Properties of dirty two-bands superconductors with repulsive interband interaction: normal modes, length scales, vortices and magnetic response

Disorder in two-band superconductors with repulsive interband interaction induces a frustrated competition between the phase-locking preferences of the various potential and kinetic terms. This frustrated interaction can result in the formation of an $s+is$ superconducting state, that breaks the time-reversal symmetry. In this paper we study the normal modes and their associated coherence lengths in such materials. We especially focus on the consequences of the soft modes stemming from the frustration and time-reversal-symmetry breakdown. We find that two-bands superconductors with such impurity-induced frustrated interactions display a rich spectrum of physical properties that are absent in their clean counterparts. It features a mixing of Leggett's and Anderson-Higgs modes, and a soft mode with diverging coherence length at the impurity-induced second order phase transition from $s_{\pm}/s_{++}$ states to the $s+is$ state. Such a soft mode generically results in long-range attractive intervortex forces that can trigger the formation of vortex clusters. We find that, if such clusters are formed, their size and internal flux density have a characteristic temperature dependence that could be probed in muon-spin-rotation experiments. We also comment on the appearance of spontaneous magnetic fields due to spatially varying impurities.Comment: Added discussion of spontaneous magnetic fields due to spatially varying impurities; Replaced with a version in print in Phys. Rev. B; 17 pages, 8 figure

A fast algorithm for Direct Numerical Simulation of natural convection flows in arbitrarily-shaped periodic domains

A parallel algorithm is presented for the Direct Numerical Simulation of buoyancy-induced flows in open or partially confined periodic domains, containing immersed cylindrical bodies of arbitrary cross-section. The governing equations are discretized by means of the Finite Volume method on Cartesian grids. A semi-implicit scheme is employed for the diffusive terms, which are treated implicitly on the periodic plane and explicitly along the homogeneous direction, while all convective terms are explicit, via the second-order Adams-Bashfort scheme. The contemporary solution of velocity and pressure fields is achieved by means of a projection method. The numerical resolution of the set of linear equations resulting from discretization is carried out by means of efficient and highly parallel direct solvers. Verification and validation of the numerical procedure is reported in the paper, for the case of flow around an array of heated cylindrical rods arranged in a square lattice. Grid independence is assessed in laminar flow conditions, and DNS results in turbulent conditions are presented for two different grids and compared to available literature data, thus confirming the favorable qualities of the method

Appearance of quasiperiodicity within a period doubling route to chaos of a swaying thermal plume

The birth, evolution and disappearance of quasiperiodic dynamics in buoyancy-driven flow arising from an enclosed horizontal cylinder are analysed here, by numerical means, in the limit of the 2D approximation. The governing equations are solved on orthogonal Cartesian grids, giving special treatment to the internal, non-aligned boundaries. Thanks to the adoption of a high level of re finement of the Rayleigh number range, quasiperiodicity was observed to emerge from a periodic limit cycle (P1), and to turn into its omologous orbit with doubled period (P2), eventually evolving into a classical period-doubling route to chaos, for further increases of the Rayleigh number. The present study gives a deeper insight to what appears to be an imperfect period doubling bifurcation through a quasiperiodic T2-torus. The approach used is based on the classical tools for time series analysis. The distribution of the power spectral densities is used to search for and characterise the existence of relations between the frequencies of the P1, T2 and P2 dynamics. The topology of the orbits, as well as their evolution within the quasiperiodic window, are analysed with the aid of phase space representation and Poincar è maps

Heat transfer along the route to chaos of a swaying thermal plume

Detailed analyses have been recently reported on the low order dynamics of a thermal plume arising from a horizontal cylindrical heat source concentric: to an air-\ufb01lled isothermally cooled square enclosure, together with those of the related \ufb02ow structures, in the limit of the 2D approximation. In particular. within the range of O < Ra < 3 RaL-T, With Ram corresponding to the loss of stability of the stationary buoyant plume, the entire evolution from a periodic limit cycle (P1) to the birth of chaos through a period\ubbdoubling cascade has been fullyexplored. With this respect, special attention has been given to the window of quasiperiodic dynamics onto a T;-torus that is observed to separate the monoperiodic dynamics from the biperiodic dynamics onto a P1 and a Pg-liniit cycle, respectively. The results of these analyses hint at the bimodal nature of the overall dynamics. in general, and of the subharmonic cascade, in particular, which are still under investigation. Although relevant on a dynamical perspective, a with a main re\ufb02ection on the laminar-turbulent transition, the observed oscillations appear to be characterised by comparable amplitudes and to be determined by similar evolutions of the \ufb02ow pattern evolutions, so that their role on the overall heat transfer rate is expected to be marginal. Vi/'ithin this frame, the present study aims at reporting the in\ufb02uence played by the observed dynamics of the thermal plume and of the [low structures on the global heat transferrate. In particular, the aim is the assessment of the correlation between the Rayleigh number and the average Nusselt number on the cylinder surface, as well as the effect on the latter of the observed series of bifurcations

Single-step preparation of inverse opal titania films by the doctor blade technique

The difficulty to infiltrate solid-state hole semiconductors within micron-thick porous titania films is one of the major limiting factors for the achievement of efficient solid-state dye-sensitized solar cells. It was already shown that through the ordered interconnected pores of an inverse opal, the large surface area of several microns thick titania film can be easily decorated with a dye and filled with a solid-state hole semiconductor. In this paper, we show that ordered inverse opal mesoporous thick films of TiO2 with these characteristics can be obtained by using a slurry of monodispersed polystyrene spheres and a titania-lactate precursor deposited by the doctor blade technique. The mechanism of formation of the inverse opal is also discussed

Bifurcations of Natural Convection Flows from an Enclosed Cylindrical Heat Source

