We investigate the evolutionary Prisoner's dilemma game on the simplest spatial networks constructed as geometrical graphs. The optimal cooperation enhancement against the topology randomness is found. It is proposed that the optimal behavior of the cooperation results from the competition between individuals with high degrees and with low degrees: the former assists the formation of cooperator clusters and the latter tends to prevent the formation of such clusters.

We report the sudden appearance of distillability between two statistically independent reservoirs modelled as qutrit-qutrit systems. This feature of bipartite quantum systems is different from the previously observed phenomenon of entanglement sudden birth. It is found that the states of reservoirs first become bound entangled, thus exhibiting entanglement sudden birth, consequently followed by the sudden birth of distillability, and it is shown that whenever distillability is lost abruptly from principal system, it also necessarily appears abruptly among reservoirs' degrees of freedom. This surprising observation reflects yet another peculiarity of dynamical aspects of quantum entanglement.

Fermions, as another major class of quantum particles, could be taken as carriers for quantum information processing beyond spins or bosons. In this work, we consider the fermionic generalization of the one-way quantum computation model and find that one-way quantum computation can also be simulated with fermions. In detail, using the n→2n encoding scheme from a spin system to a fermion system, we introduce the fermionic cluster state, then the universal computing power with a fermionic cluster state is demonstrated explicitly. Furthermore, we show that the fermionic cluster state can be created only by measurements on at most four modes with |+>_{f} (fermionic Bell state) being free.

We discuss the properties of ferromagnetic orders on the Lieb lattice and show that a symmetry protected quadratic-flat band crossing point will dramatically affect the magnetic ordering. In the presence of a weak on-site repulsive interaction, the ground state is a nematic ferromagnetic order with simultaneously broken time-reversal and rotational symmetries. When the interaction strength increases, the rotational symmetry will restore at a critical value, and the system enters a conventional ferromagnetic regime. The mean-field transition temperatures for both the nematic and conventional ferromagnetic phases are in the order of interaction. This observation suggests that these magnetic orders have the potential to be realized and detected in cold atomic systems within realistic experimental conditions.

We propose a novel scheme for a space free-fall based test of the new equivalence principle (NEP) with two rotating extended bodies made of the same material. The measurement will be carried out by placing the two concentric spinning masses of very different momenta inside a differential electrostatic accelerometer in a drag-free compensated orbit. A difference in the forces necessary to maintain the common trajectory will be an indication of a violation of equivalence or the existence of spin-spin force between the rotating mass and the Earth. The conceptual design of the inertial sensor and its operation mode is presented. Details specific to the model and performance requirements are discussed by using up-to-date space technologies to test the NEP with an accuracy of better than 10^{−15}.

We study the dependence of quasi-normal modes of neutron stars on their equation of state (EOS). We construct neutron star configurations of different EOSs while having the same mass M and radius R, and investigate how their l=2 fundamental mode frequencies would be different. We find that both the real and imaginary parts of the l=2 frequencies are related to the r^{−1} moment of the configurations.

Theoretical calculations based on a multiscale model are proposed to interpret the dielectric anomalous enhancement observed around x=0.2 in the (PbTiO_{3})_{1−x}-(CoFe_{2}O_{4})_{x} (0≤x≤1) epitaxial nanocomposite spread film. First principles calculation combined with thermodynamics statistics reveals that the dynamic ratio between different PbTiO_{3} phases under an external electric field is responsible for the dielectric anomaly. To verify this model with direct microstructure evidence, high resolution and high accuracy synchrotron radiation x-ray diffraction of (PbTiO_{3})_{0.8}-(CoFe_{2}O_{4})_{0.2} epitaxial composite film under an in situ electric field is collected, in which an obvious modulation of the phase balance of PbTiO_{3} is observed.

Multi-soliton solution to a multi-component coupled Ito system is investigated based on the Hirota bilinear method. By virtue of the perturbation method, we firstly derive one- and two-soliton solutions for the coupled Ito system possessing four components. Then the multi-soliton solution for the multi-component coupled Ito system is summarized into a general form expressed by pfaffians. Finally, this general pfaffian-type soliton solution is proved by pfaffian techniques.

Using the photon spectrum of a high energy charged parton, we investigate the J/ψ production via the two photon interaction mechanism in ultra-peripheral pp collisions. It is shown that the contributions from the direct electromagnetic and the corresponding fragmentation processes are meaningful for the J/ψ productions in ultra-peripheral pp collisions at LHC energy.

