Abstract: We demonstrate the in situ engineering of superconducting nanocircuitry by targeted modulation of material properties through high applied current densities. We show that the sequential repetition of such customized electro-annealing in a niobium (Nb) nanoconstriction can broadly tune the superconducting critical temperature T-c and the normal-state resistance R-n in the targeted area. Once a sizable R-n is reached, clear magneto-resistance oscillations are detected along with a Fraunhofer-like field dependence of the critical current, indicating the formation of a weak link but with further adjustable characteristics. Advanced Ginzburg-Landau simulations fully corroborate this picture, employing the detailed parametrization from the electrical characterization and high resolution electron microscope images of the region within the constriction where the material has undergone amorphization by electro-annealing.

Abstract: Reducing the size of a superconductor below its characteristic length scales can either enhance or suppress its critical temperature (T-c). Depending on the bulk value of the electron-phonon coupling strength, electronic and phonon confinement effects will play different roles in the modification of T-c. Experimentally disentangling each contribution has remained a challenge. We have measured both the phonon density of states and T-c of Sn nanowires with diameters of 18, 35, and 100 nm in order to quantify the effects of phonon confinement on superconductivity. We observe a shift of the phonon frequency towards the low-energy region and an increase in the electron-phonon coupling constant that can account for the measured increase in T-c.

Abstract: Diffusive properties of interacting magnetic dipoles confined in a parabolic narrow channel and in the presence of a periodic modulated (corrugated) potential along the unconfined direction are studied using Brownian dynamics simulations. We compare our simulation results with the analytical result for the effective diffusion coefficient of a single particle by Festa and d'Agliano [Physica A 90, 229 (1978)] and show the importance of interparticle interaction on the diffusion process. We present results for the diffusion of magnetic dipoles as a function of linear density, strength of the periodic modulation and commensurability factor.

Abstract: We introduce a differential geometry description of the path lines, stream lines and particles contours in hydrodynamics. We present a generalized form of a Korteweg-de Vries type of equation for the exterior of a circle. Nonlinearities from the boundary conditions, surface tension and the Euler equations are taken into account, but the flow is considered inviscid and irrotational. For the circular case we describe the traveling waves shapes, solitons and the particles trajectories.

Abstract: We solve the linear GinzburgLandau (GL) equation in the presence of a uniform magnetic field with cylindrical symmetry and we find analytic expressions for the eigenfunctions in terms of the confluent hypergeometric functions. The discrete spectrum results from an implicit equation associated to the boundary conditions and it is resolved in analytic form using the continued fractions formalism. We study the dependence of the spectrum and the eigenfunctions on the sample size and the surface conditions for solid and hollow cylindrical superconductors. Finally, the solutions of the nonlinear GL formalism are constructed as expansions in the linear GL eigenfunction basis and selected by minimization of the free energy. We present examples of vortex states and their energies for different samples in enhancing/suppressing superconductivity surroundings.

Abstract: The response of electron systems to electrodynamic fields that change rapidly in space is endowed by unique features, including an exquisite spatial nonlocality. This can reveal much about the materials' electronic structure that is invisible in standard probes that use gradually varying fields. Here, we use graphene plasmons, propagating at extremely slow velocities close to the electron Fermi velocity, to probe the nonlocal response of the graphene electron liquid. The near-field imaging experiments reveal a parameter-free match with the full quantum description of the massless Dirac electron gas, which involves three types of nonlocal quantum effects: single-particle velocity matching, interaction-enhanced Fermi velocity, and interaction-reduced compressibility. Our experimental approach can determine the full spatiotemporal response of an electron system.

