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The two-dimensional (2D) kagome lattice is a versatile platform to explore exotic quantum states. The recently discovered kagome superconductors AV3Sb5 (A= Cs, Rb, K) containing vanadium kagome lattices exhibit a variety of intriguing phenomena, such as a charge density wave (CDW) with time-reversal symmetry breaking and possible unconventional superconductivity. In particular, in bulk samples the CDW displays a three-dimensional character and tends to be suppressed by external or chemical pressure. However, the characteristics and stability of the CDW order in atomically thin flakes approaching the 2D limit remain unexplored. Here, through combined electrical transport, scanning transmission electron microscopy (STEM) and Raman scattering measurements, we report an intertwined-order phase diagram of CsV3Sb5 flakes down to the monolayer. After successfully confirming the stability of the kagome lattice down to at least 4 layers, we observe a non-monotonic evolution of the CDW transition temperature TCDW with a reduction of flake thickness. TCDW first decreases to a minimum value of 72 K at 27 layers and then increases abruptly, reaching a record-high value of 120 K at 5 layers. The superconducting transition temperature (Tc) features an inverse variation with TCDW. Flakes with less than 5 layers, however, become more insulating with decreasing thickness. Raman scattering measurements reveal a weakened electron-phonon coupling with the reduction of sample thickness, suggesting that a crossover from electron-phonon coupling to dominantly electronic interactions could account for the non-monotonic thickness dependence of TCDW. Our work demonstrates the novel effects of dimension reduction and carrier doping on quantum states in thin flakes and provides crucial insights into the complex mechanism of the CDW order in the family of AV3Sb5 kagome metals.

The lump solutions and interaction solutions are mainly investigated for the (2 + 1)-dimensional KPI equation. According to relations of the undetermined parameters of the test functions, the N-soliton solutions are showed by computations of the Maple using the Hirota bilinear form for (2 + 1)-dimensional KPI equation. One type of the lump solutions for (2 + 1)-dimensional KPI equation has been deduced by the limit method of the N-soliton solutions. In addition, the interaction solutions between the lump and N-soliton solutions of it are studied by the undetermined interaction functions. The sufficient conditions for the existence of the interaction solutions are obtained. Furthermore, the new breather solutions for the (2 + 1)-dimensional KPI equation are considered by the homoclinic test method via new test functions including more parameters than common test functions.

In today’s world, environmental problems are becoming increasingly serious, and countries and regions are attaching great importance to them. Low-carbon and circular economy have become a strategic choice for China’s sustainable economic development. As the public’s awareness of environmental protection becomes stronger and stronger, the managers of companies ought to consider the maximum economic benefits. Meanwhile, they are supposed to focus on the green image of enterprises, so as to win in the market competition. The probabilistic linguistic term sets (PLTSs) are useful for expressing uncertain and fuzzy cognitions of the DMs over attributes. In this paper, we extend the Evaluation based on Distance from Average Solution (EDAS) method to the multiple attribute group decision making (MAGDM) with PLTSs. Firstly, concept, comparative formula, and distances of PLTSs are introduced in a nutshell. Then, the extended EDAS method is used to cope with the problems of MAGDM in PLTSs. In addition, for the sake of verifying the applicability of the expanding method, a calculation example about the sorting of green supplier is utilized. Consequently, the example shows that the method is easy to understand and operate. This method can be employed to choose the appropriate solution in other problems of selecting.

Condensed matter systems in low dimensions exhibit emergent physics that does not exist in three dimensions. When electrons are confined to one dimension (1D), some significant electronic states appear, such as charge density wave, spin-charge separations, and Su-Schrieffer-Heeger (SSH) topological state. However, a clear understanding of how the 1D electronic properties connects with topology is currently lacking. Here we systematically investigated the characteristic 1D Dirac fermion electronic structure originated from the metallic NbTe2 chains on the surface of the composition-tunable layered compound NbSixTe2 (x = 0.40 and 0.43) using angle-resolved photoemission spectroscopy. We found the Dirac fermion forms a Dirac nodal line structure protected by the combined $$\widetilde {M_y}$$ M y ̃ and time-reversal symmetry T and proves the NbSixTe2 system as a topological semimetal, in consistent with the ab-initio calculations. As x decreases, the interaction between adjacent NbTe2 chains increases and Dirac fermion goes through a dimension-crossover from 1D to 2D, as evidenced by the variation of its Fermi surface and Fermi velocity across the Brillouin zone in consistence with a Dirac SSH model. Our findings demonstrate a tunable 1D Dirac electron system, which offers a versatile platform for the exploration of intriguing 1D physics and device applications.