By using various proximity potentials, the fusion barrier heights and positions are calculated for proton and helium induced reactions with targets in the mass range 51≤A ≤130 and 12≤A≤233, respectively. The calculated fusion barriers are parameterized by using the relations R_{B}^{Par}=aX_{1}+b and V_{B}^{Par}=cX_{2}, where X_{1} and X_{2} are A_{2}^{1/3} and Z_{1}Z_{2}/R_{B}^{Par}, respectively. The values of the constants a, b and c are different for different versions of proximity potentials. We find that the parameterized forms derived by using Proximity 1977 yield values closer to the empirical data in proton as well as helium induced reactions and can be used further to estimate directly the barrier parameters for the fusion reactions of proton and helium with any target.

The linear correlated constants A_{D} (centrifugal correction of the spin-orbit coupling constant) and γ (the spin-rotation constant) involved in the second negative (A^{2}Π_{u}-X^{2}Π_{g}) system of O_{2}^{+} are determined by nonlinear least-squares fitting the spectra of ^{16}O_{2}^{+} and ^{18}O_{2}^{+} using the isotopic effect. In addition, the molecular constants of the other O_{2}^{+} isotopologues are predicted.

An accurate and rapid method is proposed to optimize anharmonic linear surface-electrode ion trap design. Based on the method, we analyze the impact of the architectural parameters, including the width, number, and applied voltage of prerequisite active electrodes, on the number and spacing of trapped ions. Sets of optimal anharmonic trap design are given. Then the optimal designs are verified by using an ant colony optimization algorithm. The results show that the maximum ion position errors and maximum ion spacing errors are less than 1 μm up to 80. The mean of the maximum errors is nearly linear with respect to the number of trapped ions.

Frequency comparison is one of the most efficient ways to evaluate the performance of a frequency standard. Based on the pre-existing ^{40}Ca^{+} optical frequency standard, we set up the second ^{40}Ca^{+} optical frequency standard, which has been improved in the materials and structure of ion traps for better control of the magnetic field. After the compensation, the residual magnetic field at the position of the ion is adjusted to be ∼500 nT with a long time jitter of ∼10 nT, which is better than the pre-existing ^{40}Ca^{+} optical frequency standard. We realize the '4-point-closed-loop locking' on the second ^{40}Ca^{+} optical frequency standard after a series of preparatory works. Through half an hour of measurement time, the two frequency standards exhibited a stability of 2.1×10^{−13}τ^{−1/2} and a relative frequency difference of 1.5 (2.9) Hz.

FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS)

A high-power cw end-pumped laser device is demonstrated with a slab crystal of Nd:GdVO_{4} operating at 1063 nm. Diode laser stacks at 880 nm are used to pump Nd:GdVO_{4} into emitting level ^{4}F_{3/2}. The 149 W output power is presented when the absorbed pump power is 390 W and the optical-to-optical conversion efficiency is 38.2%. When the output power is 120 W, the M^{2} factors are 2.3 in both directions. Additionally, mode overlap inside the resonator is analyzed to explain the beam quality deterioration.

A coupled-resonator structure consisting of a stub resonator and a nanodisk resonator is proposed and numerically investigated by using a two-dimensional finite element method. Simulation results show that two resonant modes occur in the transmission spectra, and the sharp and asymmetric Fano-lines increase with the wavelength resolution. We also analyze the properties of two resonant modes of the structure and design a similar structure supporting only one resonant mode, which has better wavelength resolution. Our models are important for improving the wavelength resolution in plasmonic devices and the sensitivity in sensors.

Quantum correlation without entanglement in a two-atom-vacuum field system is investigated. The influence of the atomic dipole-dipole interaction on quantum correlation is also examined. We find that, when both atoms are initially in separable excited states, the quantum discord of two atoms appears while their entanglement wholly vanishes throughout the evolution. We explain our results in detail. Our results provide a novel method of achieving a quantum correlation resource without entanglement in the real system.

