Comment on ``Quasiparticle Spectra around a Single Vortex in a d-wave Superconductor''

In a recent Letter Morita, Kohmoto and Maki analyzed the structure of quasiparticle states near a single vortex in a d-wave superconductor using an approximate version of the Bogoliubov - de Gennes theory. Their principal result is the existence of a bound state within the core region at finite energy with full rotational symmetry, which they assert explains the recent scanning tunneling microscopy results on YBCO single crystals. Here we argue that the approximation used in this work is fundamentally inadequate for the description of a d-wave vortex and that the obtained circular symmetry of the local density of states is an unphysical artifact of this approximation.Comment: 1 page REVTeX, to appear in PR

Effect of the Vortices on the Nuclear Spin Relaxation Rate in the Unconventional Pairing States of the Organic Superconductor (TMTSF)2_2PF6_6

This Letter theoretically discusses quasiparticle states and nuclear spin relaxation rates $T_1^{-1}$ in a quasi-one-dimensional superconductor (TMTSF)$_2$PF$_6$ under a magnetic field applied parallel to the conduction chains. We study the effects of Josephson-type vortices on $T_1^{-1}$ by solving the Bogoliubov de Gennes equation for $p$-, $d$- or $f$-wave pairing interactions. In the presence of line nodes in pairing functions, $T_1^{-1}$ is proportional to $T$ in sufficiently low temperatures because quasiparticles induced by vortices at the Fermi energy relax spins. We also try to identify the pairing symmetry of (TMTSF)$_2$PF$_6$.Comment: 4+ pages, 4 figure

Optical-logic-array processor using shadowgrams. II. Optical Parallel digital image processing

This paper was published in Journal of the Optical Society of America A and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/JOSAA.2.001237 Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law

Optical logic array processor using shadowgrams

This paper was published in Journal of the Optical Society of America and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/JOSA.73.000800 Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law

Optical-logic-array processor using shadowgrams. III. Parallel neighborhood operations and an architecture of an optical digital-computing system

This paper was published in Journal of the Optical Society of America A and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/JOSAA.2.001245 Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law

Field dependence of the vortex structure in chiral p-wave superconductors

To investigate the different vortex structure between two chiral pairing p_x +(-) i p_y, we calculate the pair potential, the internal field, the local density of states, and free energy in the vortex lattice state based on the quasiclassical Eilenberger theory, and analyze the magnetic field dependence. The induced opposite chiral component of the pair potential plays an important role in the vortex structure. It also produces H^{1/2}-behavior of the zero-energy density of states at higher field. These results are helpful when we understand the vortex states in Sr2RuO4.Comment: 11 pages, 10 figures, to be published in Phys. Rev.

Majorana bound state in rotating superfluid 3He-A between parallel plates

A concrete and experimentally feasible example for testing the putative Majorana zero energy state bound in a vortex is theoretically proposed for a parallel plate geometry of superfluid $^3$He-A phase. We examine the experimental setup in connection with ongoing rotating cryostat experiments. The theoretical analysis is based on the well-established Ginzburg--Landau functional, supplemented by microscopic calculations of the Bogoliubov--de Gennes equation, both of which allow the precise location of the parameter regions of the Majorana state to be found in realistic situations.Comment: 5 pages, 4 figure

Electronic structure and spontaneous internal field around non-magnetic impurities in spin-triplet chiral p-wave superconductors

The electronic structure around an impurity in spin triplet p-wave superconductors is studied by the Bogoliubov-de Gennes theory on a tight-binding model, where we have chosen $\sin{p_x}{+}{\rm i}\sin{p_y}$-wave or $\sin{(p_x+p_y)}{+}{\rm i}\sin{({-}p_x{+}p_y)}$-wave states which are considered to be candidates for the pairing state in Sr$_{2}$RuO$_{4}$. We calculate the spontaneous current and the local density of states around the impurity and discuss the difference between the two types of pairing. We propose that it is possible to discriminate the two pairing states by studying the spatial dependence of the magnetic field around a pair of impurities.Comment: 4 pages, 4 figure

Vortex state in double transition superconductors

Novel vortex phase and nature of double transition field are investigated by two-component Ginzburg-Landau theory in a situation where fourfold-twofold symmetric superconducting double transition occurs. The deformation from 60 degree triangular vortex lattice and a possibility of the vortex sheet structure are discussed. In the presence of the gradient coupling, the transition changes to a crossover at finite fields. These characters are important to identify the multiple superconducting phase in PrOs_4_Sb_12.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Majorana surface states of superfluid 3He A- and B-phases in a slab

Motivated by experiments on the superfluid 3He confined in a thin slab, we design a concrete experimental setup for observing the Majorana surface states. We solve the quasi-classical Eilenberger equation, which is quantitatively reliable, to evaluate several quantities, such as local density of states (LDOS), mass current for the A-phase, and spin current for the B-phase. In connection with realistic slab samples, we consider the upper and lower surfaces and the side edges including the corners with several thicknesses. Consequently the influence on the Majorana zero modes from the spatial variation of l-vector for the A-phase in thick slabs and the energy splitting of the zero-energy quasi-particles for the B-phase confined in thin slabs are demonstrated. The corner of slabs in the B-phase is accompanied by the unique zero-energy LDOS of corner modes. On the basis of the quantitative calculation, we propose several feasible and verifiable experiments to check the existence of the Majorana surface states, such as the measurement of specific heat, edge current, and anisotropic spin susceptibility.Comment: 13 pages, 10 figures, published versio