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The hostile condition in a fusion tokomak reactor poses the main challenge in the development and design of in-vessel components such as divertor and breeding blanket due to fusion relevant irradiation conditions (14 MeV) and large thermal loads. The current work describes the employment of an integrated experimental-numerical approach to assess the microstructure evolution of dislocation loops and voids in tungsten proposed for fusion application. Cluster dynamics (CD) model is implemented and simulations are performed on the irradiated tungsten Disk shape Compact Tension (DCT) specimen used in the experimental test. TEM characterisation is performed on the DCT specimen irradiated at 400 {\deg}C and 600 {\deg}C with around 1 dpa, respectively. The dpa rate and cascade overlap rate from the experiments and SPECTRA-PKA code, respectively, are implemented in the CD model. Based on the comparison between experimental and computational results, the dose and temperature dependence of irradiation-induced defects (dislocation loops, voids, c15 clusters) are clearly observed. Trap mediated diffusion is studied and the impact of cascades with the pre-existing defects is analysed through full cascade overlap mode and the consequent influence on the defect concentration is evaluated. The exchange of self-interstitial atoms (SIAs) and the change in the size of loops through reaction between <111> and <100> loops are studied in detail by means of the transfer rate of the SIAs.

Ordered electronic states have been extensively explored in cuprates and iron-based unconventional superconductors, but seldom observed in the epitaxial FeSe/SrTiO3(001) monolayer (FeSe/STO) with an enhanced superconducting transition temperature (Tc). Here, by using scanning tunneling microscopy/ spectroscopy (STM/STS), we reveal a checkerboard charge order in the epitaxial FeSe/STO monolayer, with a period of four times the inter-Fe-atom distance along two perpendicular directions of the Fe lattice. This ordered state is uniquely present in the superconducting FeSe/STO monolayer, even at liquid nitrogen temperature, but absent in the non-superconducting FeSe monolayer or bilayer. Quasiparticle interference (QPI) measurements further confirm it as a static order without an energy-dependent dispersion and gapped out within the superconductivity gap. The intensity of the charge order shows an enhancement near the superconducting transition temperature, thus implying a correlation with the high-Tc superconductivity in the FeSe/STO monolayer. This study provides a new basis for exploring the ordered electronic states and their interplay with high-Tc superconductivity in the FeSe monolayer., Comment: 22 pages, 4 figures

This paper concerns the stabilizing effect of viscosity on the vortex sheets. It is found that although a vortex sheet is not a time-asymptotic attractor for the compressible Navier-Stokes equations, a viscous wave that approximates the vortex sheet on any finite time interval can be constructed explicitly, which is shown to be time-asymptotically stable in the $ L^\infty $-space with small perturbations, regardless of the amplitude of the vortex sheet. The result shows that the viscosity has a strong stabilizing effect on the vortex sheets, which are generally unstable for the ideal compressible Euler equations even for short time [26,8,1]. The proof is based on the $ L^2 $-energy method.In particular, the asymptotic stability of the vortex sheet under small spatially periodic perturbations is proved by studying the dynamics of these spatial oscillations. The first key point in our analysis is to construct an ansatz to cancel these oscillations. Then using the Galilean transformation, we are able to find a shift function of the vortex sheet such that an anti-derivative technique works, which plays an important role in the energy estimates. Moreover, by introducing a new variable and using the intrinsic properties of the vortex sheet, we can achieve the optimal decay rates to the viscous wave., Comment: In the second version, a new remark is added behind the Theorems and some typos in the proof are corrected

This paper shows that for the three-dimensional compressible isentropic Navier-Stokes equations, the planar viscous shocks are time-asymptotically stable to suitably small initial perturbations with zero masses. In particular, the perturbations consist of not only $ H^3 $-perturbations, but also periodic ones that oscillate at spatial infinity. In the former case, the final shock locations can be predicted in terms of the initial conditions, while in the latter the locations are subject to the dynamics of the oscillations. The stability analysis is based on the $L^2$-energy method. The key point is that the bad effect due to the compression of the shock waves can be removed by a combination of an anti-derivative technique and the use of Poincar\'{e} inequality in the normal and transversal directions, respectively., Comment: Accepted by SCIENCE CHINA Mathematics; see http://engine.scichina.com/doi/10.1007/s11425-023-2307-3

The large time behavior of the solutions to a multi-dimensional viscous conservation law is considered in this paper. It is shown that the solution time-asymptotically tends to the planar rarefaction wave if the initial perturbations are multi-dimensional periodic. The time-decay rate is also obtained. Moreover, a Gagliardo-Nirenberg type inequality is established in the domain $ \mathbb R \times \mathbb T^{n-1} (n\geq2) $, where $\mathbb T^{n-1}$ is the $ n-1 $-dimensional torus.

