Table of contents

Pattern recognition is a central topic in learning theory, with numerous applications such as voice and text recognition, image analysis and computer diagnosis. The statistical setup in classification is the following: we are given an i.i.d. training set (X₁, Y₁), ... , (X_n, Y_n), where X_i represents a feature and Y_i∊{0, 1} is a label attached to that feature. The underlying joint distribution of (X, Y) is unknown, but we can learn about it from the training set, and we aim at devising low error classifiers f: X→Y used to predict the label of new incoming features. In this paper, we solve a quantum analogue of this problem, namely the classification of two arbitrary unknown mixed qubit states. Given a number of 'training' copies from each of the states, we would like to 'learn' about them by performing a measurement on the training set. The outcome is then used to design measurements for the classification of future systems with unknown labels. We found the asymptotically optimal classification strategy and show that typically it performs strictly better than a plug-in strategy, which consists of estimating the states separately and then discriminating between them using the Helstrom measurement. The figure of merit is given by the excess risk equal to the difference between the probability of error and the probability of error of the optimal measurement for known states. We show that the excess risk scales as n⁻¹ and compute the exact constant of the rate.

The influence of the viscosity gradient (due to shear flow) on low-frequency collective modes in a strongly coupled dusty plasma is analyzed. It is shown that for a well-known viscoelastic plasma model, the velocity shear-dependent viscosity leads to instability of the shear mode. The inhomogeneous viscous force and velocity shear coupling supply the free energy for the instability. The combined strength of the shear flow and viscosity gradient dominates over any stabilizing force and makes the shear mode unstable. The implications of this novel instability and its applications are briefly described.

Atmospheric clouds, electrosprays and protoplanetary nebula (dusty plasma) contain electrically charged particles embedded in turbulent flows, often under the influence of an externally imposed, approximately uniform gravitational or electric force. We have developed a theoretical description of the dynamics of such systems of charged, sedimenting particles in turbulence, allowing radial distribution functions (RDFs) to be predicted for both monodisperse and bidisperse particle size distributions. The governing parameters are the particle Stokes number (particle inertial time scale relative to turbulence dissipation time scale), the Coulomb-turbulence parameter (ratio of Coulomb 'terminal' speed to the turbulence dissipation velocity scale) and the settling parameter (the ratio of the gravitational terminal speed to the turbulence dissipation velocity scale). The theory is compared to measured RDFs for water particles in homogeneous, isotropic air turbulence. The RDFs are obtained from particle positions measured in three dimensions using digital holography. The measurements verify the general theoretical expression, consisting of a power law increase in particle clustering due to particle response to dissipative turbulent eddies, modulated by an exponential electrostatic interaction term. Both terms are modified as a result of the gravitational diffusion-like term, and the role of 'gravity' is explored by imposing a macroscopic uniform electric field to create an enhanced, effective gravity.

By carefully choosing parameters and including more semi-core orbitals as valence electrons, we have constructed a high-quality projected augmented wave dataset that yields results comparable to existing full-potential linearized augmented plane-wave calculations. The dataset was then applied to BaFe₂As₂ to study the effects of different levels of structure optimization, as well as different choices of exchange-correlation functionals. It was found that the local density approximation exchange-correlation functional fails to find the correct spin-density-wave anti-ferromagnetic (SDW-AFM) ground state under full optimization, while the Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional obtains the correct state but significantly overestimates the magnetism. The electronic structure of the SDW-AFM state is not very sensitive to structure optimizations with the PBE exchange-correlation functional because the positions of the As atoms are preserved under optimizations. We further investigated the Ba atom diffusion process on the BaFe₂As₂ surface using the nudged elastic bands method. The Ba atom was found to be stable above the center of the squares formed by the surface As atoms, and a diffusion barrier of 1.2 eV was found. Our simulated scanning tunneling microscopy image suggests an ordered surface Ba atom structure, in agreement with Massee et al (2009 Phys. Rev. B 80 140507; van Heumen E et al 2010 arXiv:1009.3493v1).

Time- and angle-resolved two-photon photoemission (2PPE) spectroscopies have been used to investigated the electronic structure, electron dynamics and localization at the interface between tetra-tert-butyl imine (TBI) and Au(111). At a TBI coverage of one monolayer (ML), the two highest occupied molecular orbitals, HOMO and HOMO-1, are observed at an energy of −1.9  and −2.6 eV below the Fermi level (E_F), respectively, and coincide with the d-band features of the Au substrate. In the unoccupied electronic structure, the lowest unoccupied molecular orbital (LUMO) has been observed at 1.6 eV with respect to E_F. In addition, two delocalized states that arise from the modified image potential at the TBI/metal interface have been identified. Their binding energies depend strongly on the adsorption structure of the TBI adlayer, which is coverage dependent in the submonolayer (⩽1 ML) regime. Thus the binding energy of the lower interface state (IS) shifts from 3.5 eV at 1.0 ML to 4.0 eV at 0.5 ML, which is accompanied by a pronounced decrease in its lifetime from 100 fs to below 10 fs. This is a result of differences in the wave function overlap with electronic states of the Au(111) substrate at different binding energies. This study shows that in order to fully understand the electronic structure of organic adsorbates at metal surfaces, not only adsorbate- and substrate-induced electronic states have to be considered but also ISs, which are the result of a potential formed by the interaction between the adsorbate and the substrate.