The polarization rotation of a linearly polarized optical (probe) field caused by a left-circularly polarized pumping beam is studied in an opened two-level system of a ^{87}Rb atom. Letting a linearly polarized optical field (probe) and left-circularly polarized pumping beams co-propagate through a Rb vapor, we observe the featurable polarization rotation signals of the linearly polarized probe field via the asymmetric optical pumping with low intensities. Based on this phenomenon, a polarization-controlled light switching can be demonstrated at a low light level. Such a scheme of polarization rotation can be extended in a solid or semi-conduct material and find a practical application in all-optical information processing.

Emission properties of self-assembled green-emitting InGaN quantum dots (QDs) grown on sapphire substrates by using metal organic chemical vapor deposition are studied by temperature-dependent photoluminescence (PL) measurements. As temperature increases (15–300 K), the PL peak energy shows an anomalous V-shaped (redshift–blueshift) variation instead of an S-shaped (redshift–blueshift–redshift) variation, as observed typically in green-emitting InGaN/GaN multi-quantum wells (MQWs). The PL full width at half maximum (FWHM) also shows a V-shaped (decrease–increase) variation. The temperature dependence of the PL peak energy and FWHM of QDs are well explained by a model similar to MQWs, in which carriers transferring in localized states play an important role, while the confinement energy of localized states in the QDs is significantly larger than that in MQWs. By analyzing the integrated PL intensity, the larger confinement energy of localized states in the QDs is estimated to be 105.9 meV, which is well explained by taking into account the band-gap shrinkage and carrier thermalization with temperature. It is also found that the nonradiative combination centers in QD samples are much less than those in QW samples with the same In content.

Group velocity mismatch becomes the main obstacle for frequency conversion of ultrashort pulses due to dispersion. To solve the problem, one design is proposed for group velocity compensated second harmonic generation in a periodically modulated BBO crystal structure: the α-BBO/β-BBO multi-layer microstructure. The results show that the device can be well applied from the visible red to the near infrared region.

We theoretically analyze the transient properties of a probe field absorption dispersion in a quantum-dot nanostructure driven by terahertz signal radiation. Here a four-level quantum-dot nanostructure is designed numerically by Schrödinger and Poisson's equations. We show that in the presence of the THz signal, the medium becomes phase dependent and the absorption dispersion can be dramatically influenced by the relative phase between applied fields.

Pixelated micropolarizer arrays (PMAs) have recently been used as key components to achieve real-time phase measurement. PMA fabrication by electron beam lithography and inductively coupled plasma-reactive ion etching is proposed in this work. A 320×240 aluminum PMA with 7.4 μm pitch is successfully fabricated by the proposed technique. The period of the grating is 140 nm, and the polarization directions of each of the 2×2 units are 0°, 45°, 90°, and 135°. The scanning electron microscopy and optical microscopy results show that the PMA has a good surface characteristic and polarization performances. When the PMA is applied to phase-shifting interferometry, four fringe patterns of different polarization directions are obtained from only one single frame image, and then the object wave phase is calculated in real time.

We investigate the fourth-order spatial correlation properties of pseudo-thermal light in the photon counting regime, and apply the Klyshko advanced-wave picture to describe the process of four-photon coincidence counting measurement. We deduce the theory of a proof-of-principle four-photon coincidence counting configuration, and find that if the four randomly radiated photons come from the same radiation area and are indistinguishable in principle, the fourth-order correlation of them is 24 times larger than that when four photons come from different radiation areas. In addition, we also show that the higher-order spatial correlation function can be decomposed into multiple lower-order correlation functions, and the contrast and visibility of low-order correlation peaks are less than those of higher orders, while the resolutions all are identical. This study may be useful for better understanding the four-photon interference and multi-channel correlation imaging.

We present an all-fiber configuration of passive beam combining using an all-fiber feedback loop and demonstrate passive coherent combining of a four-channel nanosecond pulsed laser. The output power, pulse characteristics, polarization extinction ratio and far field laser intensities of the combined output laser are investigated. The experimental results validate that passive phasing using an all-fiber feedback loop provides a simple while robust method for coherent beam combining of pulsed lasers. If replacing the fiber coupler used into a high power tapered fused bundle fiber combiner, this scheme is promising to scale the output power up to the kW level.