Abstract: The precise control of skyrmionics and magnonics in magnetic materials is key to the development of novel spin-based technology and information transport applications. Essentially, the inherent stability of magnetic skyrmions (provided by their topological charge) together with their extremely small size (down to a few nanometers) and the ultralow threshold current necessary to move them in nanostructures are the main advantages of skyrmionics. Not least, magnonics offers lower power consumption compared to electronics and the excitation of high frequency (sub-100~nm wavelength) magnons makes it possible for the creation of nanometric devices for ultrafast information transport. Even though extensive research has been carried out in recent years, the precise manipulation of skyrmions and spin waves (magnons) in nanostructures is not fully mastered and needs to be addressed before making functional skyrmionic and magnonic devices. In this thesis, we reveal multiple alternatives for the manipulation of skyrmions and spin-waves in different materials, such as bulk chiral magnets, heterochiral structures, magnet-supperconductor hybrids and two-dimentional magnetic materials. We make use of a multiscale model to numerically simulate the magnetic states at each considered material, from micromagnetic to atomistic control. We first explore the different nucleation mechanisms, activation energy, and the time evolution of the skyrmion formation in chiral magnetic films, crucial for the realization of skyrmion-based devices. We show that the skyrmion lattice is formed from the conical phase progressively, most probably by the formation of chiral bobbres, followed by the cylindrical growth of individual skyrmions from the film surface. That reflects a rod-like (one-dimensional) nucleation of the skyrmion phase, with an activation barrier of several electronvolts per skyrmion for the case of MnSi (Manganese monosilicide). In addition, we reveal the interesting blinking (creation-annihilation) behavior of skyrmions close to the phase boundary between the conical and skyrmion phases, where we recall that such switching between topologically distinct states has been proposed as a bit operation for information storage. Next, we discuss the motion of ferromagnetic and antiferromagnetic skyrmions in heterochiral magnets. We report the characteristic deflection of ferromagnetic skyrmions when moving across a heterochiral interface, where the extent of such deflection is tuned by the applied spin-polarized current and the magnitude of Dzyaloshinskii-Moriya interaction. Following, we show that the antiferromagnetic skyrmion achieves much higher velocities than its ferromagnetic counterpart, yet experiences far stronger confinement in nanoengineered heterochiral tracks, which reinforces antiferromagnetic skyrmions as a favorable choice for skyrmion-based devices. After that, we study the interesting coupling of magnetic skyrmions and superconducting vortices in magnet-superconductor heterostructures. We perform numerical simulations, based on experimental observations, to demonstrate that the stray field of magnetic skyrmions can nucleate antivortices in an adjacent superconducting film, giving rise to a hybrid topological object, the skyrmion-vortex pair, which harbor promising features for skyrmionics and quantum computing applications. We then explore the manipulation of a single skyrmion-vortex pair when currents are applied into both superconducting and magnetic parts of the heterostructure, which is of importance for the facilitated skyrmion guidance in racetrack applications. Afterwards, we make use of the high tunability of magnetic parameters in two-dimensional magnetic materials to reveal the rich phase diagram of exotic magnetic configurations in magnetic monolayers with suppressed nearest-neighbour exchange, where we show that several unique cycloidal, checkerboard, row-wise and spin-ice states are stabilized by the competition between the second-nearest-neighbor exchange, Dzyaloshinskii-Moriya, and dipolar interactions. Additionally, we show the coexistence of ferromagnetic and antiferromagnetic spin-cycloids, as well as novel types of skyrmions and chiral domain walls. Finally, in the last part of the thesis, we present the spin wave properties in the two-dimensional magnetic materials CrBr$3$ and CrI$3$. Using spin-dynamics simulations parametrized from first principles, we reveal that the spin wave dispersion in such materials can be tuned in a broad range of frequencies by strain-engineering, and that a designed pattern of strain, as well as structural defects (halide vacancies) can be turned useful in the design of spin-wave guides. Lastly, we discuss the realization of magnonic crystals by moiré-periodic modulation of magnetic parameters in van der Waals heterostructures, where we show that the several nanometer small periodicities in such samples are ideal for the interference of terahertz spin waves. Recalling the wide range of possibilities for manipulating spin waves in such two-dimensional materials, we therefore suggest these systems as a front-runner for prospective terahertz magnonic applications.

Abstract: Recently, we have used a projection operator to fix the number of particles in a second quantization approach in order to deal with the canonical ensemble. Having been applied earlier to handle various problems in nuclear physics that involve fixed particle numbers, the projector formalism was extended to grant access as well to quantum-statistical averages in condensed matter physics, such as particle densities and correlation functions. In this light, the occupation numbers of the subsequent single-particle energy eigenstates are key quantities to be examined. The goal of this paper is (1) to provide a sound extension of the projector formalism directly addressing the occupation numbers as well as the chemical potential, and (2) to demonstrate how the emerging problems related to numerical instability for fermions can be resolved to obtain the canonical statistical quantities for both fermions and bosons. (C) 2018 Elsevier B.V. All rights reserved.