We report on the spin dependence of elastic and inelastic electron tunneling through transition metal atoms. Mn, Fe and Cu atoms were deposited onto a monolayer of Cu₂N on Cu(100) and individually addressed with the probe tip of a scanning tunneling microscope. Electrons tunneling between the tip and the substrate exchange energy and spin angular momentum with the surface-bound magnetic atoms. The conservation of energy during the tunneling process results in a distinct onset threshold voltage above which the tunneling electrons create spin excitations in the Mn and Fe atoms. Here we show that the additional conservation of spin angular momentum leads to different cross-sections for spin excitations depending on the relative alignment of the surface spin and the spin of the tunneling electron. For this purpose, we developed a technique for measuring the same local spin with a spin-polarized and a non-spin-polarized tip by exchanging the last apex atom of the probe tip between different transition metal atoms. We derive a quantitative model describing the observed excitation cross-sections on the basis of an exchange scattering process.

By functionalizing the tip of an atomic force microscope (AFM) with a molecule or an atom that significantly contributes to the tip–sample interaction, the resolution can be dramatically enhanced. The interaction and therefore the resolution crucially depend on the chemical nature of the tip termination. Employing a tip functionalized with a CO molecule, atomic resolution of a pentacene molecule was recently demonstrated. In this work, the interaction between the CO tip and the pentacene imaged are studied with first principles calculations. The calculated frequency shifts compare very well with the experiment. The different energy contributions are analyzed and the Pauli energy is computed. We demonstrate that the source of the high resolution is Pauli repulsion, whereas van der Waals and electrostatic interactions only add a diffuse attractive background.

We present recent results obtained using angle-resolved photoemission spectroscopy performed on 1T-TiSe₂. Emphasis is put on the peculiarity of the bandstructure of TiSe₂ compared to other transition metal dichalcogenides, which suggests that this system is an excellent candidate for the realization of the excitonic insulator phase. This exotic phase is discussed in relation to the BCS theory, and its spectroscopic signature is computed via a model adapted to the particular bandstructure of 1T-TiSe₂. A comparison between photoemission intensity maps calculated with the spectral function derived for this model and experimental results is shown, giving strong support for the exciton condensate phase as the origin of the charge density wave transition observed in 1T-TiSe₂. The temperature-dependent order parameter characterizing the exciton condensate phase is discussed, both on a theoretical and an experimental basis, as well as the chemical potential shift occurring in this system. Finally, the transport properties of 1T-TiSe₂ are analyzed in the light of the photoemission results.

In situ real-time angle-resolved photoelectron spectroscopy is used to measure the electronic structure changes at the surfaces of the layered charge-density-wave materials 1T-TiSe₂ and 1T-TaS₂ during Rb deposition. For 1T-TiSe₂, Rb adsorption at a sample temperature of 80 K causes a transition from a dirty semiconductor to a metal, in the course of which the p(2×2×2) charge-density wave is completely suppressed. For 1T-TaS₂, Rb adsorption at room temperature is rapidly followed by intercalation, leading to a pronounced metal-to-insulator transition that is correlated with a structural change from the pristine nearly commensurate superlattice to a commensurate . charge-density-wave phase. The implications of the results on the charge-density-wave mechanisms in both compounds are discussed with particular reference to the possible interplay of electron–phonon and electron–electron interactions. It is suggested that strong electron–phonon coupling drives the charge-density wave (CDW) phase transitions in pristine 1T-TiSe₂ as well as in Rb intercalated 1T-TaS₂, i.e. the transitions are interpreted as primarily Peierls-like instabilities or, in other words, Jahn–Teller band instabilities.

In recent years, nonlinear processing with continuous-wave lasers has been demonstrated to be a facile means of rapid nanopatterning of organic monolayers down to the sub-100 nm range. In this study, we report on laser patterning of thiol-based organic monolayers with sub-wavelength resolution. Au-coated silicon substrates are functionalized with 1-hexadecanethiol. Irradiation with a focused beam of an Ar⁺ laser operating at λ=514 nm allows one to locally remove the monolayer. Subsequently, the patterns are transferred into the Au film via selective etching in a ferri-/ferrocyanide solution. Despite a 1/e² spot diameter of about 2.8 μm, structures with lateral dimensions down to 250 nm are fabricated. The underlying nonlinear dependence of the patterning process on laser intensity is traced back to the interplay between the laser-induced transient local temperature rise and the thermally activated desorption of the thiol molecules. A simple thermokinetic analysis of the data allows us to determine the effective kinetic parameters. These results complement our previous work on photothermal laser patterning of ultrathin organic coatings, such as silane-based organic monolayers, organo/silicon interfaces and supported membranes. A general introduction to nonlinear laser processing of organic monolayers is presented.

