZSiNRs) under the irradiation of an external electromagnetic field at low temperatures. The 8- and 16-ZSiNRs are demonstrated to exhibit a broad energy regime of absorption coefficient, refractive index, extinction coefficient, and reflectivity from infrared to ultraviolet, utilizing the dipole-transition theorem for semiconductors. The optical spectra for 8- and 16-ZSiNRs may be classified into two types of the transitions, one between valence and conduction subbands with the same parity, and the other among the edge state and bulk state subbands. With the increase of the ribbon width, the optical spectra for ZSiNRs are proved to exhibit red shift and blue shift at the lower and higher energy regimes, respectively. The obtained novel features are believed to be of significance in designs of silicene-based optoelectronic devices.

Knots and links are fascinating and intricate topological objects. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here we find that knotted structures also exist in a peculiar class of three-dimensional topological insulators—the Hopf insulators. In particular, we demonstrate that the momentum-space spin textures of Hopf insulators are twisted in a nontrivial way, which implies the presence of various knot and link structures. We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates. The extracted Hopf invariants, knots, and links are validated to be robust to typical experimental imperfections. Our work establishes the existence of knotted structures in Hopf insulators, which may have potential applications in spintronics and quantum information processing.

FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS)

A Babinet-inverted optical nanoantenna analogue of electromagnetically induced transparency based on the coupling between two magnetic dipole antennas and a magnetic octupole antenna in a Au film waveguide is demonstrated. Simulation results indicate that a pronounced elimination occurs in the radiating spectrum due to the coupling-induced radiation suppression. A two-oscillator electromagnetically induced transparency model is used to describe the antenna. The coupling coefficient between the magnetic dipole antennas and the magnetic octupole antenna is calculated using the model and is found to decline exponentially with the increase of the distance between them. Such an antenna can be directly integrated with optical waveguides or transmission lines, thus is of fundamental significance for the applications in nano-optics, such as the optical device miniaturizations and photonic circuit integrations.

Lorentz force electrical impedance tomography (LFEIT) inherits the merit of high resolution by ultrasound stimulation and the merit of high contrast through electromagnetic field detection. To reduce the instantaneous peak power of the stimulating signal to the transducer, the sinusoidal pulse and step-frequency technique is investigated in LFEIT. The theory of application of step-frequency technique in LFEIT is formulated with the direct demodulation method and the in-phase quadrature demodulation method. Compared with the in-phase quadrature demodulation method, the direct demodulation method has simple experimental setup but could only detect half of the range. Experiments carried out with copper foils confirmed that LFEIT using the step-frequency technique could detect the electrical conductivity variations precisely, which suggests an alternative method of realization of LFEIT.

CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES

To explain the stabilization mechanism of the carbon-ion-implanted GaN under the diamond growth environment, the luminescence characteristics and structure evolution correlative with sites' carbon atoms located for high-fluence carbon-ion-implanted GaN are discussed. GaN is implanted with carbon ion using fluence of $2\times10^{17}$ cm$^{-2 }$ and energy of 45 keV. Then the implanted samples are annealed at 800$^{\circ}\!$C for 20 min and 1 h under the N$_{2}$ atmosphere. The luminescence characteristics of carbon-ion-implanted GaN are evaluated by photoluminescence spectrum at wavelength 325 nm. The lattice damage of GaN is characterized by Raman spectrum and the corresponding vacancy-defect evolution before and after annealing is measured by slow positron annihilation. The results show that most of the carbon atoms will be located at the interstitial sites after carbon ion implantation due to the weak mobility. As the implanted samples are annealed, strong yellow luminescence is emitted and the vacancies for Ga (V$_{\rm Ga})$ are reduced resulting from the migration of interstitial carbon (C$_{\rm i})$ and formation of complexes (C$_{\rm Ga}$ and/or C$_{\rm Ga}$-C$_{\rm i}$) between them. As the annealing time is prolonged, the carbon ions accommodated by the vacancies are saturated, vacancy clusters with carbon atoms appear and the concentration of C$_{\rm Ga}$ diminishes, which will have an adverse effect on the diamond film nucleation and growth.

