Classification of scale-free networks

While the emergence of a power law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the betweenness centrality displays a power-law distribution with an exponent \eta which is robust and use it to classify the scale-free networks. We have observed two universality classes with \eta \approx 2.2(1) and 2.0, respectively. Real world networks for the former are the protein interaction networks, the metabolic networks for eukaryotes and bacteria, and the co-authorship network, and those for the latter one are the Internet, the world-wide web, and the metabolic networks for archaea. Distinct features of the mass-distance relation, generic topology of geodesics and resilience under attack of the two classes are identified. Various model networks also belong to either of the two classes while their degree exponents are tunable.Comment: 6 Pages, 6 Figures, 1 tabl

Curvature-induced spin-orbit coupling and spin relaxation in a chemically clean single-layer graphene

The study of spin-related phenomena in materials requires knowledge on the precise form of effective spin-orbit coupling of conducting carriers in the solid-states systems. We demonstrate theoretically that curvature induced by corrugations or periodic ripples in single-layer graphenes generates two types of effective spin-orbit coupling. In addition to the spin-orbit coupling reported previously that couples with sublattice pseudospin and corresponds to the Rashba-type spin-orbit coupling in a corrugated single-layer graphene, there is an additional spin-orbit coupling that does not couple with the pseudospin, which can not be obtained from the extension of the curvature-induced spin-orbit coupling of carbon nanotubes. Via numerical calculation we show that both types of the curvature-induced spin-orbit coupling make the same order of contribution to spin relaxation in chemically clean single-layer graphene with nanoscale corrugation. The spin relaxation dependence on the corrugation roughness is also studied.Comment: 8 pages, 4 figure

Fracture of a viscous liquid

When a viscous liquid hits a pool of liquid of same nature, the impact region is hollowed by the shock. Its bottom becomes extremely sharp if increasing the impact velocity, and we report that the curvature at that place increases exponentially with the flow velocity, in agreement with a theory by Jeong and Moffatt. Such a law defines a characteristic velocity for the collapse of the tip, which explains both the cusp-like shape of this region, and the instability of the cusp if increasing (slightly) the impact velocity. Then, a film of the upper phase is entrained inside the pool. We characterize the critical velocity of entrainment of this phase and compare our results with recent predictions by Eggers

Quasiparticle Interference on the Surface of Topological Crystalline Insulator Pb(1-x)Sn(x)Se

Topological crystalline insulators represent a novel topological phase of matter in which the surface states are protected by discrete point group-symmetries of the underlying lattice. Rock-salt lead-tin-selenide alloy is one possible realization of this phase which undergoes a topological phase transition upon changing the lead content. We used scanning tunneling microscopy (STM) and angle resolved photoemission spectroscopy (ARPES) to probe the surface states on (001) Pb$_{1-x}$Sn$_{x}$Se in the topologically non-trivial (x=0.23) and topologically trivial (x=0) phases. We observed quasiparticle interference with STM on the surface of the topological crystalline insulator and demonstrated that the measured interference can be understood from ARPES studies and a simple band structure model. Furthermore, our findings support the fact that Pb$_{0.77}$Sn$_{0.23}$Se and PbSe have different topological nature.Comment: 5 pages, 4 figure

Weak spin-orbit interactions induce exponentially flat mini-bands in magnetic metals without inversion symmetry

In metallic magnets like MnSi the interplay of two very weak spin-orbit coupling effects can strongly modify the Fermi surface. In the absence of inversion symmetry even a very small Dzyaloshinsky-Moriya interaction of strength delta<<1 distorts a ferromagnetic state into a chiral helix with a long pitch of order 1/delta. We show that additional small spin-orbit coupling terms of order delta in the band structure lead to the formation of exponentially flat minibands with a bandwidth of order exp(-1/sqrt(delta)) parallel to the direction of the helix. These flat minibands cover a rather broad belt of width sqrt(delta) on the Fermi surface where electron motion parallel to the helix practically stops. We argue that these peculiar band-structure effects lead to pronounced features in the anomalous skin effect.Comment: 7 pages, minor corrections, references adde

Improved Photocatalytic Performance via Air-Plasma Modification of Titanium Dioxide: Insights from Experimental and Simulation Investigation

Commercial titanium dioxide is successfully plasma-treated under ambient conditions for different time periods, leading to reduced crystallite size and the creation of oxygen vacancies. Density functional theory-based calculations reveal the emergence of additional localized states close to the conduction band, primarily associated with under-coordinated titanium atoms in non-stoichiometric titanium-oxide systems. The plasma-treated samples exhibit improved photocatalytic performance in the degradation of methylene blue compared to untreated samples. Moreover, the 4-hour plasma-treated photocatalyst demonstrates commendable stability and reusability. This work highlights the potential of cost-effective plasma treatment as a simple modification technique to significantly enhance the photocatalytic capabilities of titanium dioxide.Comment: Manuscript and Supplementary material include

Lattice dynamics and correlated atomic motion from the atomic pair distribution function

The mean-square relative displacements (MSRD) of atomic pair motions in crystals are studied as a function of pair distance and temperature using the atomic pair distribution function (PDF). The effects of the lattice vibrations on the PDF peak widths are modelled using both a multi-parameter Born von-Karman (BvK) force model and a single-parameter Debye model. These results are compared to experimentally determined PDFs. We find that the near-neighbor atomic motions are strongly correlated, and that the extent of this correlation depends both on the interatomic interactions and crystal structure. These results suggest that proper account of the lattice vibrational effects on the PDF peak width is important in extracting information on static disorder in a disordered system such as an alloy. Good agreement is obtained between the BvK model calculations of PDF peak widths and the experimentally determined peak widths. The Debye model successfully explains the average, though not detailed, natures of the MSRD of atomic pair motion with just one parameter. Also the temperature dependence of the Debye model largely agrees with the BvK model predictions. Therefore, the Debye model provides a simple description of the effects of lattice vibrations on the PDF peak widths.Comment: 9 pages, 11 figure