Electron imaging in space and time is achieved in microscopy with timed (near relativistic) electron packets of picometer wavelength coincident with light pulses of femtosecond duration. The photons (with an energy of a few electronvolts) are used to impulsively heat or excite the specimen so that the evolution of structures from their nonequilibrium state can be followed in real time. As such, and at relatively low fluences, there is no interaction between the electrons and the photons; certainly that is the case in vacuum because energy–momentum conservation is not possible. In the presence of nanostructures and at higher fluences, energy–momentum conservation is possible and the electron packet can either gain or lose light quanta. Recently, it was reported that, when only electrons with gained energy are filtered, near-field imaging enables the visualization of nanoscale particles and interfaces with enhanced contrast (Barwick et al 2009 Nature462 902). To explore a variety of applications, it is important to express, through analytical formulation, the key parameters involved in this photon-induced near-field electron microscopy (PINEM) and to predict the associated phenomena of, e.g., forty-photon absorption by the electron packet. In this paper, we give an account of the theoretical and experimental results of PINEM. In particular, the time-dependent quantum solution for ultrafast electron packets in the nanostructure scattered electromagnetic (near) field is solved in the high kinetic energy limit to obtain the evolution of the incident electron packet into a superposition of discrete momentum wavelets. The characteristic length and time scales of the halo of electron–photon coupling are discussed in the framework of Rayleigh and Mie scatterings, providing the dependence of the PINEM effect on size, polarization, material and spatiotemporal localization. We also provide a simple classical description that is based on features of plasmonics. A major part of this paper is devoted to the comparisons between the theoretical results and the recently obtained experimental findings about the imaging of materials and biological systems.

Stereoscopic visualization adds an additional dimension to the viewer's experience, giving them a sense of distance. In a general relativistic visualization, distance can be measured in a variety of ways. We argue that the affine distance, which matches the usual notion of distance in flat spacetime, is a natural distance to use in curved spacetime. As an example, we apply affine distance to the visualization of the interior of a black hole. Affine distance is not the distance perceived with normal binocular vision in curved spacetime. However, the failure of binocular vision is simply a limitation of animals that have evolved in flat spacetime, not a fundamental obstacle to depth perception in curved spacetime. Trinocular vision would provide superior depth perception.

In this paper, we report an investigation of the ferromagnetic state and the nature of ferromagnetic transition of nanoparticles of La_0.67Ca_0.33MnO₃ using magnetic measurements and neutron diffraction. The investigation was performed on nanoparticles with crystal size down to 15 nm. The neutron data show that even down to a size of 15 nm the nanoparticles show finite spontaneous magnetization (M_S) although the value is much reduced compared to the bulk sample. We observed a non-monotonic variation of the ferromagnetic-to-paramagnetic transition temperature T_C with size d and found that T_C initially enhances upon size reduction, but for d<50 nm it decreases again. The initial enhancement in T_C was related to an increase in the bandwidth that occurred due to a compaction of the Mn–O bond length and a straightening of the Mn–O–Mn bond angle, as determined from the neutron data. The size reduction also changes the nature of the ferromagnetic-to-paramagnetic transition from first order to second order with critical exponents approaching mean field values. This was explained as arising from a truncation of the coherence length by the finite sample size.

Among natural biological flocks/swarms or mass social activities, when the collective behavior of the followers has been dominated by the direction or opinion of one leader group, it seems difficult for later-coming leaders to reverse the orientation of the mass followers, especially when they are in quantitative minority. This paper, however, reports a counter-intuitive phenomenon, i.e. Following the Later-coming Minority, provided that the later-comers obey a favorable distribution pattern that enables them to spread their influence to as many followers as possible within a given time and to be dense enough to govern these local followers they can influence directly from the beginning. We introduce a discriminant index to quantify the whole group's orientation under competing leaderships, with which the eventual orientation of the mass followers can be predicted before launching the real dynamical procedure. From the application point of view, this leadership effectiveness index also helps us to design an economical way for the minority later-coming leaders to defeat the dominating majority leaders solely by optimizing their spatial distribution pattern provided that the premeditated goal is available. Our investigation provides insights into effective leadership in biological systems with meaningful implications for social and industrial applications.

A proper description of the velocity gradient tensor is crucial for understanding the dynamics of turbulent flows, in particular the energy transfer from large to small scales. Insight into the statistical properties of the velocity gradient tensor and into its coarse-grained generalization can be obtained with the help of a stochastic 'tetrad model' that describes the coarse-grained velocity gradient tensor based on the evolution of four points. Although the solution of the stochastic model can be formally expressed in terms of path integrals, its numerical determination in terms of the Monte-Carlo method is very challenging, as very few configurations contribute effectively to the statistical weight. Here, we discuss a strategy that allows us to solve the tetrad model numerically. The algorithm is based on the importance sampling method, which consists here of identifying and sampling preferentially the configurations that are likely to correspond to a large statistical weight, and selectively rejecting configurations with a small statistical weight. The algorithm leads to an efficient numerical determination of the solutions of the model and allows us to determine their qualitative behavior as a function of scale. We find that the moments of order n⩽4 of the solutions of the model scale with the coarse-graining scale and that the scaling exponents are very close to the predictions of the Kolmogorov theory. The model qualitatively reproduces quite well the statistics concerning the local structure of the flow. However, we find that the model generally tends to predict an excess of strain compared to vorticity. Thus, our results show that while some physical aspects are not fully captured by the model, our approach leads to a very good description of several important qualitative properties of real turbulent flows.

