Crossover from hc/e to hc/2e current oscillations in rings of s-wave superconductors

We analyze the crossover from an hc/e-periodicity of the persistent current in flux threaded clean metallic rings towards an hc/2e-flux periodicity of the supercurrent upon entering the superconducting state. On the basis of a model calculation for a one-dimensional ring we identify the underlying mechanism, which balances the hc/e versus the hc/2e periodic components of the current density. When the ring circumference exceeds the coherence length of the superconductor, the flux dependence is strictly hc/2e periodic. Further, we develop a multi-channel model which reduces the Bogoliubov - de Gennes equations to a one-dimensional differential equation for the radial component of the wave function. The discretization of this differential equation introduces transverse channels, whose number scales with the thickness of the ring. The periodicity crossover is analyzed close the critical temperature

Growth of a vortex polycrystal in type II superconductors

We discuss the formation of a vortex polycrystal in type II superconductors from the competition between pinning and elastic forces. We compute the elastic energy of a deformed grain boundary, that is strongly non-local, and obtain the depinning stress for weak and strong pinning. Our estimates for the grain size dependence on the magnetic field strength are in good agreement with previous experiments on NbMo. Finally, we discuss the effect of thermal noise on grain growth.Comment: 4 pages, 2 figure

Electron-beam-induced shift in the apparent position of a pinned vortex in a thin superconducting film

When an electron beam strikes a superconducting thin film near a pinned vortex, it locally increases the temperature-dependent London penetration depth and perturbs the circulating supercurrent, thereby distorting the vortex's magnetic field toward the heated spot. This phenomenon has been used to visualize vortices pinned in SQUIDs using low-temperature scanning electron microscopy. In this paper I develop a quantitative theory to calculate the displacement of the vortex-generated magnetic-flux distribution as a function of the distance of the beam spot from the vortex core. The results are calculated using four different models for the spatial distribution of the thermal power deposited by the electron beam.Comment: 9 pages, 6 figures, resubmitted to PRB with referee-suggested revisions, includes new paragraph on numerical evaluatio

Tackling Exascale Software Challenges in Molecular Dynamics Simulations with GROMACS

GROMACS is a widely used package for biomolecular simulation, and over the last two decades it has evolved from small-scale efficiency to advanced heterogeneous acceleration and multi-level parallelism targeting some of the largest supercomputers in the world. Here, we describe some of the ways we have been able to realize this through the use of parallelization on all levels, combined with a constant focus on absolute performance. Release 4.6 of GROMACS uses SIMD acceleration on a wide range of architectures, GPU offloading acceleration, and both OpenMP and MPI parallelism within and between nodes, respectively. The recent work on acceleration made it necessary to revisit the fundamental algorithms of molecular simulation, including the concept of neighborsearching, and we discuss the present and future challenges we see for exascale simulation - in particular a very fine-grained task parallelism. We also discuss the software management, code peer review and continuous integration testing required for a project of this complexity.Comment: EASC 2014 conference proceedin

Fourier Acceleration of Langevin Molecular Dynamics

Fourier acceleration has been successfully applied to the simulation of lattice field theories for more than a decade. In this paper, we extend the method to the dynamics of discrete particles moving in continuum. Although our method is based on a mapping of the particles' dynamics to a regular grid so that discrete Fourier transforms may be taken, it should be emphasized that the introduction of the grid is a purely algorithmic device and that no smoothing, coarse-graining or mean-field approximations are made. The method thus can be applied to the equations of motion of molecular dynamics (MD), or its Langevin or Brownian variants. For example, in Langevin MD simulations our acceleration technique permits a straightforward spectral decomposition of forces so that the long-wavelength modes are integrated with a longer time step, thereby reducing the time required to reach equilibrium or to decorrelate the system in equilibrium. Speedup factors of up to 30 are observed relative to pure (unaccelerated) Langevin MD. As with acceleration of critical lattice models, even further gains relative to the unaccelerated method are expected for larger systems. Preliminary results for Fourier-accelerated molecular dynamics are presented in order to illustrate the basic concepts. Possible extensions of the method and further lines of research are discussed.Comment: 11 pages, two illustrations included using graphic

Dynamics of ions in the selectivity filter of the KcsA channel

The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion’s dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications

Investigation of the Spark channel of Electrical Discharges Near the Minimum Ignition Energy

In this work, we investigate the expansion of the hot gas kernel and pressure wave induced by electrical discharges near the minimum ignition energy experimentally by means of a schlieren setup and numerically through one-dimensional simulations. The effects of discharge energy and energy density on the expansion are discussed. Via comparison of experimental values with numerical simulations, an estimate of the overall losses of the discharge is presented

Elasticity-driven interaction between vortices in type-II superconductors

The contribution to the vortex lattice energy which is due to the vortex-induced strains is calculated covering all the magnetic field range which defines the vortex state. This contribution is compared with previously reported ones what shows that, in the most part of the vortex state, it has been notably underestimated until now. The reason of such underestimation is the assumption that only the vortex cores induce strains. In contrast to what is generally assumed, both core and non-core regions are important sources of strains in high-$\kappa$ superconductors.Comment: 10 pages, 1 figure, revtex

Quantitative nanoscale vortex-imaging using a cryogenic quantum magnetometer

Microscopic studies of superconductors and their vortices play a pivotal role in our understanding of the mechanisms underlying superconductivity. Local measurements of penetration depths or magnetic stray-fields enable access to fundamental aspects of superconductors such as nanoscale variations of superfluid densities or the symmetry of their order parameter. However, experimental tools, which offer quantitative, nanoscale magnetometry and operate over the large range of temperature and magnetic fields relevant to address many outstanding questions in superconductivity, are still missing. Here, we demonstrate quantitative, nanoscale magnetic imaging of Pearl vortices in the cuprate superconductor YBCO, using a scanning quantum sensor in form of a single Nitrogen-Vacancy (NV) electronic spin in diamond. The sensor-to-sample distance of ~10nm we achieve allows us to observe striking deviations from the prevalent monopole approximation in our vortex stray-field images, while we find excellent quantitative agreement with Pearl's analytic model. Our experiments yield a non-invasive and unambiguous determination of the system's local London penetration depth, and are readily extended to higher temperatures and magnetic fields. These results demonstrate the potential of quantitative quantum sensors in benchmarking microscopic models of complex electronic systems and open the door for further exploration of strongly correlated electron physics using scanning NV magnetometry.Comment: Main text (5 pages, 4 figures) plus supplementary material (5 pages, 6 figures). Comments welcome. Further information under http://www.quantum-sensing.c