Abstract: For many decades the Boltzmann distribution function has been used to calculate the non-equilibrium properties of mobile particles undergoing the combined action of various scattering mechanisms and externally applied force fields. When the latter give rise to the occurrence of inhomogeneous potential profiles across the region through which the particles are moving, the numerical solution of the Boltzmann equation becomes a highly complicated task. In this work we highlight a particular algorithm that can be used to solve the time dependent Boltzmann equation as well as its quantum mechanical extension, the WignerBoltzmann equation. As an illustration, we show the calculated distribution function describing electrons propagating under the action of both a uniform and a pronouncedly non-uniform electric field.

Abstract: Knowing the exact number of particles N, and taking this knowledge into account, the quantum canonical ensemble imposes a constraint on the occupation number operators. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary but fixed N. On the other hand, fixing only the average number of particles, one may remove the above constraint and simply factorize the traces in Fock space into traces over single-particle states. As is well known, that would be the strategy of the grand-canonical ensemble which, however, comes with an additional Lagrange multiplier to impose the average number of particles. The appearance of this multiplier can be avoided by invoking a projection operator that enables a constraint-free computation of the partition function and its derived quantities in the canonical ensemble, at the price of an angular or contour integration. Introduced in the recent past to handle various issues related to particle-number projected statistics, the projection operator approach proves beneficial to a wide variety of problems in condensed matter physics for which the canonical ensemble offers a natural and appropriate environment. In this light, we present a systematic treatment of the canonical ensemble that embeds the projection operator into the formalism of second quantization while explicitly fixing N, the very number of particles rather than the average. Being applicable to both bosonic and fermionic systems in arbitrary dimensions, transparent integral representations are provided for the partition function Z(N) and the Helmholtz free energy F-N as well as for two- and four-point correlation functions. The chemical potential is not a Lagrange multiplier regulating the average particle number but can be extracted from FN+1 – F-N, as illustrated for a two-dimensional fermion gas. (C) 2017 Elsevier B.V. All rights reserved.

Abstract: Chimera state is a recently discovered dynamical phenomenon in arrays of nonlocally coupled oscillators, that displays a self-organized spatial pattern of coexisting coherence and incoherence. We discuss the appearance of the chimera states in networks of phase oscillators with attractive and with repulsive interactions, i.e. when the coupling respectively favors synchronization or works against it. By systematically analyzing the dependence of the spatiotemporal dynamics on the level of coupling attractivity/repulsivity and the range of coupling, we uncover that different types of chimera states exist in wide domains of the parameter space as cascades of the states with increasing number of intervals of irregularity, so-called chimera's heads. We report three scenarios for the chimera birth: (1) via saddle-node bifurcation on a resonant invariant circle, also known as SNIC or SNIPER, (2) via blue-sky catastrophe, when two periodic orbits, stable and saddle, approach each other creating a saddle-node periodic orbit, and (3) via homoclinic transition with complex multistable dynamics including an “eight-like” limit cycle resulting eventually in a chimera state.

Abstract: Graphene’s remarkable electronic properties have fuelled the vision of a graphene-based platform for lighter, faster and smarter electronics and computing applications. One of the challenges is to devise ways to tailor graphene’s electronic properties and to control its charge carriers. Here we show that a single-atom vacancy in graphene can stably host a local charge and that this charge can be gradually built up by applying voltage pulses with the tip of a scanning tunnelling microscope. The response of the conduction electrons in graphene to the local charge is monitored with scanning tunnelling and Landau level spectroscopy, and compared to numerical simulations. As the charge is increased, its interaction with the conduction electrons undergoes a transition into a supercritical regime where itinerant electrons are trapped in a sequence of quasi-bound states which resemble an artificial atom. The quasi-bound electron states are detected by a strong enhancement of the density of states within a disc centred on the vacancy site which is surrounded by halo of hole states. We further show that the quasi-bound states at the vacancy site are gate tunable and that the trapping mechanism can be turned on and off, providing a mechanism to control and guide electrons in graphene.