Transformation optics is used to prove that a spherical waveguide filled with an isotropic material with radial refractive index n=1/r has radially polarized modes (i.e. the electric field is only radial) with the same perfect focusing properties as the Maxwell fish-eye (MFE) lens. An approximate version of that device, comprising a thin waveguide with a homogeneous core, paves the way to experimentally attaining perfect imaging in the MFE lens.

We study the evolution of initially extended distributions in the coined quantum walk (QW) on the line. By analysing the dispersion relation of the process, continuous wave equations are derived whose form depends on the initial distribution shape. In particular, for a class of initial conditions, the evolution is dictated by the Schrödinger equation of a free particle. As that equation also governs paraxial optical diffraction, all of the phenomenology of the latter can be implemented in the QW. This allows us, in particular, to devise an initially extended condition leading to a uniform probability distribution whose width increases linearly with time, with increasing homogeneity.

In this paper, we analyze the 'singular statistics' of pseudointegrable Šeba billiards, i.e. billiards perturbed by zero-range perturbations. We have shown that the computation of a spectrum is reduced to the calculation of the uniquely defined renormalized Green's function. We relate a spectrum of the billiard to the scattering length, which is the only parameter describing the perturbation. We show that taking into account the growing number of resonances, one observes a transition from 'semi-Poissonian'-like statistics to Poissonian. This observation is in agreement with the argument that a classical particle does not feel a point perturbation.

We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac points that are present throughout the band structure and verify for the special case of a particle–hole symmetric potential their presence at zero energy. We also consider the cases of a single trench and a p–n junction embedded in neutral graphene, which are shown to support confined states. An analysis of conductance across these structures demonstrates that these confined states create quantum interference effects, which evidence their presence.

We report on a scalable electrostatic process to transfer epitaxial graphene onto alkali-containing glass substrates. Multilayer epitaxial graphene (MEG) was grown by heating silicon carbide () to high temperatures (1650–1700 °C) in an argon-mediated environment. Optical lithography was used to define patterned graphene regions, typically 20×20 μm², which were then transferred to Pyrex substrates. For the electrostatic transfer, a large electric potential (1.2 kV) was applied between the donor MEG sample (anode) and the heated acceptor glass substrate (cathode). Atomic force microscopy scans of the transferred graphene showed that the morphology of the transferred multilayer graphene resembles that of the donor MEG. Raman spectroscopy analysis confirmed that the graphene can be transferred without inducing defects. The sheet resistance of the transferred graphene was as low as 150 Ω/□. The transfer of small (1–2 μm wide) and large (∼70×70 μm²) graphene patterns to Zerodur demonstrates the versatility of this transfer technique.

The effects induced by the deposition of Li on 1 and 0 ML graphene grown on SiC(0001) and after subsequent heating were investigated using low-energy electron microscopy (LEEM) and x-ray photo-emission electron microscopy (XPEEM). For 1 ML samples, the collected photoelectron angular distribution patterns showed the presence of single π-cones at the six equivalent K-points in the Brillouin zone before Li deposition but the presence of two π-cones (π-bands) after Li deposition and after heating to a few hundred °C. For 0 ML samples, no π-band could be detected close to the Fermi level before deposition, but distinct π-cones at the K-points were clearly resolved after Li deposition and after heating. Thus Li intercalation was revealed in both cases, transforming the carbon buffer layer (0 ML) to graphene. On 1 ML samples, but not on 0 ML, a (√3×√3) R30° diffraction pattern was observed immediately after Li deposition. This pattern vanished upon heating and then wrinkles/cracks appeared on the surface. Intercalation of Li was thus found to deteriorate the quality of the graphene layer, especially for 1 ML samples. These wrinkles/cracks did not disappear even after heating at temperatures ⩾500 °C, when no Li atoms remained on the substrate.

We review recent developments on the electronic properties of graphene under the influence of adsorbates. Potassium and hydrogen adsorbed on graphene induce very different effects on the graphene electron gas because of the different types—ionic versus covalent—of chemical bonds formed. Potassium readily donates electrons to graphene, and the resulting Fermi sea shows strong electron–plasmon scattering but weak defect scattering. In contrast, hydrogen adsorption saturates a carbon π bond, leading to the removal of electrons from the graphene. Such hydrogen bonds act as a lattice defect, leading to a sharp reduction in conductivity and an insulating temperature dependence of the resistivity. The marked contrast in the behaviour of these adsorbates derives from the different symmetry classes of their defect geometries.

The effects of applied microwave power, gas flow rate and precursor composition on the substrate-free gas-phase synthesis of graphene were investigated. Graphene was produced through the delivery of ethanol droplets into argon plasmas, and a decrease in the flow rate of the gas used to generate the plasmas resulted in the formation of graphitic particles and bulk graphite structures. Carbonaceous soot particles were created by delivering isopropyl alcohol into the reactor, while no solid matter was created from methanol. Increasing the applied microwave power was found to have no effect on the structures of the synthesized materials. These findings indicated that the synthesis of graphene in the gas phase was the result of the slow inception and extremely fast growth of aromatic nuclei in the plasma afterglows.