The depression of the superfluid transition temperature in He by a heat flow Q is studied. A small sealed cell with a capillary is introduced and a stable and flat superfluid transition temperature plateau is easily obtained by controlling the temperature of the variable-temperature platform and the bottom chamber of the sealed cell. Owing to the depression effect of the superfluid transition temperature by the heat flow, the heat flow through the capillary is changed by the temperature control to obtain multiple temperature plateaus of different heat flows. The thermometer self-heating effect, the residual heat leak of the 4.2 K environment, the temperature difference on the He II liquid column, the Kapiza thermal resistance between the liquid helium and the copper surface of the sealed cell, the temperature gradient of the sealed cell, the static pressure of the He II liquid column and other factors have influence on the depression effect and the influence is analyzed in detail. Twenty experiments of the depression of the superfluid transition temperature in ^{4}He by heat flow are made with four sealed cells in one year. The formula of the superfluid transition temperature pressured by the heat flow is T_{λ}(Q)=−0.00000103Q+2.1769108, and covers the range 229≤Q≤6462 μW/cm^{2}.

The dynamical behavior of an intruder immersed in a two-dimensional shaken granular bed is experimentally investigated. With two types of background particles, f– Γ phase diagrams depicting the intruder's motion are measured and compared. It is found that even with the same size and density ratio of the intruder to the background particles, the intruder exhibits a distinct behavior at given vibrational conditions: rising behavior in one granular bed; sinking behavior in another granular bed. We slightly tune the size and density ratio to confirm the reliability of the experimental results. In addition, we examine the influences of interstitial air, convection and the initial position on the intruder's motion, speculating that the opposite motion could be traced to the material properties of the background particles.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

A new scheme of radiation pressure acceleration for generating high-quality protons by using two overlapping-parallel laser pulses is proposed. Particle-in-cell simulation shows that the overlapping of two pulses with identical Gaussian profiles in space and trapezoidal profiles in the time domain can result in a composite light pulse with a spatial profile suitable for stable acceleration of protons to high energies. At ∼2.46×10^{21} W/cm^{2} intensity of the combination light pulse, a quasi-monoenergetic proton beam with peak energy ∼200 MeV/nucleon, energy spread <15%, and divergency angle <4° is obtained, which is appropriate for tumor therapy. The proton beam quality can be controlled by adjusting the incidence points of two laser pulses.

Fluctuations of cathode cavity pressure and arc voltage are observed experimentally in a dc plasma torch with a long inter-electrode channel. The results show that they have the same frequency of around 4 kHz under typical experimental conditions. The observed phase difference between the pressure and the voltage, which is influenced by the path length between the pressure sensor and the cathode cavity, varies with different input powers. Combined with numerical simulation, the position of the pressure perturbation origin is estimated, and the results show that it is located at 0.01–0.05 m upstream of the inter-electrode channel outlet.

CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES

Time-resolved electron diffraction employing MeV electron beams is demonstrated experimentally at the center for ultrafast diffraction and microscopy of Shanghai Jiao Tong University. A high-quality diffraction pattern is recorded by a single shot of electron pulse. Synchronization between the pump laser and the probe electron beam is achieved through measurement of electron deflection caused by the laser-induced plasmas in a metal tip. We study the ultrafast structural dynamics of the gold lattice excited by a femtosecond laser through tracing the change of Bragg peaks intensity at different time delays. It is expected that the combination of MeV ultrashort electron beams and femtosecond laser pulses will open many new opportunities in the ultrafast and ultrasmall world.

The growth kinetics of the intermetallic compound layer between molten pure Sn and ZrCu_{30}Al_{10}Ni_{5} bulk metallic glass (BMG) is mainly controlled by the diffusion mechanism at stage I at which the value of the time exponent is approximately 1/2, also there is unusual or unique stage II whose time exponent of the growth is suppressed to 1/3. It is deduced that phase transition such as nucleation, coalescence occurring in the vicinity of the interface of the diffusion layer within the BMG and the average size growing as one-third power of time, called the Lifshitz–Slezov law. A more elegant means of attack is based upon the Fokker–Planck approach, which permits us to calculate directly the probability of the distribution of steady-state thickness fluctuations. Physical implications of the analytical results also give the one-third power of time of distance scale. The transmission of Sn particles through a disorder system of the BMG, scattered by the local fluctuation levels, is the source of the time exponent from 1/2 to 1/3 as a macroscopic cumulative effect.

We present the elastic and dynamical properties of YB_{4} from first-principles calculations. It is found that the optimized lattice constants and bulk modulus (182 GPa) agree well with the experimental data. The structural stability of tetragonal YB_{4} is confirmed by the calculated elastic constants and phonon spectra. YB_{4} holds a Debye temperature of 874 K and has small elastic anisotropy. The estimated hardness of YB_{4} is about 17 GPa, indicating that YB_{4} is a hard solid while not a superhard one.