We study the asymptotic stability of a planar rarefaction wave (in the $ x_1 $- direction) for the 3-d isentropic Navier-Stokes equations, where the initial perturbation is periodic on the torus $ \mathbb{T}^3 $ with zero average. To solve this Cauchy problem in which the initial data is periodic with respect to only $ x_2 $ and $ x_3 $ but not to $ x_1, $ we construct a suitable ansatz carrying the oscillations of the solution in the $ x_1 $- direction, but remaining to be periodic in the transverse $ x_2 $- and $ x_3 $- directions. In such a way, the difference between the ansatz and the solution can be integrable on the region $ \mathbb{R}\times\mathbb{T}^2, $ which allows us to utilize the energy method with the aid of a Gagliardo-Nirenberg type inequality on $ \mathbb{R}\times\mathbb{T}^2 $ to prove the result.

The stability of solutions under periodic perturbations for both inviscid and viscous conservation laws is an interesting and important problem. In this paper, a large-amplitude viscous shock under space-periodic perturbation for the isentropic Navier-Stokes equations is considered. It is shown that if the initial perturbation around the shock is suitably small and satisfies a zero-mass type condition (2.17), then the solution of the N-S equations tends to the viscous shock with a shift, which is partially determined by the periodic oscillations. In other words, the viscous shock is nonlinearly stable even though the perturbation oscillates at the far fields. The key point is to construct a suitable ansatz $ (\tilde{v},\tilde{u}) $, which carries the same oscillations of the solution $ (v,u) $ at the far fields, so that the difference $ (v-\tilde{v},u-\tilde{u}) $ belongs to the $ H^2(R) $ space for all $ t\geq 0. $

This paper is concerned with the asymptotic stability of a composite wave of two viscous shocks under spatially periodic perturbations for the 1-D full compressible Navier-Stokes equations. It is proved that as time increases, the solution approaches the background composite wave with a shift for each shock, where the shifts can be uniquely determined if both the periodic perturbations and strengths of two shocks are small. The key of the proof is to construct a suitable ansatz such that the anti-derivative method works.

Puckered honeycomb Sb monolayer, the structural analog of black phosphorene, has been recently successfully grown by means of molecular beam epitaxy. However, little is known to date about the growth mechanism for such puckered honeycomb monolayer. In this study, by using scanning tunneling microscopy in combination with first-principles density functional theory calculations, we unveil that the puckered honeycomb Sb monolayer takes a kinetics-limited two-step growth mode. As the coverage of Sb increases, the Sb atoms firstly form the distorted hexagonal lattice as the half layer, and then the distorted hexagonal half-layer transforms into the puckered honeycomb lattice as the full layer. These results provide the atomic-scale insight in understanding the growth mechanism of puckered honeycomb monolayer, and can be instructive to the direct growth of other monolayers with the same structure., Comment: 16 pages, 4 figures

The interfacial charge transfer from the substrate may influence the electronic structure of the epitaxial van der Waals (vdW) monolayers and thus their further technological applications. For instance, the freestanding Sb monolayer in puckered honeycomb phase ({\alpha}-antimonene), the structural analog of black phosphorene, was predicted to be a semiconductor, but the epitaxial one behaves as a gapless semimetal when grown on the Td-WTe2 substrate. Here, we demonstrate that interface engineering can be applied to tune the interfacial charge transfer and thus the electron band of epitaxial monolayer. As a result, the nearly freestanding (semiconducting) {\alpha}-antimonene monolayer with a band gap of ~170 meV was successfully obtained on the SnSe substrate. Furthermore, a semiconductor-semimetal crossover is observed in the bilayer {\alpha}-antimonene. This study paves the way towards modifying the electron structure in two-dimensional vdW materials through interface engineering., Comment: 18 pages, 4 figures

Two-dimensional (2D) ferromagnetic materials have been exhibiting promising potential in applications, such as spintronics devices. To grow epitaxial magnetic films on silicon substrate, in the single-layer limit, is practically important but challenging. In this study, we realized the epitaxial growth of MnSn monolayer on Si(111) substrate, with an atomically thin Sn/Si(111)-$2\sqrt{3}\times2\sqrt{3}$- buffer layer, and controlled the MnSn thickness with atomic-layer precision. We discovered the ferromagnetism in MnSn monolayer with the Curie temperature (Tc) of ~54 K. As the MnSn film is grown to 4 monolayers, Tc increases accordingly to ~235 K. The lattice of the epitaxial MnSn monolayer as well as the Sn/Si(111)-$2\sqrt{3}\times2\sqrt{3}$ is perfectly compatible with silicon, and thus an sharp interface is formed between MnSn, Sn and Si. This system provides a new platform for exploring the 2D ferromagnetism, integrating magnetic monolayers into silicon-based technology, and engineering the spintronics heterostructures., Comment: 12 pages, 3 figures, to appear in Chin. Phys. Lett. (Express Letters)

