Equational reasoning with context-free families of string diagrams

String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout rewriting. However, one often wishes to express not just single equations, but entire families of equations between diagrams of arbitrary size. To do this we define a class of context-free grammars, called B-ESG grammars, that are suitable for defining entire families of string graphs, and crucially, of string graph rewrite rules. We show that the language-membership and match-enumeration problems are decidable for these grammars, and hence that there is an algorithm for rewriting string graphs according to B-ESG rewrite patterns. We also show that it is possible to reason at the level of grammars by providing a simple method for transforming a grammar by string graph rewriting, and showing admissibility of the induced B-ESG rewrite pattern.Comment: International Conference on Graph Transformation, ICGT 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-21145-9_

Non-volatile resistive switching in dielectric superconductor YBCO

We report on the reversible, nonvolatile and polarity dependent resistive switching between superconductor and insulator states at the interfaces of a Au/YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO)/Au system. We show that the superconducting state of YBCO in regions near the electrodes can be reversibly removed and restored. The possible origin of the switching effect may be the migration of oxygen or metallic ions along the grain boundaries that control the intergrain superconducting coupling. Four-wire bulk resistance measurements reveal that the migration is not restricted to interfaces and produce significant bulk effects.Comment: 4 pages, 4 figures, corresponding author: C. Acha ([email protected]

Enhanced and continuous electrostatic carrier doping on the SrTiO3_{3} surface

Paraelectrical tuning of a charge carrier density as high as 10$^{13}$\,cm$^{-2}$ in the presence of a high electronic carrier mobility on the delicate surfaces of correlated oxides, is a key to the technological breakthrough of a field effect transistor (FET) utilising the metal-nonmetal transition. Here we introduce the Parylene-C/Ta$_{2}$O$_{5}$ hybrid gate insulator and fabricate FET devices on single-crystalline SrTiO$_{3}$, which has been regarded as a bedrock material for oxide electronics. The gate insulator accumulates up to $\sim10^{13}$cm$^{-2}$ carriers, while the field-effect mobility is kept at 10\,cm$^2$/Vs even at room temperature. Further to the exceptional performance of our devices, the enhanced compatibility of high carrier density and high mobility revealed the mechanism for the long standing puzzle of the distribution of electrostatically doped carriers on the surface of SrTiO$_{3}$. Namely, the formation and continuous evolution of field domains and current filaments.Comment: Supplementary Information: <http://www.nature.com/srep/2013/130424/srep01721/extref/srep01721-s1.pdf

Hysteresis Switching Loops in Ag-manganite memristive interfaces

Multilevel resistance states in silver-manganite interfaces are studied both experimentally and through a realistic model that includes as a main ingredient the oxygen vacancies diffusion under applied electric fields. The switching threshold and amplitude studied through Hysteresis Switching Loops are found to depend critically on the initial state. The associated vacancy profiles further unveil the prominent role of the effective electric field acting at the interfaces. While experimental results validate main assumptions of the model, the simulations allow to disentangle the microscopic mechanisms behind the resistive switching in metal-transition metal oxide interfaces.Comment: 14 pages, 3 figures, to be published in Jour. of Appl. Phy

First-Order Insulator-to-Metal Mott Transition in the Paramagnetic 3D System GaTa4Se8

The nature of the Mott transition in the absence of any symmetry braking remains a matter of debate. We study the correlation-driven insulator-to-metal transition in the prototypical 3D Mott system GaTa4Se8, as a function of temperature and applied pressure. We report novel experiments on single crystals, which demonstrate that the transition is of first order and follows from the coexistence of two states, one insulating and one metallic, that we toggle with a small bias current. We provide support for our findings by contrasting the experimental data with calculations that combine local density approximation with dynamical mean-field theory, which are in very good agreement.Comment: 5 pages and 4 figures. Supplemental material: 2 pages, 2 figure

Zero-temperature magnetism in the periodic Anderson model in the limit of large dimensions

We study the magnetism in the periodic Anderson model in the limit of large dimensions by mapping the lattice problem into an equivalent local impurity self-consistent model. Through a recently introduced algorithm based on the exact diagonalization of an effective cluster hamiltonian, we obtain solutions with and without magnetic order in the half-filled case. We find the exact AFM-PM phase boundary which is shown to be of $2^{nd}$ order and obeys $\frac{V^2}{U} \approx const.$ We calculate the local staggered moments and the density of states to gain insights on the behavior of the AFM state as it evolves from itinerant to a local-moment magnetic regimeComment: 9 pages + 9 figures, to appear in Phys. Rev. B, 1 Sept. 1995 issu

Optical Conductivity in Mott-Hubbard Systems

We study the transfer of spectral weight in the optical spectra of a strongly correlated electron system as a function of temperature and interaction strength. Within a dynamical mean field theory of the Hubbard model that becomes exact in the limit of large lattice coordination, we predict an anomalous enhancement of spectral weight as a function of temperature in the correlated metallic state and report on experimental measurements which agree with this prediction in $V_2O_3$. We argue that the optical conductivity anomalies in the metal are connected to the proximity to a crossover region in the phase diagram of the model.Comment: 12 pages and 4 figures, to appear in Phys. Rev. Lett., v 75, p 105 (1995

Transfer of Spectral Weight in Spectroscopies of Correlated Electron Systems

We study the transfer of spectral weight in the photoemission and optical spectra of strongly correlated electron systems. Within the LISA, that becomes exact in the limit of large lattice coordination, we consider and compare two models of correlated electrons, the Hubbard model and the periodic Anderson model. The results are discussed in regard of recent experiments. In the Hubbard model, we predict an anomalous enhancement optical spectral weight as a function of temperature in the correlated metallic state which is in qualitative agreement with optical measurements in $V_2O_3$. We argue that anomalies observed in the spectroscopy of the metal are connected to the proximity to a crossover region in the phase diagram of the model. In the insulating phase, we obtain an excellent agreement with the experimental data and present a detailed discussion on the role of magnetic frustration by studying the $k-$resolved single particle spectra. The results for the periodic Anderson model are discussed in connection to recent experimental data of the Kondo insulators $Ce_3Bi_4Pt_3$ and $FeSi$. The model can successfully explain the different energy scales that are associated to the thermal filling of the optical gap, which we also relate to corresponding changes in the density of states. The temperature dependence of the optical sum rule is obtained and its relevance for the interpretation of the experimental data discussed. Finally, we argue that the large scattering rate measured in Kondo insulators cannot be described by the periodic Anderson model.Comment: 19 pages + 29 figures. Submitted to PR