The buckling of an elastic thin film on a compliant substrate under small perturbation in normal deflection and tangential displacement is studied with the effect of surface energy and interfacial slip. It is revealed that Poisson's ratio of the soft substrate and the interfacial slip can be neglected for film's thickness smaller than tens of nanometers. The effect of surface energy nevertheless renders the critical strain for the onset of wrinkling and the wave length dependent on the thickness highly nonlinearly. The potential of using buckling of thin films on compliant substrates for determination of surface parameters has been discussed.

Patterning SiC substrates with focused ion beam for growth of confined graphene nanostructures is interesting for fabrication of graphene devices. However, by imposing an ion beam, the morphology of illuminated SiC substrate surface is inevitably damaged, which imposes significant effects on the subsequent growth of graphene. By using confocal Raman spectroscopy, we investigate the effects of ion beam illumination on the quality of graphene layers that are grown on 6H-SiC (0001) substrates with two different growth methods. With the first method, the 6H-SiC (0001) substrate is flash annealed in ultra-high vacuum. Prominent defects in graphene grown on illuminated areas are revealed by the emergence of Raman D peak. Significant changes in D peak intensity are observed with Ga^{+} ion fluence as low as 10^{5} μm^{−2}. To eliminate the damage from the ion beam illumination, hydrogen etching is employed in the second growth method, with which prominent improvement in the quality of crystalline graphene is revealed by its Raman features. The defect density is significantly reduced as inferred from the disappearance of D peak. The Raman shift of G peak and 2D peak indicates strain-released graphene layers as grown in such a method. Such results provide essential information for patterning graphene nano-devices.

WEN Jing, GUO Hua, YAN Chen-Hui, WANG Zhen-Yu, CHANG Kai, DENG Peng, ZHANG Teng, ZHANG Zhi-Dong, JI Shuai-Hua, WANG Li-Li, HE Ke, MA Xu-Cun, CHEN Xi, XUE Qi-Kun

Chin. Phys. Lett. 2014, 31 (11):
116802
doi:
10.1088/0256-307X/31/11/116802 Full Text:
[PDF 959 KB]
(1)

Atomically flat thin films of topological semimetal Na_{3}Bi are grown on double-layer graphene formed on 6H–SiC(0001) substrates by molecular beam epitaxy. By combined techniques of molecular beam epitaxy, scanning tunneling microscopy and angle resolved photoelectron spectroscopy, the growth conditions for Na_{3}Bi thin films on double-layer graphene are successfully established. The band structure of Na_{3}Bi grown on graphene is mapped along Γ–M and Γ– K directions. Furthermore, the energy band of Na_{3}Bi at higher energy is uncovered by doping Cs atoms on the surface.

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

Graphene has been demonstrated to be able to detect individual gas molecules [Schedin et al. Nat. Mater. 6 (2007) 652], which has attracted a lot of sensor research activities. Here we report for the first time that graphene is capable of detecting the ordering degree of absorbed water molecules. The efficiency of doping varies from the degrees of molecular ordering. The simulated results show that the highly ordered water molecules contribute more to the doping effect, which reduces the conductance of the water/graphene system.

Based on the generalized gradient approximation (GGA) in density functional theory (DFT) and using the first-principle plane wave ultrasoft pseudopotential method, we construct and optimize the structures of intrinsic and oxygen vacancy (V_{O}) ZnO bulks and nanowires (NWs) in the Castep module. Moreover, the calculation of band structures and the optical properties are carried out. The calculated results exhibit that the oxygen vacancy exerts a more significant influence on the electronic structures of the ZnO bulks instead of the NWs. What is more, the influences of the V_{O} on the optical properties are mainly embodied in the ultraviolet region, and the main optical parameters of ZnO bulks and NWs with V_{O} are anisotropic.

