Elucidating the microscopic origin of nematic order in iron-based superconducting materials is important because the interactions that drive nematic order may also mediate the Cooper pairing. Nematic order breaks fourfold rotational symmetry in the i
ron plane, which is believed to be driven by either orbital or spin degrees of freedom. However, as the nematic phase often develops at a temperature just above or coincides with a stripe magnetic phase transition, experimentally determining the dominant driving force of nematic order is difficult. Here, we use neutron scattering to study structurally the simplest iron-based superconductor FeSe, which displays a nematic (orthorhombic) phase transition at $T_s=90$ K, but does not order antiferromagnetically. Our data reveal substantial stripe spin fluctuations, which are coupled with orthorhombicity and are enhanced abruptly on cooling to below $T_s$. Moreover, a sharp spin resonance develops in the superconducting state, whose energy (~4 meV) is consistent with an electron boson coupling mode revealed by scanning tunneling spectroscopy, thereby suggesting a spin fluctuation-mediated sign-changing pairing symmetry. By normalizing the dynamic susceptibility into absolute units, we show that the magnetic spectral weight in FeSe is comparable to that of the iron arsenides. Our findings support recent theoretical proposals that both nematicity and superconductivity are driven by spin fluctuations.
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of social netw
orks including common-interest networks, collaboration networks, and actor networks. Simply put, a random intersection graph is constructed by assigning each node a set of items in some random manner and then putting an edge between any two nodes that share a certain number of items. Broadly speaking, our work is about analyzing random intersection graphs, and models generated by composing it with other random graph models including random geometric graphs and ErdH{o}s-Renyi graphs. These compositional models are introduced to capture the characteristics of various complex natural or man-made networks more accurately than the existing models in the literature. For random intersection graphs and their compositions with other random graphs, we study properties such as ($k$-)connectivity, ($k$-)robustness, and containment of perfect matchings and Hamilton cycles. Our results are typically given in the form of asymptotically exact probabilities or zero-one laws specifying critical scalings, and provide key insights into the design and analysis of various real-world networks.
One-dimensional geometric random graphs are constructed by distributing $n$ nodes uniformly and independently on a unit interval and then assigning an undirected edge between any two nodes that have a distance at most $r_n$. These graphs have receive
d much interest and been used in various applications including wireless networks. A threshold of $r_n$ for connectivity is known as $r_n^{*} = frac{ln n}{n}$ in the literature. In this paper, we prove that a threshold of $r_n$ for the absence of isolated node is $frac{ln n}{2 n}$ (i.e., a half of the threshold $r_n^{*}$). Our result shows there is a curious gap between thresholds of connectivity and the absence of isolated node in one-dimensional geometric random graphs; in particular, when $r_n$ equals $frac{cln n}{ n}$ for a constant $c in( frac{1}{2}, 1)$, a one-dimensional geometric random graph has no isolated node but is not connected. This curious gap in one-dimensional geometric random graphs is in sharp contrast to the prevalent phenomenon in many other random graphs such as two-dimensional geometric random graphs, ErdH{o}s-Renyi graphs, and random intersection graphs, all of which in the asymptotic sense become connected as soon as there is no isolated node.
Random $s$-intersection graphs have recently received considerable attention in a wide range of application areas. In such a graph, each vertex is equipped with a set of items in some random manner, and any two vertices establish an undirected edge i
n between if and only if they have at least $s$ common items. In particular, in a uniform random $s$-intersection graph, each vertex independently selects a fixed number of items uniformly at random from a common item pool, while in a binomial random $s$-intersection graph, each item in some item pool is independently attached to each vertex with the same probability. For binomial/uniform random $s$-intersection graphs, we establish threshold functions for perfect matching containment, Hamilton cycle containment, and $k$-robustness, where $k$-robustness is in the sense of Zhang and Sundaram [IEEE Conf. on Decision & Control 12]. We show that these threshold functions resemble those of classical ErdH{o}s-R{e}nyi graphs, where each pair of vertices has an undirected edge independently with the same probability.
High-temperature (high-Tc) superconductivity in the copper oxides arises from electron or hole doping of their antiferromagnetic (AF) insulating parent compounds. The evolution of the AF phase with doping and its spatial coexistence with superconduct
ivity are governed by the nature of charge and spin correlations and provide clues to the mechanism of high-Tc superconductivity. Here we use a combined neutron scattering and scanning tunneling spectroscopy (STS) to study the Tc evolution of electron-doped superconducting Pr0.88LaCe0.12CuO4-delta obtained through the oxygen annealing process. We find that spin excitations detected by neutron scattering have two distinct modes that evolve with Tc in a remarkably similar fashion to the electron tunneling modes in STS. These results demonstrate that antiferromagnetism and superconductivity compete locally and coexist spatially on nanometer length scales, and the dominant electron-boson coupling at low energies originates from the electron-spin excitations.
We use neutron scattering to study the structural distortion and antiferromagnetic (AFM) order in LaFeAsO$_{1-x}$F$_{x}$ as the system is doped with fluorine (F) to induce superconductivity. In the undoped state, LaFeAsO exhibits a structural distort
ion, changing the symmetry from tetragonal (space group $P4/nmm$) to orthorhombic (space group $Cmma$) at 155 K, and then followed by an AFM order at 137 K. Doping the system with F gradually decreases the structural distortion temperature, but suppresses the long range AFM order before the emergence of superconductivity. Therefore, while superconductivity in these Fe oxypnictides can survive in either the tetragonal or the orthorhombic crystal structure, it competes directly with static AFM order.
We use powder neutron diffraction to study the spin and lattice structures of polycrystalline samples of nonsuperconducting PrFeAsO and superconducting PrFeAsO0.85F0.15 and PrFeAsO0.85. We find that PrFeAsO exhibits an abrupt structural phase transit
ions at 153 K, followed by static long range antiferromagnetic order at 127 K. Both the structural distortion and magnetic order are identical to other rare-earth oxypnictides. Electron-doping the system with either Fluorine or oxygen deficiency suppresses the structural distortion and static long range antiferromagnetic order, therefore placing these materials into the same class of FeAs-based superconductors.
