Critical currents in superconductors with quasiperiodic pinning arrays: One-dimensional chains and two-dimensional Penrose lattices

We study the critical depinning current J_c, as a function of the applied magnetic flux Phi, for quasiperiodic (QP) pinning arrays, including one-dimensional (1D) chains and two-dimensional (2D) arrays of pinning centers placed on the nodes of a five-fold Penrose lattice. In 1D QP chains of pinning sites, the peaks in J_c(Phi) are shown to be determined by a sequence of harmonics of long and short periods of the chain. This sequence includes as a subset the sequence of successive Fibonacci numbers. We also analyze the evolution of J_c(Phi) while a continuous transition occurs from a periodic lattice of pinning centers to a QP one; the continuous transition is achieved by varying the ratio gamma = a_S/a_L of lengths of the short a_S and the long a_L segments, starting from gamma = 1 for a periodic sequence. We find that the peaks related to the Fibonacci sequence are most pronounced when gamma is equal to the "golden mean". The critical current J_c(Phi) in QP lattice has a remarkable self-similarity. This effect is demonstrated both in real space and in reciprocal k-space. In 2D QP pinning arrays (e.g., Penrose lattices), the pinning of vortices is related to matching conditions between the vortex lattice and the QP lattice of pinning centers. Although more subtle to analyze than in 1D pinning chains, the structure in J_c(Phi) is determined by the presence of two different kinds of elements forming the 2D QP lattice. Indeed, we predict analytically and numerically the main features of J_c(Phi) for Penrose lattices. Comparing the J_c's for QP (Penrose), periodic (triangular) and random arrays of pinning sites, we have found that the QP lattice provides an unusually broad critical current J_c(Phi), that could be useful for practical applications demanding high J_c's over a wide range of fields.Comment: 18 pages, 15 figures (figures 7, 9, 10, 13, 15 in separate "png" files

Isomer Dependence in the Assembly and Lability of Silver(I) Trifluoromethanesulfonate Complexes of the Heteroditopic Ligands, 2-, 3-, and 4-[Di(1\u3cem\u3eH\u3c/em\u3e-pyrazolyl)methyl]phenyl(di-\u3cem\u3ep\u3c/em\u3e-tolyl)phosphine

Three isomers of a new heteroditopic ligand that contains a di(1H-pyrazolyl)methyl (−CHpz2) moiety connected to a di(p-tolyl)phosphine group via a para-, meta-, or ortho-phenylene spacer (pL, mL, and oL, respectively) have been synthesized by using a palladium(0)-catalyzed coupling reaction between HP(p-tolyl)2 and the appropriate isomer of (IC6H4)CHpz2. The 1:1 complexes of silver(I) trifluoromethanesulfonate, Ag(OTf), were prepared to examine the nature of ligand coordination and the type of supramolecular isomer (monomeric, cyclic oligomeric, or polymeric) that would be obtained. The single crystal X-ray diffraction studies showed that [Ag(pL)](OTf), 1, and [Ag(mL)](OTf), 2, possessed cyclic dimeric dications, whereas [Ag(oL)](OTf), 3, was a coordination polymer. The polymeric chain in 3 could be disrupted by reaction with triphenylphosphine, and the resulting complex, [Ag(oL)(PPh3)](OTf), 4, possessed a monometallic cation where the ligand was bound to silver in a chelating κ2P,N- coordination mode. The solution structures of 1–4 were probed via a combination of IR, variable-temperature multinuclear (1H, 13C, 31P) NMR spectroscopy, as well as by electron spray ionization (ESI)(+) mass spectrometry. A related complex [Ag(m-IC6H4CHpz2)2](OTf), 5, was also prepared, and its solid-state and solution spectroscopic properties were studied for comparison purposes. These studies suggest that the cyclic structures of 1 and 2 are likely preserved but are dynamic in solution at room temperature. Moreover, both 3 and 4 have dynamic solution structures where 3 is likely extensively dissociated in CH3CN or acetone rather than being polymeric as in the solid state

Does Koopmans’ Paradigm for 1-Electron Oxidation Always Hold? Breakdown of IP/E\u3csub\u3eox\u3c/sub\u3e Relationship for \u3cem\u3ep\u3c/em\u3e-Hydroquinone Ethers and the Role of Methoxy Group Rotation

Koopmans’ paradigm states that electron loss occurs from HOMO, thus forming the basis for the observed linear relationships between HOMO/IP, HOMO/Eox, and IP/Eox. In cases where a molecule undergoes dramatic structural reorganization upon 1-electron oxidation, the IP/Eoxrelationship does not hold, and the origin of which is not understood. For example, X-ray crystallography of the neutral and cation radicals of bicyclo[2.2.1]heptane-annulated p-hydroquinone ethers (THE and MHE) showed that they undergo electron-transfer-induced conformational reorganization and show breakdown of the IP/Eox relationship. DFT calculations revealed that Koopmans’ paradigm still holds true because the electron-transfer-induced subtle conformational reorganization, responsible for the breakdown of IP/Eox relationship, is also responsible for the reordering of HOMO and HOMO-1. Perceived failure of Koopmans’ paradigm in cases of THE and MHE assumes that both vertical and adiabatic electron detachments involve the same HOMO; however, this study demonstrates that the vertical ionization and adiabatic oxidation occur from different molecular orbitals due to reordering of HOMO/HOMO-1. The underpinnings of this finding will spur widespread interest in designing next-generation molecules beyond HQEs, whose electronic structures can be modulated by electron-transfer-induced conformation reorganization

Quintessence and phantom cosmology with non-minimal derivative coupling

We investigate cosmological scenarios with a non-minimal derivative coupling between the scalar field and the curvature, examining both the quintessence and the phantom cases in zero and constant potentials. In general, we find that the universe transits from one de Sitter solution to another, determined by the coupling parameter. Furthermore, according to the parameter choices and without the need for matter, we can obtain a Big Bang, an expanding universe with no beginning, a cosmological turnaround, an eternally contracting universe, a Big Crunch, a Big Rip avoidance and a cosmological bounce. This variety of behaviors reveals the capabilities of the present scenario.Comment: 8 pages, 8 figure