Dependences of the order parameter (Δ) and the electron effective mass (m_{e}^{⋆}) on the temperature for the chlorine halide superconductor are determined in the present work. The high values of the pressure (p_{1}=320 GPa and p_{2}=360 GPa), for which the critical temperature is equal to [T_{C}]_{p1}=30.6 K and [T_{C}]_{p2}=41.5 K, are taken into consideration. It is found that the dependence of the order parameter on the temperature deviates from the predictions of the classical Bardeen–Cooper–Schrieffer theory, due to the existence of the significant strong-coupling and retardation effects. The values of the order parameter, for the temperature close to zero Kelvin, are equal to [Δ(0)]_{p1}=4.89 meV and [Δ(0)]_{p2}=6.82 meV. The obtained results allowed next to calculate the dimensionless ratio R_{Δ}≡2Δ(0)/k_{B}T_{C}, which is equal to 3.71 and 3.81 in respect to p_{1} and p_{2}. In the last step, it is proven that the electron effective mass is weakly dependent on the temperature in the area of the existence of the superconducting state and reaches its maximum at the critical temperature. For the considered values of the pressure, we obtain [m_{e}^{⋆}]_{p1}^{max}=1.69m_{e} and [m_{e}^{⋆}]_{p2}^{max}=1.78m_{e}, where the symbol m_{e} denotes the electron band mass.

Phase transition and band structure of Cu_{2}O are systematically investigated by using the HSE06 range-separated hybrid functional. Cubic Cu_{2}O under pressure transforms to the metastable hexagonal phase. Our further investigations reveal that the first-order phase transition is driven by the elastic and dynamical instabilities. Furthermore, the stable band gap of cubic phase is always direct and greatly enhanced by pressure, whereas the hexagonal phase shows the semi-metallic band structure.

Since the demand of metamaterial (MM) based devices for practical applications is increased, the method with input impedance of dipole aims to produce fast results with reasonable accuracy for its design proposed. In this work, the unit of MM is equivalent to a dipole and then MM could be treated as a dipole array. An analysis is performed based on classical microwave dipole and numerical simulation by using the finite-difference time-domain for different MM configurations in the form of dipoles array. Additionally, a quality factor (Q-factor) based analysis is shown to yield simulation results which are in good agreement with the experiment. In essence, this shows that we could use antenna theory and numerical method to analyze MM thus opening the doors for a more efficient parameter optimization method.

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

Wide bandgap AlGaN (x=0.7–1) p-n junction is realized on a silicon substrate through polarization induced doping. Polarization induced positive charge field is produced by linearly grading from AlN to Al_{0.7}Ga_{0.3}N, and negative charge field is generated by an inverted grading from Al_{0.7}Ga_{0.3}N to AlN. The polarization charge field induced hole density is on the order of 10^{18} cm^{−3} in the graded Al_{x}Ga_{1−x}N:Be (x=0.7–1) p-n junction. Polarization doping provides a feasible way to mass produce III-nitride devices on silicon substrates.

Aiming at fast analysis of wide angle electromagnetic scattering problems, compressed sensing theory is introduced and applied, and a new kind of sparse representation of induced currents is constructed based on prior knowledge that originates from excitation vectors in method of moments. Using the new kind of sparse representation in conjugation with compressed sensing, one can recover unknown currents accurately with fewer measurements than some conventional sparse representations in mathematical sense. Hence, times of calculation by traditional method of moments used to obtain the required measurements can be reduced, which will improve the computational efficiency.

We present the experimental evidences showing that three different electron injection models play roles in Alq_{3} based organic light-emitting diodes in sequence when the thickness of LiF interlayer is changed. It is found that the device with a 0.2 nm LiF layer displays the largest current with declined luminescence. However, the one with a 0.6 nm LiF layer displays the second largest current and the highest luminescence of all. Combining with the photoluminescent test results, three models, namely chemical reaction at ternary interface, dipole effect at binary interface and tunneling enhancement effect, are expected to play roles in sequence when the LiF thickness is increased from 0 nm to 4 nm.

Double gamma-ray bursts (DGRBs) have two well-separated sub-bursts in the main prompt emission and the typical time interval between them is in the hundreds of seconds. Among DGRBs, gamma-ray bursts (DGRBs) 110801A and 120716A are the ones with known redshifts. However, unlike GRB 110801A, we show that the two sub-bursts of GRB 120716A is severally similar to the short- and long-duration GRBs, thus it is difficult to explain the origin of GRB 120716A by the popular models on the central engine of GRBs. We suggest that some mechanisms of x-ray flares in GRBs, i.e., a post-merger millisecond pulsars or the jet precession in a black hole hyperaccretion system may produce the DGRB.