Vortex Molecular Crystal and Vortex Plastic Crystal States in Honeycomb and Kagome Pinning Arrays

Using numerical simulations, we investigate vortex configurations and pinning in superconductors with honeycomb and kagome pinning arrays. We find that a variety of novel vortex crystal states can be stabilized at integer and fractional matching field densities. The honeycomb and kagome pinning arrays produce considerably more pronounced commensuration peaks in the critical depinning force than triangular pinning arrays, and also cause additional peaks at noninteger matching fields where a portion of the vortices are located in the large interstitial regions of the pinning lattices. For the honeycomb pinning array, we find matching effects of equal strength at most fillings B/B_\phi=n/2 for n>2, where n is an integer, in agreement with recent experiments. For kagome pinning arrays, pronounced matching effects generally occur at B/B_\phi=n/3 for n>3, while for triangular pinning arrays pronounced matching effects are observed only at integer fillings B/B_\phi=n. At the noninteger matching field peaks in the honeycomb and kagome pinning arrays, the interstitial vortices are arranged in dimer, trimer, and higher order n-mer states that have an overall orientational order. We call these n-mer states "vortex molecular crystals" and "vortex plastic crystals" since they are similar to the states recently observed in colloidal molecular crystal systems. We argue that the vortex molecular crystals have properties in common with certain spin systems such as Ising and n-state Potts models. We show that kagome and honeycomb pinning arrays can be useful for increasing the critical current above that of purely triangular pinning arrays.Comment: 19 pages, 22 postscript figures. Version to appear in Phys. Rev.

Honeycomb Arrays

A honeycomb array is an analogue of a Costas array in the hexagonal grid; they were first studied by Golomb and Taylor in 1984. A recent result of Blackburn, Etzion, Martin and Paterson has shown that (in contrast to the situation for Costas arrays) there are only finitely many examples of honeycomb arrays, though their bound on the maximal size of a honeycomb array is too large to permit an exhaustive search over all possibilities. The present paper contains a theorem that significantly limits the number of possibilities for a honeycomb array (in particular, the theorem implies that the number of dots in a honeycomb array must be odd). Computer searches for honeycomb arrays are summarised, and two new examples of honeycomb arrays with 15 dots are given

Meissner effect in honeycomb arrays of multi-walled carbon nanotubes

We report Meissner effect for type-II superconductors with a maximum Tc of 19 K, which is the highest value among those in new-carbon related superconductors, found in the honeycomb arrays of multi-walled CNTs (MWNTs). Drastic reduction of ferromagnetic catalyst and efficient growth of MWNTs by deoxidization of catalyst make the finding possible. The weak magnetic anisotropy, superconductive coherence length (- 7 nm), and disappearance of the Meissner effect after dissolving array structure indicate that the graphite structure of an MWNT and those intertube coupling in the honeycomb array are dominant factors for the mechanism.Comment: 6 page

Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries

We demonstrate single-atom trapping in two-dimensional arrays of microtraps with arbitrary geometries. We generate the arrays using a Spatial Light Modulator (SLM), with which we imprint an appropriate phase pattern on an optical dipole trap beam prior to focusing. We trap single $^{87}{\rm Rb}$ atoms in the sites of arrays containing up to $\sim100$ microtraps separated by distances as small as $3\;\mu$m, with complex structures such as triangular, honeycomb or kagome lattices. Using a closed-loop optimization of the uniformity of the trap depths ensures that all trapping sites are equivalent. This versatile system opens appealing applications in quantum information processing and quantum simulation, e.g. for simulating frustrated quantum magnetism using Rydberg atoms.Comment: 9 pages, 10 figure

