An ensemble of random graphs with identical degree distribution

Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast, in this paper, we report a fact that two arbitrarily chosen networks with identical degree distribution can have completely different other topological structure, such as diameter, spanning trees number, pearson correlation coefficient, and so forth. Besides that, for a given degree distribution (as power-law distribution with exponent $\gamma=3$ discussed here), it is reasonable to ask how many network models with such a constraint we can have. To this end, we generate an ensemble of this kind of random graphs with $P(k)\sim k^{-\gamma}$ ($\gamma=3$), denoted as graph space $\mathcal{N}(p,q,t)$ where probability parameters $p$ and $q$ hold on $p+q=1$, and indirectly show the cardinality of $\mathcal{N}(p,q,t)$ seems to be large enough in the thermodynamics limit, i.e., $N\rightarrow\infty$, by varying values of $p$ and $q$. From the theoretical point of view, given an ultrasmall constant $p_{c}$, perhaps only graph model $N(1,0,t)$ is small-world and other are not in terms of diameter. And then, we study spanning trees number on two deterministic graph models and obtain both upper bound and lower bound for other members. Meanwhile, for arbitrary $p(\neq1)$, we prove that graph model $N(p,q,t)$ does go through two phase transitions over time, i.e., starting by non-assortative pattern and then suddenly going into disassortative region, and gradually converging to initial place (non-assortative point). Among of them, one "null" graph model is built

Spin excitations in K0.84_{0.84}Fe1.99_{1.99}Se2_2 superconductor as studied by M\"ossbauer spectroscopy

M\"ossbauer spectroscopy was used to probe the site specific information of the $K_{0.84}Fe_{1.99}Se_2$ superconductor. Possibility of coexistence of superconductivity and magnetism is discussed. A spin excitation gap, $\Delta E \approx$5\,meV, is observed by analyzing the temperature dependence of the hyperfine magnetic field (HMF) at the iron site within the spin wave theory. Using a simple model suggested in the literature, the temperature dependence of the HMF is well reproduced, suggesting that, below room temperature, the iron-selenide superconductors can be regarded as ferromagnetically coupled spin blocks that interact with each other antiferromagnetically to form the observed checkerboard-like magnetic structure

Charge redistribution at the antiferromagnetic phase transition in SrFeAsF compound

The relationship between spin, electron, and crystal structure has been one of the foremost issues in understanding the superconducting mechanism since the discovery of iron-based high temperature superconductors. Here, we report M\"ossbauer and first-principles calculations studies of the parent compound SrFeAsF with the largest temperature gap ($\sim$50\,K) between the structural and antiferromagnetic (AFM) transitions. Our results reveal that the structural transition has little effect on the electronic structure of the compound SrFeAsF while the development of the AFM order induces a redistribution of the charges near the Fermi level.Comment: 6 Pages, 7 Figure

Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies

Although topological mechanical metamaterials have been extensively studied from a theoretical perspective, their experimental characterization has been lagging. To address this shortcoming, we present a systematic laser-assisted experimental characterization of topological kagome lattices, aimed at elucidating their in-plane phononic and topological characteristics. We specifically explore the continuum elasticity limit, which is established when the ideal hinges that appear in the theoretical models are replaced by ligaments capable of supporting bending deformation, as observed for instance in realistic physical lattices. We reveal how the zero-energy floppy edge modes predicted for ideal configurations morph into finite-frequency phonon modes that localize at the edges. By probing the lattices with carefully designed excitation signals, we are able to extract and characterize all the features of a complex low-frequency acoustic regime in which bulk modes and topological edge modes overlap and entangle in response. The experiments provide unequivocal evidence of the existence of strong asymmetric wave transport regimes at finite frequencies.Comment: 8 pages, 10 figure

Study of 57Fe Mossbauer effect in RFe2Zn20 ( R = Lu, Yb, Gd)

We report measurements of 57Fe Mossbauer spectra for RFe2Zn20 ( R = Lu, Yb, Gd) from ~ 4.5 K to room temperature. The obtained isomer shift values are very similar for all three compounds, their temperature dependence was analyzed within the Debye model and resulted in an estimate of the Debye temperatures of 450-500 K. The values of quadrupole splitting at room temperature change with the cubic lattice constant a in a linear fashion. For GdFe2Zn20, ferromagnetic order is seen as an appearance of a sextet in the spectra. The 57Fe site hyperfine field for T = 0 was evaluated to be ~ 2.4 T