The location of the electric vehicle charging station is deemed to be a multiple attribute group decision making (MAGDM) issue involving many experts and many conflicting attributes. In practical MAGDM issues, the information of uncertain and fuzzy cognitive decision is well-depicted by linguistic term sets (LTSs). These LTSs could be simply shifted into the probabilistic linguistic sets (PLTSs). In such paper, we design some novel probabilistic linguistic weighted Dice similarity measures (PLWDSM) and the probabilistic linguistic weighted generalized Dice similarity measures (PLWGDSM). Subsequently, the PLWGDSM-based MAGDM methods are presented under PLTSs. In the end, a practical case which concerns about the location planning of electric vehicle charging stations is offered to demonstrate the proposed PLWGDSM’s applicability and advantages.

The intriguing quasiparticles in solids, known as Dirac, Weyl, and Majorana fermions, etc. with properties akin to those theoretically predicted but never realized in high-energy physics, have excited intensive research activities in recent years. The transition metal dipnictides are attractive because of their extremely large magnetoresistance that is usually attributed to the carrier compensation effect. We briefly review herein the crystal growth, magneto-transport measurements, and theoretical studies of tantalum dipnictides TaAs2 and TaP2, with the emphasis being put on discussion of the nontrivial topological states in both materials. The analysis of quantum oscillations of the magnetoresistance unveils nonzero Berry phase. The chiral negative longitudinal magnetoresistance further points to possible Weyl state, which was recently theoretically suggested as the result of the magnetic field-induced Zeeman splitting effect no matter how large the field is. The analysis of these intriguing behaviors could brush up our understanding about the family of materials and would be valuable for future work on investigating the magnetic field-induced topological phase transition in such semimetals.

The finite dimension estimates of Hausdorff dimension and fractal dimension of the attractor of the dissipative quantum Zakharov equations are mainly studied by using the estimates of the Lyapunov exponents. The main results on the attractor are obtained through studying the linear system $\operatorname{DS}(t)$ , which is the differential system of solution operator $S(t)$ for the dissipative quantum Zakharov equations at the initial value $(m_{0},n_{0},E_{0})$ .

Experiments show that TaAs is a three-dimensional topological Weyl semimetal. Three-dimensional (3D) topologicalWeyl semimetals (TWSs) represent a state of quantum matter with unusual electronic structures that resemble both a ‘3D graphene’ and a topological insulator. Their electronic structure displays pairs of Weyl points (through which the electronic bands disperse linearly along all three momentum directions) connected by topological surface states, forming a unique arc-like Fermi surface (FS). Each Weyl point is chiral and contains half the degrees of freedom of a Dirac point, and can be viewed as a magnetic monopole in momentum space. By performing angle-resolved photoemission spectroscopy on the non-centrosymmetric compound TaAs, here we report its complete band structure, including the unique Fermi-arc FS and linear bulk band dispersion across the Weyl points, in agreement with the theoretical calculations1,2. This discovery not only confirms TaAs as a 3DTWS, but also provides an ideal platform for realizing exotic physical phenomena (for example, negative magnetoresistance, chiral magnetic effects and the quantum anomalous Hall effect) which may also lead to novel future applications.

In this paper, we investigate a global random attractor for a stochastic local modified Swift-Hohenberg equation with multiplicative noise in Stratonovich sense. Through the Ornstein-Uhlenbeck (O-U) transformation, we obtain the random dynamical system associated with the stochastic local modified Swift-Hohenberg equation. Using the properties of the O-U process, we derive the specific uniform a priori estimates, using which we prove the existence of global random attractor for the corresponding random dynamical system.

In Corynebacterium glutamicum, acetohydroxy acid synthase (AHAS, encoded by ilvBN) is regulated by the end products in biosynthesis pathway, which catalyzes the first common reaction in the biosynthesis of branched-chain amino acids (BCAAs). In this study, conserved A42, A89 and K136 residues in AHAS regulatory subunit were chosen for site-directed mutagenesis, and the resulting mutations A42V, A89V and K136E exhibited higher resistance to inhibition by BCAAs than wild type AHAS. Furthermore, double-mutation was carried out on A42V, A89V and K136E mutations. Expectedly, A42V-A89V mutation exhibited nearly complete resistance to inhibition by all three BCAAs, which retained above 93% enzyme activity even at 10 mM. Strains were further studied to investigate the effects of over-expressing different mutant ilvBN on the biosynthesis of BCAAs. It was found that production of BCAAs was increased with the increase of resistance to BCAAs. However, the increase of isoleucine and leucine was slower than valine which showed a significant increase (up to 86.30 mM). Furthermore, strains harboring plasmids with different mutant ilvBN could significantly decrease production of alanine (main byproduct). This work gives additional understanding of roles of A42, A89 and K136 residues and makes the A42V, A89V, K136E and A42V-A89V mutations a good starting point for further development by protein engineering.