Chiral fermions in solid state feature "Fermi arc" states, connecting the surface projections of the bulk chiral nodes. The surface Fermi arc is a signature of nontrivial bulk topology. Unconventional chiral fermions with an extensive Fermi arc traversing the whole Brillouin zone have been theoretically proposed in CoSi. Here, we use scanning tunneling microscopy / spectroscopy to investigate quasiparticle interference at various terminations of a CoSi single crystal. The observed surface states exhibit chiral fermion-originated characteristics. These reside on (001) and (011) but not (111) surfaces with pi-rotation symmetry, spiral with energy, and disperse in a wide energy range from ~-200 to ~+400 mV. Owing to the high-energy and high-space resolution, a spin-orbit coupling-induced splitting of up to ~80 mV is identified. Our observations are corroborated by density functional theory and provide strong evidence that CoSi hosts the unconventional chiral fermions and the extensive Fermi arc states., Comment: 20 pages, 4 figures

This paper is concerned with the large time behaviors of the entropy solutions to one-dimensional scalar convex conservation laws, of which the initial data are assumed to approach two arbitrary $ L^\infty $ periodic functions as $ x\rightarrow-\infty $ and $ x\rightarrow+\infty, $ respectively. We show that the solutions approach the Riemann solutions at algebraic rates as time increases. Moreover, a new discovery in this paper is that the difference between the two periodic perturbations at two infinities may generate a constant shift on the background shock wave, which is different from the result in [11], where the two periodic perturbations are the same.

Atomically thin two-dimensional (2D) crystals have gained tremendous attentions owing to their potential impacts to the future electronics technologies, as well as the exotic phenomena emerging in these materials. Monolayer of {\alpha} phase Sb ({\alpha}-antimonene) that shares the same puckered structure as black phosphorous, has been predicted to be stable with precious properties. However, the experimental realization still remains challenging. Here, we successfully grow high-quality monolayer {\alpha}-antimonene, with the thickness finely controlled. The {\alpha}-antimonene exhibits great stability upon exposure to air. Combining scanning tunneling microscope, density functional theory calculations and transport measurement, it is found that the electron band crossing the Fermi level exhibits a linear dispersion with a fairly small effective mass, and thus a good electrical conductivity. All of these properties make the {\alpha}-antimonene promising in the future electronic applications., Comment: 14 pages, 5 figures

This paper studies the asymptotic stability of shock profiles and rarefaction waves under space-periodic perturbations for one-dimensional convex scalar viscous conservation laws. For the shock profile, we show that the solution approaches the background shock profile with a constant shift in the $ L^\infty(\mathbb{R}) $ norm at exponential rates. The new phenomena contrasting to the case of localized perturbations is that the constant shift cannot be determined by the initial excessive mass in general, which indicates that the periodic oscillations at infinities make contributions to this shift. And the vanishing viscosity limit for the shift is also shown. The key elements of the poof consist of the construction of an ansatz which tends to two periodic solutions as $ x \rightarrow \pm\infty, $ respectively, and the anti-derivative variable argument, and an elaborate use of the maximum principle. For the rarefaction wave, we also show the stability in the $ L^\infty(\mathbb{R}) $ norm., Comment: 43 pages, 3 figures

In this paper we study large time behaviors toward shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar conservation laws. The asymptotic stabilities and decay rates of shock waves and rarefaction waves under periodic perturbations are proved.

The two-dimensional topological insulators (2DTI) host a full gap in the bulk band, induced by spin-orbit coupling (SOC) effect, together with the topologically protected gapless edge states. However, the SOC-induced gap is usually small, and it is challenging to suppress the bulk conductance and thus to realize the quantum spin Hall (QSH) effect. In this study, we find a novel mechanism to effectively suppress the bulk conductance. By using the quasiparticle interference (QPI) technique with scanning tunneling spectroscopy (STS), we demonstrate that the QSH candidate single-layer 1T'-WTe$_2$ has a semi-metal bulk band structure with no full SOC-induced gap. Surprisingly, in this two-dimensional system, we find the electron interactions open a Coulomb gap which is always pinned at the Fermi energy (E$_F$). The opening of the Coulomb gap can efficiently diminish the bulk state at the E$_F$ and is in favor of the observation of the quantized conduction of topological edge states., Comment: 13 pages, 4 figures

Stanene has been predicted to be a two-dimensional topological insulator (2DTI). Its low-buckled atomic geometry and the enhanced spin-orbit coupling are expected to cause a prominent quantum spin hall (QSH) effect. However, most of the experimentally grown stanene to date displays a metallic state without a real gap, possibly due to the chemical coupling with the substrate and the stress applied by the substrate. Here,we demonstrate an efficient way of tuning the atomic buckling in stanene to open a topologically nontrivial energy gap. Via tuning the growth kinetics, we obtain not only the low-buckled 1x1 stanene but also an unexpected high-buckled R3xR3 stanene on the Bi(111) substrate. Scanning tunneling microscopy (STM) study combined with density functional theory (DFT) calculation confirms that the R3xR3 stanene is a distorted 1x1 structure with a high-buckled Sn in every three 1x1 unit cells. The high-buckled R3xR3 stanene favors a large band inversion at the {\Gamma} point, and the spin orbital coupling open a topologically nontrivial energy gap. The existence of edge states as verified in both STM measurement and DFT calculation further confirms the topology of the R3xR3 stanene. This study provides an alternate way to tune the topology of monolayer 2DTI materials., Comment: 9 pages, 5 figures