Mechanically-induced disorder in CaFe2As2: a 57Fe Mossbauer study

57Fe Mossbauer spectroscopy was used to perform a microscopic study on the extremely pressure and strain sensitive compound, CaFe2As2, with different degrees of strain introduced by grinding and annealing. At the base temperature, in the antiferromagnetic/orthorhombic phase, compared to a sharp sextet Mossbauer spectrum of single crystal CaFe2As2, which is taken as an un-strained sample, an obviously broadened sextet and an extra doublet were observed for ground CaFe2As2 powders with different degrees of strain. The Mossbauer results suggest that the magnetic phase transition of CaFe2As2 can be inhomogeneously suppressed by the grinding induced strain to such an extent that the antiferromagnetic order in parts of the grains forming the powdered sample remain absent all the way down to 4.6 K. However, strain has almost no effect on the temperature dependent hyperfine magnetic field in the grains with magnetic order. Additional electronic and asymmetry information was obtained from the isomer shift and quadrupole splitting. Similar isomer shift values in the magnetic phase for samples with different degrees of strain, indicate that the stain does not bring any significant variation of the electronic density at 57Fe nucleus position. The absolute values of quadrupole shift in the magnetic phase decrease and approach zero with increasing degrees of strain, indicating that the strain reduces the average lattice asymmetry at Fe atom position

Transition to collapsed tetragonal phase in CaFe2As2 single crystals as seen by 57Fe Mossbauer spectroscopy

Temperature dependent measurements of 57Fe Mossbauer spectra on CaFe2As2 single crystals in the tetragonal and collapsed tetragonal phases are reported. Clear features in the temperature dependencies of the isomer shift, relative spectra area and quadrupole splitting are observed at the transition from the tetragonal to the collapsed tetragonal phase. From the temperature dependent isomer shift and spectral area data, an average stiffening of the phonon modes in the collapsed tetragonal phase is inferred. The quadrupole splitting increases by ~25% on cooling from room temperature to ~100 K in the tetragonal phase and is only weakly temperature dependent at low temperatures in the collapsed tetragonal phase, in agreement with the anisotropic thermal expansion in this material. In order to gain microscopic insight about these measurements we perform ab initio density functional theory calculations of the electric field gradient and the electron density of CaFe2As2 in both phases. By comparing the experimental data with the calculations we are able to fully characterize the crystal structure of the samples in the collapsed-tetragonal phase through determination of the As z-coordinate. Based on the obtained temperature dependent structural data we are able to propose charge saturation of the Fe - As bond region as the mechanism behind the stabilization of the collapsed-tetragonal phase at ambient pressure

A New Variation of Hat Guessing Games

Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set. Simultaneously, each player tries to guess the color of his/her own hat by looking at colors of hats worn by other players. In this paper, we consider a new variation of this game, in which we require at least $k$ correct guesses and no wrong guess for the players to win the game, but they can choose to "pass". A strategy is called {\em perfect} if it can achieve the simple upper bound $\frac{n}{n+k}$ of the winning probability. We present sufficient and necessary condition on the parameters $n$ and $k$ for the existence of perfect strategy in the hat guessing games. In fact for any fixed parameter $k$, the existence of perfect strategy can be determined for every sufficiently large $n$. In our construction we introduce a new notion: $(d_1,d_2)$-regular partition of the boolean hypercube, which is worth to study in its own right. For example, it is related to the $k$-dominating set of the hypercube. It also might be interesting in coding theory. The existence of $(d_1,d_2)$-regular partition is explored in the paper and the existence of perfect $k$-dominating set follows as a corollary.Comment: 9 pages; The main theorem was improve

Strong anisotropy effect in iron-based superconductor CaFe0.882_{0.882}Co0.118_{0.118}AsF

The anisotropy of the Fe-based superconductors is much smaller than that of the cuprates and the theoretical calculations. A credible understanding for this experimental fact is still lacking up to now. Here we experimentally study the magnetic-field-angle dependence of electronic resistivity in the superconducting phase of iron-based superconductor CaFe$_{0.882}$Co$_{0.118}$AsF, and find the strongest anisotropy effect of the upper critical field among the iron-based superconductors based on the framework of Ginzburg-Landau theory. The evidences of energy band structure and charge density distribution from electronic structure calculations demonstrate that the observed strong anisotropic effect mainly comes from the strong ionic bonding in between the ions of Ca$^{2+}$ and F$^-$, which weakens the interlayer coupling between the layers of FeAs and CaF. This finding provides a significant insight into the nature of experimentally observed strong anisotropic effect of electronic resistivity, and also paves an avenue to design exotic two dimensional artificial unconventional superconductors in future.Comment: 5 pages, 3 figures, accepted to Supercond. Sci. Techno

Growth and characterization of CaFe1−x_{1-x}Cox_xAsF single crystals by CaAs flux method

Millimeter sized single crystals of CaFe$_{1-x}$Co$_x$AsF were grown using a self-flux method. It is found that high-quality single crystals can be grown from three approaches with different initial raw materials. The chemical compositions and crystal structure were characterized carefully. The c-axis lattice constant is suppressed by the Co substitution. Superconductivity with the critical transition $T_c$ as high as 21 K was confirmed by both the resistivity and magnetic susceptibility measurements in the sample with $x$ = 0.12. Moreover, it is found that $T_c$ can be enhanced for about 1 K under the very small hydrostatic pressure of 0.22 GPa, which is more quickly than that reported in the polycrystalline samples. Our results is a promotion for the physical investigations of 1111 phase iron-pnictide superconductors.Comment: 11 pages, 4 figures, submitted to Journal of Crystal Growt