The experiments presented here were based on the conclusions of our previous results. In order to avoid introduction of expression plasmid and to balance the NADH/NAD ratio, the NADH biosynthetic enzyme, i.e., NAD-dependent glyceraldehyde-3-phosphate dehydrogenase (GADPH), was replaced by NADP-dependent GADPH, which was used to biosynthesize NADPH rather than NADH. The results indicated that the NADH/NAD ratio significantly decreased, and glucose consumption and L-lysine production drastically improved. Moreover, increasing the flux through L-lysine biosynthetic pathway and disruption of ilvN and hom, which involve in the branched amino acid and L-methionine biosynthesis, further improved L-lysine production by Corynebacterium glutamicum. Compared to the original strain C. glutamicum Lys5, the L-lysine production and glucose conversion efficiency (α) were enhanced to 81.0 ± 6.59 mM and 36.45% by the resulting strain C. glutamicum Lys5-8 in shake flask. In addition, the by-products (i.e., L-threonine, L-methionine and L-valine) were significantly decreased as results of genetic modification in homoserine dehydrogenase (HSD) and acetohydroxyacid synthase (AHAS). In fed-batch fermentation, C. glutamicum Lys5-8 began to produce L-lysine at post-exponential growth phase and continuously increased over 36 h to a final titer of 896 ± 33.41 mM. The L-lysine productivity was 2.73 g l(-1) h(-1) and the α was 47.06% after 48 h. However, the attenuation of MurE was not beneficial to increase the L-lysine production because of decreasing the cell growth. Based on the above-mentioned results, we get the following conclusions: cofactor NADPH, precursor, the flux through L-lysine biosynthetic pathway and DCW are beneficial to improve L-lysine production in C. glutamicum.

Metals cannot exhibit ferroelectricity because static internal electric fields are screened by conduction electrons, but in 1965, Anderson and Blount predicted the possibility of a ferroelectric metal, in which a ferroelectric-like structural transition occurs in the metallic state. Up to now, no clear example of such a material has been identified. Here we report on a centrosymmetric (R-3c) to non-centrosymmetric (R3c) transition in metallic LiOsO3 that is structurally equivalent to the ferroelectric transition of LiNbO3. The transition involves a continuous shift in the mean position of Li+ ions on cooling below 140K. Its discovery realizes the scenario described by Anderson and Blount, and establishes a new class of materials whose properties may differ from those of normal metals., Manuscript of published version, including Supplementary Information. See also News & Views article by V. Keppens, Nature Materials 12, 952 (2013)

In this paper, we study the quantum Zakharov system, which describes the nonlinear interaction between the quantum Langmuir and quantum ion-acoustic waves. The global well-posedness result of this system in the energy and above energy spaces is obtained in the case d = 1, 2, 3. Moreover, the classical limit behavior of the quantum Zakharov system is also investigated as the quantum parameter tends to zero.

High quality La0.67Ca0.33MnO3 (LCMO) film was deposited via a novel pulsed electron deposition technique on SrTiO3(100) single crystal substrate. The micro-bridge with different widths was fabricated by using electron beam lithography (EBL) technique and their transport properties were studied. For the micro-bridges with width of 2 and 1.5 μm, the insulator-to-metal transition temperature (T P) keeps unchanged compared with the film. For the micro-bridges with width of 1 μm, the T P shifts towards the lower temperature by 50 K. When the width decreases down to 500 nm, the insulator-to-metal transition disappears. The magnetoresistance behavior of these micro-bridges was studied, and the results show that the low field magnetoresistance (LFMR) decreases and the high field magnetoresistances (HFMR) keep almost unchanged as the width of micro-bridge is reduced.

Nature Physics 11, 728–732 (2015); published online 17 August 2015; corrected after print 3 September 2015. In the version of this Letter originally published a description of arc-like Fermi surfaces in the abstract contained a typographical error. This error has been corrected in the online versions.