A numerical analysis of transitional natural convection from a confined thermal source is presented. The system considered is an air-filled, square-sectioned 2D enclosure containing a horizontal heated cylinder. The resulting flow is investigated with respect to the variation of the Rayleigh number, for three values of the aspect ratio A. The first bifurcation of the low-Ra fixed-point solution is tracked for each A-value. Chaotic flow features are detailed for the case A = 2.5. The supercritical behaviour of the system is investigated using nonlinear analysis tools and phase-space representations, and the effect of the flow on heat transfer is discussed

Topological defects in dirty two-band superconductors

LAUREA MAGISTRALELa superconduttività a più componenti è un'estensione naturale della teoria convenzionale, nel caso il materiale abbia più di una banda superconduttrice. La facilità con cui si estende il modello tuttavia non rispecchia la moltitudine dei nuovi fenomeni. Questa tesi analizza alcuni di questi fenomeni, nel contesto di un modello Ginzburg-Landau a due bande microscopicamente derivato. In particolare questo modello ha un'interazione repulsiva come accoppiamento fra bande, e termini diffusivi interbanda dovuti ad impurità. Il modello cerca di descrivere alcune proprietà dei superconduttori a base di ferro, una nuova classe di superconduttori ad alta temperatura critica recentemente scoperti. Le impurità avranno un ruolo centrale, permettendo una transizione da uno stato s+- ad uno s++. Questa transizione può avvenire in modo discontinuo, producendo una nuovo tipo di vortice, il vortice a "fossato", oppure può avvenire in modo continuo, attraverso uno stato intermedio s+is. Quest'ultimo è un esempio di stato che rompe la simmetria rispetto all'inversione temporale (BTRS), impossibile da trovare in superconduttori convenzionali, e che presenta properietà magnetiche particolari, come la presenza di campi magnetici spontanei dentro il materiale, a differenza della classica elettrodinamica di London. Gli stati BTRS hanno anche effetti sull'interazione fra vortici, aprendo la possibilità alla superconduttività di tipo 1.5, un nuovo stato intermedio che involve la formazione di raggruppamenti di vortici. Oltre ai vortici, altri difetti topologici sono possibili, come gli Skyrmion e la pareti di dominio, che verranno studiati durante la tesi. Tutti i fenomeni sopracitati sono stati analizzati nel dettaglio all'interno del modello e simulati numericamente, attraverso il metodo degli elementi finiti.Multicomponent superconductivity arises as a natural extension of the conventional theory, when materials have more than one superconducting band. The triviality of the extension does not reflect at all the multitude of new possible exotic phenomena. The topic of this thesis is to analyze some of them, in the context of a microscopically derived Ginzburg-Landau two-band model. In particular the model studied has repulsive interband coupling interaction and interband impurity scattering. The model hopes to describe some of the physics of iron-based superconductors, a new class of high temperature superconductors recently discovered. The impurity will have a central role in the model, allowing transitions between gap states, from s+- to s++. This transition can happen abruptly with a crossover, producing a new form of vortex matter, the so called "moat-core" vortices or can happen smoothly through an intermediate s+is state. The latter is an example of broken time-reversal symmetry state (BTRS), impossible in conventional superconductivity, and presenting peculiar magnetic properties, like the appearance of spontaneous magnetic field inside the material, in contrast with the usual London electrodynamics. BTRS states also affects vortex interaction, opening the possibility of type-1.5 superconductivity, an intermediate new state involving vortex clusterization. Apart from vortex, other topological defects are possible in multicomponent systems, like Skyrmions and domain walls, that will be studied during the thesis. All the phenomena above mentioned have been extensively analyzed inside the model and numerically simulated, within a finite element framework

Recording the Learning Curve during the Mastery of Glassblowing

Fire and inspiration melted glass art’s enchanting ways into the center of my passions. Lampworking is a small-scale method of glass blowing, which is the term to refer to an art form where one shapes molten glass into a variety of items. To create glass art, propane and oxygen supply a flame torch which melts the glass. Gravity and rhythmic hands work symbiotically to shape glass rods and tubes. The result is unique three-dimensional visual art.After years of aspiring to work with borosilicate glass, the opportunity to incorporate the endeavor with academia presented itself. Through months of time and dedication, I was able to connect glass art with psychology by monitoring and recording the learning curve of a novice lampworker. Simply defined, a learning curve is a graphical representation of the increase of Learning or Proficiency (Vertical axis) with Experience (Horizontal axis.)Beginning with my first time using a torch, I kept a journal of my daily experiences, advancements, and accomplishments over the course of 14 weeks. This journal allowed me to observe the increase of knowledge and skills gained over time. Photographic and physical items were collected to provide a visual display of lampworking progress. To conclude my observation period, I constructed a final piece of psychology-inspired artwork that incorporated my highest levels of skills at the time.This project inspired me to question and observe some of the psychological processes related to art creation. It allowed me to discover and immerse myself in a mental state of flow, which involves full-capacity engagement in a goal-driven task. Tranquility, focus, challenge-skill balance, and control are some factors that accompany the flow of glasswork. The project also provided me with the basic skills I need to become an advanced glassworker. Through my involvement, I have acquired a true grasp on the value of working with one’s hands

Identifying and Constructing Complex Magnon Band Topology

Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path toward coherent spin transport for spintronics applications. In this work we explore the variety of topological magnon band structures and provide insight into how to efficiently identify topological magnon bands in materials. We do this by adapting the topological quantum chemistry approach that has used constraints imposed by time reversal and crystalline symmetries to enumerate a large class of topological electronic bands. We show how to identify physically relevant models of gapped magnon band topology by using so-called decomposable elementary band representations, and in turn discuss how to use symmetry data to infer the presence of exotic symmetry enforced nodal topology