Anti-ferromagnetic ordering in arrays of superconducting pi-rings

We report experiments in which one dimensional (1D) and two dimensional (2D) arrays of YBa2Cu3O7-x-Nb pi-rings are cooled through the superconducting transition temperature of the Nb in various magnetic fields. These pi-rings have degenerate ground states with either clockwise or counter-clockwise spontaneous circulating supercurrents. The final flux state of each ring in the arrays was determined using scanning SQUID microscopy. In the 1D arrays, fabricated as a single junction with facets alternating between alignment parallel to a [100] axis of the YBCO and rotated 90 degrees to that axis, half-fluxon Josephson vortices order strongly into an arrangement with alternating signs of their magnetic flux. We demonstrate that this ordering is driven by phase coupling and model the cooling process with a numerical solution of the Sine-Gordon equation. The 2D ring arrays couple to each other through the magnetic flux generated by the spontaneous supercurrents. Using pi-rings for the 2D flux coupling experiments eliminates one source of disorder seen in similar experiments using conventional superconducting rings, since pi-rings have doubly degenerate ground states in the absence of an applied field. Although anti-ferromagnetic ordering occurs, with larger negative bond orders than previously reported for arrays of conventional rings, long-range order is never observed, even in geometries without geometric frustration. This may be due to dynamical effects. Monte-Carlo simulations of the 2D array cooling process are presented and compared with experiment.Comment: 10 pages, 15 figure

Fabrication of Artificial Graphene in a GaAs Quantum Heterostructure

The unusual electronic properties of graphene, which are a direct consequence of its two-dimensional (2D) honeycomb lattice, have attracted a great deal of attention in recent years. Creation of artificial lattices that recreate graphene's honeycomb topology, known as artificial graphene, can facilitate the investigation of graphene-like phenomena, such as the existence of massless Dirac fermions, in a tunable system. In this work, we present the fabrication of artificial graphene in an ultra-high quality GaAs/AlGaAs quantum well, with lattice period as small as 50 nm, the smallest reported so far for this type of system. Electron-beam lithography is used to define an etch mask with honeycomb geometry on the surface of the sample, and different methodologies are compared and discussed. An optimized anisotropic reactive ion etching process is developed to transfer the pattern into the AlGaAs layer and create the artificial graphene. The achievement of such high-resolution artificial graphene should allow the observation for the first time of massless Dirac fermions in an engineered semiconductor.Comment: 13 pages text, 8 figures, plus reference

Towards an explanation for the 30 Dor (LMC) Honeycomb nebula - the impact of recent observations and spectral analysis

The unique Honeycomb nebula, most likely a peculiar supernova remnant, lies in 30 Doradus in the Large Magellanic Cloud. Due to its proximity to SN1987A, it has been serendipitously and intentionally observed at many wavelengths. Here, an optical spectral analysis of forbidden line ratios is performed in order to compare the Honeycomb high-speed gas with supernova remnants in the Galaxy and the LMC, with galactic Wolf-Rayet nebulae and with the optical line emission from the interaction zone of the SS433 microquasar and W50 supernova remnant system. An empirical spatiokinematic model of the images and spectra for the Honeycomb reveals that its striking appearance is most likely due to a fortuitous viewing angle. The Honeycomb nebula is more extended in soft X-ray emission and could in fact be a small part of the edge of a giant LMC shell revealed for the first time in this short wavelength domain. It is also suggested that a previously unnoticed region of optical emission may in fact be an extension of the Honeycomb around the edge of this giant shell. A secondary supernova explosion in the edge of a giant shell is considered for the creation of the Honeycomb nebula. A microquasar origin of the Honeycomb nebula as opposed to a simple supernova origin is also evaluated.Comment: 12 pages, 9 figures, accepted for publication in MNRA

Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate

We study theoretically the simultaneous existence of phononic and photonic band gaps in a periodic array of silicon pillars deposited on a homogeneous thin silica plate. Several lattices, namely, square, triangular, and honeycomb are investigated for a wide range of geometrical parameters. We discuss the most suitable cases for dual phononic-photonic band gaps, especially in comparison to the more conventional structures constituted by a periodic array of holes in a membrane