A new phase of RhB$_{4}$ is predicted based on first-principles calculations. The new phase belongs to the orthorhombic $Pnnm$ space group, named as $o$-RhB$_{4}$, and analysis of the calculated enthalpy shows that $o$-RhB$_{4}$ belongs to the orthorhombic $Pnnm$ space group. The calculated phonon band structure shows that the orthorhombic $Pnnm$ $o$-RhB$_{4}$ structure is stable at ambient pressure. We expect that the phase transition can be further confirmed by experiments.

We study the percolation transition in a one-species cluster aggregation network model, in which the parameter $\alpha$ describes the suppression on the cluster sizes. It is found that the model can exhibit four types of percolation transitions, two continuous percolation transitions and two discontinuous ones. Continuous and discontinuous percolation transitions can be distinguished from each other by the largest single jump. Two types of continuous percolation transitions show different behaviors in the time gap. Two types of discontinuous percolation transitions are different in the time evolution of the cluster size distribution. Moreover, we also find that the time gap may also be a measure to distinguish different discontinuous percolations in this model.

Transparent zinc oxide (ZnO) thin films are fabricated by a simple sol-gel spin-coating technique on glass substrates with different solution concentrations (0.3–1.2 M) using zinc acetate dehydrate [Zn(CH$_{3}$COO)$_{2}\cdot$2H$_{2}$O] as precursor and isopropanol and monoethanolamine (MEA) as solvent and stabilizer, respectively. The molar ratio of zinc acetate dehydrate to MEA is 1.0. X-ray diffraction, ultraviolet-visible spectroscopy and photoluminescence spectroscopy are employed to investigate the effect of solution concentration on the structural and optical properties of the ZnO thin films. The obtained results of all thin films are discussed in detail and are compared with other experimental data.

The dissipation of energy during the process of contact and separation between a tip and a sample is very important for understanding the phase images in the tapping mode of atomic force microscopes (AFMs). In this study, a method is presented to measure the dissipated energy between a tip and a sample. The experimental results are found to be in good agreement with the theoretical model, which indicates that the method is reliable. Also, this study confirms that liquid bridges are mainly produced by extrusion modes in the tapping mode of AFMs.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

First-principles calculations are performed on the influence of transition metal (TM=Cr, Mn, Fe, Co) as codopants on the electronic structure and visible-light absorption of Zn-doped SrTiO$_{3}$. The calculated results show that (Zn,Mn)-codoped SrTiO$_{3}$ requires the smallest formation energy in four codoping systems. The structures of the codoped systems display obvious lattice distortion, inducing a phase transition from cubic to rhombohedral after codoping. Some impurity Cr, Mn and Co 3$d$ states appear below the bottom of conduction band and some Fe 3$d$ states are located above the top of valence band, which leads to a significant narrowing of band gap after transition metal codoping. The enhancement of visible-light absorption are observed in transition metals (TM=Cr, Mn, Fe, Co) and Zn codoped SrTiO$_{3}$ systems. The prediction calculations suggested that the (Zn,Mn)- and (Zn,Co)-codoped SrTiO$_{3}$ could be the desirable visible-light photocatalysts.

We investigate the electronic-transport properties of two-dimensional monolayer films from Au-P-Au molecular junction to Au-Si-Au molecular junction using elastic scattering Green's function theory. In the process of replacing the P atoms with Si atoms every other line from the middle of monolayer blue phosphorus molecular structure, the substitution of Si atoms changes the properties of Au-P-Au molecular junction significantly. Interestingly, the current value has a symmetric change as a parabolic curve with the peak appearing in Au-Si$_{1}$P$_{1}$-Au molecular junction, which provides the most stable current of 15.00 nA in a wide voltage range of 0.70–2.70 V. Moreover, the current–voltage characteristics of the structures indicate that the steps tend to disappear revealing the property similar to metal when the Si atoms dominate the molecular junction.

We present first-principle calculations on the magnetism in finite rectangular nanosilicenes (RNSs). An antiferromagnetic (AFM) state at two zigzag edges is found when the RNSs approach a critical size. This AFM state originates from the localized $p_{z}$ orbits of Si atoms at the edges, similar to those in the infinitely long zigzag-edged silicon nanoribbons. The smallest RNS that can maintain the AFM phase as the ground state is identified. It is also found that aluminum dopants can regulate the distribution of the spin density and the energy difference between AFM and FM states.