Using first-principles calculations, we show that the formation of carbohydrates directly from carbon and water is energetically favored when graphene is subjected to an unequal chemical environment across the two sides, with a difference in the chemical potential of protons and hydroxyl groups. The resultant carbohydrate structure is two-dimensional (2D), with the hydrogen atoms exclusively attached on one side of the graphene and the hydroxyl groups on the other side, the latter forming a herringbone reconstruction that optimizes hydrogen bonding. We show that graphene undergoes a metal–insulator transition upon hydration that is readily detectable from the significant shift in the vibration spectrum. The hydrate form of graphene offers new applications for graphene in electronics, either deposited on a substrate or in solution.

In this paper, we evaluate the adsorption/desorption of ammonia molecules on a graphene surface by studying the Fermi level shift. On the basis of a physically plausible model, the adsorption and desorption rates of ammonia molecules on graphene have been extracted from the measured Fermi level shift as a function of exposure time. An electric-field-induced flipping behavior of the ammonia molecules on graphene is suggested based on field effect transistor (FET) measurements.

The mechanical, electrical and chemical properties of chemically modified graphene (CMG) are intrinsically linked to its structure. Here, we report on our study of the topographic structure of free-standing CMG using atomic force microscopy (AFM) and electron diffraction. We find that, unlike graphene, suspended sheets of CMG are corrugated and distorted on nanometre length scales. AFM reveals not only long-range (100 nm) distortions induced by the support, as previously observed for graphene, but also short-range corrugations with length scales down to the resolution limit of 10 nm. These corrugations are static not dynamic, and are significantly diminished on CMG supported on atomically smooth substrates. Evidence for even shorter-range distortions, down to a few nanometres or less, is found by electron diffraction of suspended CMG. Comparison of the experimental data with simulations reveals that the mean atomic displacement from the nominal lattice position is of order 10% of the carbon–carbon bond length. Taken together, these results suggest a complex structure for CMG where heterogeneous functionalization creates local strain and distortion.

The atomic force microscope (AFM) is used to study the morphology of graphene grown on 4H-SiC. A mesh-like network of ridges with high curvature is revealed that bound atomically flat, tile-like facets of few-layer graphene (FLG). To further study the structural properties of the ridge network, nanomanipulation experiments are performed using an AFM tip to deform the ridges in both the vertical and lateral directions. From these experiments, evidence is obtained that the ridges can be displaced in both the vertical and lateral directions. In some instances, ridges are found to return to their original shape after deformation. Cross-section transmission electron microscopy (TEM) studies show that the ridges are formed by the delamination of FLG from the SiC substrate.

We have dispersed graphene in water, stabilized by a range of 12 ionic and non-ionic surfactants. In all cases, the degree of exfoliation, as characterized by flake length and thickness, was similar. The dispersed flakes were typically 750 nm long and, on average, four layers thick. However, the dispersed concentration varied from solvent to solvent. For the ionic surfactants, the concentration scaled with the square of the zeta potential of the surfactant-coated flakes. This suggests that the concentration is proportional to the magnitude of the electrostatic potential barrier, which stabilizes surfactant-coated flakes against aggregation. For the non-ionic surfactants, the dispersed graphene concentration scaled linearly with the magnitude of the steric potential barrier stabilizing the flakes. However, the data suggested that other contributions are also important.

The chemical functionalization of graphene modifies the local electron density of carbon atoms and hence electron transport. Measuring these changes allows for a closer understanding of the chemical interaction and the influence of functionalization on the graphene lattice. However, not only chemistry, in this case diazonium chemistry, has an effect on electron transport. The latter is also influenced by defects and dopants resulting from different processing steps. Here, we show that the solvents used in the chemical reaction process change the transport properties. In more detail, the investigated combination of isopropanol and heating treatment reduces the doping concentration and significantly increases the mobility of graphene. Furthermore, isopropanol treatment alone increases the concentration of dopants and introduces an asymmetry between electron and hole transport, which might be difficult to distinguish from the effect of functionalization. The results shown in this work demand a closer look at the influence of solvents used for chemical modification in order to understand their influence.

Four fundamental dimer manipulations can be used to produce a variety of localized and extended defect structures in graphene. Two-dimensional templates result in graphene allotropes, here viewed as extended defects, which can exhibit either metallic or semiconducting electrical character. Embedded allotropic ribbons—i.e. thin swaths of the new allotropes—can also be created within graphene. We examined these ribbons and found that they maintain the electrical character of their parent allotrope even when only a few atoms in width. Such extended defects may facilitate the construction of single atomic layer carbon circuitry.

