We have introduced a novel Majorana representation of S=1/2 spins using the Jordan-Wigner transformation and have shown that a generalized spin model of Kitaev defined on a brick-wall lattice is equivalent to a model of non-interacting Majorana fermions with Z2 gauge fields without redundant degrees of freedom. The quantum phase transitions of the system at zero temperature are found to be of topological type and can be characterized by nonlocal string order parameters. In appropriate dual representations, these string order parameters become local order parameters and the basic concept of Landau theory of continuous phase transition can be applied.The Landau theory of second order phase transitions has fertilized modern statistical and condensed matter physics. Essential is to use local order parameters to describe the continuous phase transition between a disordered and an ordered phase associated with symmetry breaking.[1] However, a quantum phase transition driven entirely by quantum fluctuations at zero temperature can occur between two disordered phases without any symmetry breaking. [2,3] A typical example is the topological phase transition between two neighboring quantum Hall plateaus in the fractional quantum Hall effect. [4] As no conventional Landau-type order parameters can be used, a comprehensive characterization of this kind of quantum phase transitions has become one of the most challenging issues in condensed matter theory.In this work, we present a theoretical analysis of quantum phase transitions in the following S = 1/2 spin model first introduced by Kitaev[5] H = j+l=even

The recent discovery of large magnetoresistance in tungsten ditelluride provides a unique playground to find new phenomena and significant perspective for potential applications. The large magnetoresistance effect originates from a perfect balance of hole and electron carriers, which is sensitive to external pressure. Here we report the suppression of the large magnetoresistance and emergence of superconductivity in pressurized tungsten ditelluride via high-pressure synchrotron X-ray diffraction, electrical resistance, magnetoresistance and alternating current magnetic susceptibility measurements. Upon increasing pressure, the positive large magnetoresistance effect is gradually suppressed and turned off at a critical pressure of 10.5 GPa, where superconductivity accordingly emerges. No structural phase transition is observed under the pressure investigated. In situ high-pressure Hall coefficient measurements at low temperatures demonstrate that elevating pressure decreases the population of hole carriers but increases that of the electron ones. Significantly, at the critical pressure, a sign change of the Hall coefficient is observed.

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Ecosystem structure, functioning and stability have been a focus of ecological and environmental sciences during the past two decades. The mechanisms underlying their relationship, however, are not well understood. Based on comprehensive studies in Inner Mongolia grassland, here we show that species-level stoichiometric homoeostasis was consistently positively correlated with dominance and stability on both 2-year and 27-year temporal scales and across a 1200-km spatial transect. At the community level, stoichiometric homoeostasis was also positively correlated with ecosystem function and stability in most cases. Thus, homoeostatic species tend to have high and stable biomass; and ecosystems dominated by more homoeostatic species have higher productivity and greater stability. By modulating organism responses to key environmental drivers, stoichiometric homoeostasis appears to be a major mechanism responsible for the structure, functioning and stability of grassland ecosystems.

Biodiversity generally promotes ecosystem stability. To assess whether the diversity-stability relationship observed under ambient nitrogen (N) conditions still holds under N enriched conditions, we designed a 6-year field experiment to test whether the magnitude and frequency of N enrichment affects ecosystem stability and its relationship with species diversity in a temperate grassland. Results of this experiment showed that the frequency of N addition had no effect on either the temporal stability of ecosystem and population or the relationship between diversity and stability. Nitrogen addition decreased ecosystem stability significantly through decreases in species asynchrony and population stability. Species richness was positively associated with ecosystem stability, but no significant relationship between diversity and the residuals of ecosystem stability was detected after controlling for the effects of the magnitude of N addition, suggesting collinearity between the effects of N addition and species richness on ecosystem stability, with the former prevailing over the latter. Both population stability and the residuals of population stability after controlling for the effects of the magnitude of N addition were positively associated with ecosystem stability, indicating that the stabilizing effects of component populations were still present after N enrichment. Our study supports the theory predicting that the effects of environmental factors on ecosystem functioning are stronger than those of biodiversity. Understanding such mechanisms is important and urgent to protect biodiversity in mediating ecosystem functioning and services in the face of global changes.

A large and high-quality single crystal (Li 0.84 Fe 0.16 )OHFe 0.98 Se, the optimal superconductor of newly reported (Li 1-x Fe x )OHFe 1-y Se system, has been successfully synthesized via a hydrothermal ion-exchange technique. The superconducting transition temperature (T c ) of 42 K is determined by magnetic susceptibility and electric resistivity measurements, and the zero-temperature upper critical magnetic fields are evaluated as 79 and 313 Tesla for the field along the c-axis and the ab-plane, respectively. The ratio of out-of-plane to in-plane electric resistivity,ρ c /ρ ab , is found to increases with decreasing temperature and to reach a high value of 2500 at 50 K, with an evident kink occurring at a characteristic temperature T*=120 K. The negative in-plane Hall coefficient indicates that electron carriers dominate in the charge transport, and the hole contribution is significantly reduced as the temperature is lowered to approach T*. From T* down to T c , we observe the linear temperature dependences of the in-plane electric resistivity and the magnetic susceptibility for the FeSe layers. Our findings thus reveal that the normal state of (Li 0.84 Fe 0.16 )OHFe 0.98 Se becomes highly two-dimensional and anomalous prior to the superconducting transition, providing a new insight into the mechanism of high-T c superconductivity.

We use scanning tunneling microscopy to investigate the (001) surface of cleaved SmB 6 Kondo insulator. Variable temperature dI/dV spectroscopy up to 60 K reveals a gap-like density of state suppression around the Fermi level, which is due to the hybridization between the itinerant Sm 5d band and localized Sm 4f band. At temperatures below 40 K, a sharp coherence peak emerges within the hybridization gap near the lower gap edge. We propose that the in-gap resonance state is due to a collective excitation in magnetic origin with the presence of spin-orbital coupling and mixed valence fluctuations. These results shed new lights on the electronic structure evolution and transport anomaly in SmB 6 .

Stoichiometric homeostasis, the degree to which an organism maintains its C:N:P ratios around a given species- or stage-specific value despite variation in the relative availabilities of elements in its resource supplies, is a key parameter in ecological stoichiometry. However, its regulation and role in affecting organismal and ecosystem processes is still poorly understood in vascular plants. We performed a sand culture experiment and a field nitrogen (N) and phosphorus (P) addition experiment to evaluate the strength of N, P and N:P homeostasis in higher plants in the Inner Mongolia grassland. Our results showed that homeostatic regulation coefficients (H) of vascular plants ranged from 1.93 to 14.5. H varied according to plant species, aboveground and belowground compartments, plant developmental stage, and overall plant nutrient content and N:P ratio. H for belowground and for foliage were inversely related, while H increased with plant developmental stage. H for N (H(N)) was consistently greater than H for P (H(P)) while H for N:P (H(N:P)) was consistently greater than H(N) and H(P). Furthermore, species with greater N and P contents and lower N:P were less homeostatic, suggesting that more homeostatic plants are more conservative nutrient users. The results demonstrate that H of plants encompasses a considerable range but is stronger than that of algae and fungi and weaker than that of animals. This is the first comprehensive evaluation of factors influencing stoichiometric homeostasis in vascular plants.