We perform comprehensive density functional theory calculations of strain effect on electronic structure of black phosphorus (BP) and on BP nanoribbons. Both uniaxial and biaxial strain are applied, and the dramatic change of BP's band structure is observed. Under 0–8% uniaxial strain, the band gap can be modulated in the range of 0.55–1.06 eV, and a direct–indirect band gap transition causes strain over 4% in the $y$ direction. Under 0–8% biaxial strain, the band gap can be modulated in the range of 0.35–1.09 eV, and the band gap maintains directly. Applying strain to BP nanoribbon, the band gap value reduces or enlarges markedly either zigzag nanoribbon or armchair nanoribbon. Analyzing the orbital composition and using a tight-binding model we ascribe this band gap behavior to the competition between effects of different bond lengths on band gap. These results would enhance our understanding on strain effects on properties of BP and phosphorene nanoribbon.

We carry out detailed momentum-dependent and temperature-dependent measurements on Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) superconductor in the superconducting and pseudogap states by super-high resolution laser-based angle-resolved photoemission spectroscopy. The precise determination of the superconducting gap for the nearly optimally doped Bi2212 ($T_{\rm c}=91$ K) at low temperature indicates that the momentum-dependence of the superconducting gap deviates from the standard $d$-wave form ($\cos(2{\it \Phi}$)). It can be alternatively fitted by including a high-order term ($\cos(6{\it \Phi}$)) in which the next nearest-neighbor interaction is considered. We find that the band structure near the antinodal region smoothly evolves across the pseudogap temperature without a signature of band reorganization which is distinct from that found in Bi$_2$Sr$_2$CuO$_{6+\delta}$ superconductors. This indicates that the band reorganization across the pseudogap temperature is not a universal behavior in cuprate superconductors. These results provide new insights in understanding the nature of the superconducting gap and pseudogap in high-temperature cuprate superconductors.

The magnetic properties of spinel ferrites Cu$_{1-x}$Zn$_{x}$Fe$_{2}$O$_{4}$ are studied using high-temperature series expansions combined with the Padé approximates. The exchange interactions, inter and intra-sublattices $J_{\rm AA}$, $J_{\rm BB}$ and $J_{\rm AB}$ are obtained using a probability distribution law. The critical exponent $\gamma$ associated with the magnetic susceptibility is obtained.

The long-range magnetism observed in group-V tellurides quintuple layers is the only working example of carrier-free dilute magnetic semiconductors (DMS), whereas the physical mechanism is unclear, except the speculation on the band topology enhanced van Vleck paramagnetism. Based on DFT calculations, we find a stable long-range ferromagnetic order in a single quintuple layer of Cr-doped Bi$_2$Te$_3$ or Sb$_2$Te$_3$, with the dopant separation more than 9 Å. This configuration is the global energy minimum among all configurations. Different from the conventional super exchange theory, the magnetism is facilitated by the lone pair derived anti-bonding states near the cations. Such anti-bonding states work as stepping stones merged in the electron sea and conduct magnetism. Further, spin orbit coupling induced band inversion is found to be insignificant in the magnetism. Therefore, our findings directly dismiss the common misbelief that band topology is the only factor that enhances the magnetism. We further demonstrate that removal of the lone pair derived states destroys the long-range magnetism. This novel mechanism sheds light on the fundamental understanding of long-range magnetism and may lead to discoveries of new classes of DMS.

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

We investigate deformation and spallation of explosive welded bi-steel plates under gas gun shock loading. Free surface histories are measured to obtain the Hugoniot elastic limit and spall strengths at different impact velocities. Pre- and post-shock microstructures are characterized with optical metallography, scanning electron microscopy, and electron backscatter diffraction. In addition, the Vickers hardness test is conducted. Explosive welding can result in a wavy steel/steel interface, an ultrafine grain region centered at the interface, and a neighboring high deformation region, accompanied by a hardness with the highest value at the interface. Additional shock compression induces a further increase in hardness, and shock-induced deformation occurs in the form of twinning and dislocation slip and depends on the local substructure. Spall damage nucleates and propagates along the ultrafine grain region, due to the initial cracks or weak interface bonding. Spall strengths of bimetal plates can be higher than its constituents. Plate impact offers a promising method for improving explosive welding.