The band gap opening is one of the important issues in applications of graphene and graphene nanoribbons (GNRs) to nanoscale electronic devices. As hydrogen strongly interacts with graphene and creates short-range disorder, the electronic structure is significantly modified by hydrogenation. Based on first-principles and tight-binding calculations, we investigate the electronic and transport properties of hydrogenated graphene and GNRs. In disordered graphene with low doses of H adsorbates, the low-energy states near the neutrality point are localized, and the degree of localization extends to high-energy states with increasing adsorbate density. To characterize the localization of eigenstates, we examine the inverse participation ratio and find that the localization is greatly enhanced for the defect levels, which are accumulated around the neutrality point. Our calculations support the previous result that even with a low dose of H adsorbates, graphene undergoes a metal–insulator transition. In GNRs, relaxations of the edge C atoms play a role in determining the edge structure and the hydrocarbon conformation at low and high H concentrations, respectively. In disordered nanoribbons, we find that the energy states near the neutrality point are localized and conductances through low-energy channels decay exponentially with sample size, similar to disordered graphene. For a given channel energy, the localization length tends to decrease as the adsorbate density increases. Moreover, the energy range of localization exceeds the intrinsic band gap.

This paper presents our work on the investigation of the surface structure and the electronic and magnetic properties of the graphene layer on the lattice-matched surface of a ferromagnetic material, Ni(111). Scanning tunneling microscopy imaging shows that perfectly ordered epitaxial graphene layers can be prepared by elevated temperature decomposition of hydrocarbons, with domains larger than the terraces of the underlying Ni(111). In some exceptional cases, graphene films do not show rotational alignment with the metal surface, leading to moiré structures with small periodicities. We discuss the crystallographic structure of graphene with respect to the Ni(111) surface relying both on experimental results and on recent theoretical studies. X-ray absorption spectroscopy investigations of empty valence-band states demonstrate the existence of interface states, which originate from the strong hybridization between the graphene π and Ni 3d valence-band states with the partial charge transfer of the spin-polarized electrons to the graphene π^* unoccupied states. The latter leads to the appearance of an induced magnetic moment of carbon atoms in the graphene layer, which is unambiguously confirmed by both x-ray magnetic circular dichroism and spin-resolved photoemission. Further angle-resolved photoemission investigations indicate a strong interaction between graphene and Ni(111), showing considerable modification of the valence-band states of Ni and graphene due to strong hybridization. A detailed analysis of the Fermi surface of the graphene/Ni(111) system shows very good agreement between experimental and calculated two-dimensional maps of the electronic states around the Fermi level, supporting the idea of spin-filtering. We analyze our spectroscopic results relying on the currently available band structure calculations for the graphene/Ni(111) system and discuss the perspectives of the realization of graphene/ferromagnet-based devices.

Christandl et al (2009 Phys. Rev. Lett.102 020504) provide, in particular, the possibility of studying unconditional security in the finite-key regime for all discrete-variable protocols. We spell out this bound from their general formalism. Then, we apply it in the analysis of a recently proposed protocol (Laing et al 2010 Phys. Rev. A 82 012304). This protocol is meaningful when the alignment of Alice's and Bob's reference frames is not monitored and may vary with time. In this scenario, the notion of asymptotic key rate has hardly any operational meaning, because if one waits too long a time, the average correlations are smeared out and no security can be inferred. Therefore, finite-key analysis is necessary for finding the maximal achievable secret key rate and the corresponding optimal number of signals.

Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well studied on regular structures and also shown to be sensitive to defects and imperfections in the lattice. As a simple example of a disordered system, we consider percolation lattices, in which edges or sites are randomly missing, interrupting the progress of the quantum walk. We use numerical simulation to study the properties of coined quantum walks on these percolation lattices in one and two dimensions. In one dimension (the line), we introduce a simple notion of quantum tunnelling and determine how this affects the properties of the quantum walk as it spreads. On two-dimensional percolation lattices, we show how the spreading rate varies from linear in the number of steps down to zero as the percolation probability decreases towards the critical point. This provides an example of fractional scaling in quantum-walk dynamics.

We have measured the initial vibrational-state-specific, symmetry-resolved ion-yield spectra of CO₂ and N₂O in the shape resonance regions above the K-shell ionization thresholds. For both molecules, significant diminution of the shape resonances by bending excitation in the initial electronic ground state is observed. The measured ion-yield spectra are well reproduced by calculations employing the Schwinger variational principle. The observed changes in the spectra are seen to be due to a shift of the resonances to lower energy and an initial increase in width with bending.

We show that the vibrations of a chain of trapped ions offer an interesting route to explore the physics of disordered quantum systems. By preparing the internal state of the ions in a quantum superposition, we show how the local vibrational energy becomes a stochastic variable, its statistical properties inherited from the underlying quantum parallelism of the internal state. We describe a minimally perturbing measurement of the resonance fluorescence, which allows us to study effects such as Anderson localization without the need for ground-state cooling or individual addressing and thus paves the way for high-temperature ion experiments.

We demonstrate the first guiding of cold atoms through a 88 mm long piece of photonic band gap fiber. The guiding potential is created by a far-off resonance dipole trap propagating inside the fiber with a hollow core of 12 μm. We load the fiber from a dark spot ⁸⁵Rb magneto-optical trap and observe a peak flux of more than 10⁵ atoms s⁻¹ at a velocity of 1.5 m s⁻¹. With an additional reservoir optical dipole trap, a constant atomic flux of 1.5 × 10⁴ atoms s⁻¹ is sustained for more than 150 ms. These results open up interesting possibilities to study nonlinear light–matter interaction in a nearly one-dimensional geometry and pave the way for guided matter wave interferometry.

In the evolution of cooperation, the motion of players plays an important role. In this paper, we incorporate, into an evolutionary prisoner dilemma's game on networks, a new factor that cooperators and defectors move with different probabilities. By investigating the dependence of the cooperator frequency on the moving probabilities of cooperators and defectors, μ_c and μ_d, we find that cooperation is greatly enhanced in the parameter regime of μ_c<μ_d. The snapshots of strategy pattern and the evolutions of cooperator clusters and defector clusters reveal that either the fast motion of defectors or the slow motion of cooperators always favors the formation of large cooperator clusters. The model is investigated on different types of networks such as square lattices, Erdös–Rényi networks and scale-free networks and with different types of strategy-updating rules such as the richest-following rule and the Fermi rule. The numerical results show that the observed phenomena are robust to different networks and to different strategy-updating rules.

We investigate the electromechanics of a freely suspended semiconducting carbon nanotube subjected to a magnetic field H in the current-biased regime and show that self-excitation of mechanical nanotube vibrations can occur if H exceeds a critical value H_c of the order of 10–100 mT. The effect can be detected by measuring the magnetic field dependence of the time-averaged voltage drop across the nanotube, which has a singularity at H=H_c. We discuss the applications of the device as an active, tuneable radiofrequency oscillator.

We present an x-ray dichroism study of graphite surfaces that addresses the origin and magnitude of ferromagnetism in metal-free carbon. We find that, in addition to carbon π-states, hydrogen-mediated electronic states also exhibit a net spin polarization with significant magnetic remanence at room temperature. The observed magnetism is restricted to the top ≈10 nm of the irradiated sample where the average magnetization reaches ≃15 emu g^{− 1} at room temperature. We prove that the ferromagnetism found in metal-free untreated graphite is intrinsic and has a similar origin to that found in proton-bombarded graphite. Our findings also show that the magnetic properties of graphite surfaces, thin films or two-dimensional graphene samples can be reliably studied using soft x-ray dichroism. Fundamental new insights into the magnetic properties of carbon-based systems can thus be obtained.

We discuss a new method for manipulating the optical field distribution in time and space at the focal plane of a chromatic lens. Chromatic dispersion and aberration make it possible to control the photon distribution in both time and space by properly controlling the amplitude and phase of the incident laser pulse, including shortening a laser pulse or generating a specific time-dependent transverse distribution. As an example, we discuss the generation of a quasi-three-dimensional ellipsoidal photon distribution and a proof-of-principle experiment, where favourable agreement between theoretical calculations and the data is observed.

According to recent studies (Amin et al 2008 Phys. Rev. Lett.100 060503), the effect of a thermal bath may improve the performance of a quantum adiabatic search algorithm. In this paper, we compare the effects of such a thermal environment on the algorithm performance with those of a structured environment similar to the one encountered in systems coupled to an electromagnetic field that exists within a photonic crystal. Whereas for all the parameter regimes explored here, the algorithm performance is worsened by contact with a thermal environment, the picture appears to be different when one considers a structured environment. In this case we show that by tuning the environment parameters to certain regimes, the algorithm performance can actually be improved with respect to the closed system case. Additionally, the relevance of considering the dissipation rates as complex quantities is discussed in both cases. More specifically, we find that the imaginary part of the rates cannot be neglected with the usual argument that it simply amounts to an energy shift and in fact influences crucially the system dynamics.

We present a theory of frequency-dependent counting statistics of electron transport through nanostructures within the framework of Markovian quantum master equations. Our method allows the calculation of finite-frequency current cumulants of arbitrary order, as we explicitly show for the second- and third-order cumulants. Our formulae generalize previous zero-frequency expressions in the literature and can be viewed as an extension of MacDonald's formula beyond shot noise. When combined with an appropriate treatment of tunneling using, e.g., the Liouvillian perturbation theory in Laplace space, our method can deal with arbitrary bias voltages and frequencies, as we illustrate with the paradigmatic example of transport through a single resonant level model. We discuss various interesting limits, including the recovery of the fluctuation-dissipation theorem near linear response, as well as some drawbacks inherent to the Markovian description arising from the neglect of quantum fluctuations.

Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetodielectric medium with dielectric functions that obey the Kramers–Kronig relations. The prescriptions of the phenomenological approach are derived from the canonical theory.

We report an experimental test of Leggett's non-local hidden variable theory in an orbital angular momentum (OAM) state space of light. We show that the correlations we observe are in conflict with Leggett's model, thus excluding a particular class of non-local hidden variable theories for the first time in a non-polarization state space. It is known that the violation of the Leggett inequality becomes stronger as more detection settings are used. The required measurements become feasible in an OAM subspace, and we demonstrate this by testing the inequality using three and four settings. We observe excellent agreement with quantum predictions and a violation of five and six standard deviations, respectively, compared to Leggett's non-local hidden variable theory.

The structural inversion asymmetry-induced spin–orbit interaction of conduction band electrons in zinc-blende and wurtzite semiconductor structures is analysed allowing for a three-dimensional (3D) character of the external electric field and variation of the chemical composition. The interaction, taking into account all remote bands perturbatively, is presented with two contributions: a heterointerface term and a term caused by the external electric field. They have generally comparable strength and can be written in a unified manner only for 2D systems, where they can partially cancel each other. For quantum wires and dots composed of wurtzite semiconductors, new terms appear, absent in zinc-blende structures, which acquire the standard Rashba form in 2D systems.

Radiation reaction (RR) effects on the acceleration of a thin plasma foil by a superintense laser pulse in the radiation pressure-dominated regime are investigated theoretically. A simple suitable approximation of the Landau–Lifshitz equation for the RR force and a novel leap-frog pusher for its inclusion in particle-in-cell simulations are provided. Simulations for both linear and circular polarization of the laser pulse are performed and compared. It is found that at intensities exceeding 10²³ W cm^{− 2} the RR force strongly affects the dynamics for a linearly polarized laser pulse, reducing the maximum ion energy but also the width of the spectrum. In contrast, no significant effect is found for circularly polarized laser pulses whenever the laser pulse does not break through the foil.

A systematic angle-resolved photoemission study of the electronic structure of La_2−xSr_xCuO₄ in a wide doping range is presented in this paper. In addition to the main energy band, we observed a weaker additional band, the (π, π) folded band, which shows unusual doping dependence. The appearance of the folded band suggests that a Fermi surface reconstruction is doping dependent and could already occur at zero magnetic field.

An important problem in quantum information theory is the quantification of entanglement in multipartite mixed quantum states. In this work, a connection between the geometric measure of entanglement and a distance measure of entanglement is established. We present a new expression for the geometric measure of entanglement in terms of the maximal fidelity with a separable state. A direct application of this result provides a closed expression for the Bures measure of entanglementof two qubits. We also prove that the number of elements in an optimal decomposition w.r.t. the geometric measure of entanglement is bounded from above by the Caratheodory bound, and we find necessary conditions for the structure of an optimal decomposition.

We report an investigation of the distinct quasiparticle (QP) relaxation dynamics in an electron-doped superconductor, BaFe_1.9Ni_0.1As₂, employing femtosecond pump–probe measurements. Two distinct relaxation components and one sub-nanosecond long-lived component are clearly observed in our transient reflectivity spectra. The slow relaxation component, which is on a picosecond time scale, strongly correlates with the superconducting (SC) transition, and we attribute it to the recombination dynamics of Cooper pairs. We calculated the SC gap, Δ(0)≈5.7 meV. The fast relaxation component, on a sub-picosecond scale, is ascribed to the QP relaxation from a range of large gap states to the state above the SC gap. We obtained the low end of these bandgaps to be Δ_G≈9 meV. Furthermore, we estimated the electron–phonon (e–ph) coupling constant and the Coulomb pseudopotential from the fast relaxation lifetime. The small values of the e–ph constant and the negative Coulomb pseudopotential suggest that the e–ph interaction is not the dominant contribution of the SC transition.

The front speed of the Neolithic (farmer) spread in Europe decreased as it reached Northern latitudes, where the Mesolithic (hunter-gatherer) population density was higher. Here, we describe a reaction–diffusion model with (i) an anisotropic dispersion kernel depending on the Mesolithic population density gradient and (ii) a modified population growth equation. Both effects are related to the space available for the Neolithic population. The model is able to explain the slowdown of the Neolithic front as observed from archaeological data.

We study the possibility of utilizing the superfluid to Mott-insulator quantum phase transition in an array of quantum well exciton–polariton traps to generate indistinguishable single photons in a massive parallel fashion. By means of analytical and numerical methods, the device operations and system properties are examined using realistic experimental parameters. Such a deterministic, massive parallel generation may find new applications in photonic quantum information processing.

Proposals to measure non-Abelian anyons in a superconductor by quantum interference of vortices suffer from the predominantly classical dynamics of the normal core of an Abrikosov vortex. We show how to avoid this obstruction using coreless Josephson vortices, for which the quantum dynamics has been demonstrated experimentally. The interferometer is a flux qubit in a Josephson junction circuit, which can non-destructively read out a topological qubit stored in a pair of anyons—even though the Josephson vortices themselves are not anyons. The flux qubit does not couple to intra-vortex excitations, thereby removing the dominant restriction on the operating temperature of anyonic interferometry in superconductors.

We report high-resolution spin-resolved photoemission spectroscopy (spin-ARPES) measurements on the parent compound Sb of the recently discovered three-dimensional topological insulator Bi_1−xSb_x (Hsieh et al 2008 Nature452 970, Hsieh et al 2009 Science 323 919). By modulating the incident photon energy, we are able to map both the bulk and the (111) surface band structure, from which we directly demonstrate that the surface bands are spin polarized by the spin–orbit interaction and connect the bulk valence and conduction bands in a topologically non-trivial way. A unique asymmetric Dirac surface state gives rise to a k-splitting of its spin-polarized electronic channels. These results complement our previously published works on this class of materials and re-confirm our discovery of topological insulator states in the Bi_1−xSb_x series.

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