Session J35: Superconductivity: Vortices II

Doubling of the Critical Current Density of 2G-YBCO Coated Conductors through proton irradiation

We report on magnetization and transport measurements of the critical current density of commercial 2G YBCO coated conductors before and after proton irradiation. The samples were irradiated along the c-axis with 4 MeV protons to a fluence of 1.5x10$^{\mathrm{16}}$ p/cm$^{\mathrm{2}}$. We find that at temperatures below 50 K, proton irradiation increases J$_{\mathrm{c}}$ by a factor of 2 in low fields and increases up to 2.5 in fields of 7 T. At 77 K, proton irradiation is less effective in enhancing the critical current. Doubling of J$_{\mathrm{c}}$ in fields of several Tesla and at temperatures below 50 K will be highly beneficial for applications of coated conductors in rotating machinery, generators and magnet coils. - Work supported by the US DoE-BES funded Energy Frontier Research Center (YJ), and by Department of Energy, Office of Science, Office of Basic Energy Sciences (UW, WKK), under Contract No. DE-AC02-06CH11357.   

Vortex dynamics in Co-doped and K-doped BaFe$_{2}$As$_{2}$ with point defects

The discovery of iron-based superconductors urges scientists and engineers to study not only superconducting mechanism but also possible applications. In view of this situation, it is important to study vortex dynamics for understanding fundamental properties as well as for suggesting a suitable fabrication process in this system. In particular, the interaction between vortices and defects attract tremendous attention, which is because this interaction is responsible for finite critical current density $J_c$. The interaction changes with dimensionality and morphology of defects. In cuprate superconductors, vortex manifold shows vortex glass phase with point defects and Bose glass phase with columnar defects. Besides, in both cases, $J_c$ shows pronounced enhancement compared with that in a pristine sample. We have already reported the enhancement of $J_c$ by the introduction of point or columnar defects in the case of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ crystal. In this talk, we show the results in proton-irradiated BaFe$_2$As$_2$ with electron- or hole-doping. The quantitative analysis reveals the doubling of pinning potential without changing the glassy exponent in Co-doped compounds, in addition to 2.5 times enhancement of $J_c$. Similar effects are observed in K-doped crystals.   

Fundamentals of free flux flow: proposed studies

Although much is known about free flux flow (FFF) in superconductors -- in which pinning is insignificant compared to interactions between quantized vortices -- there still remain questions concerning fundamental dynamics. Building on our previous work in correlating FFF with vortex core size (\textit{PRB} \textbf{80}, 134524), we propose three new studies examining more deeply the normal state in the vortex core and interactions between vortices. A correlation between scattering inside cores and the viscosity of FFF has not been explicitly determined; this may be investigated by probing the effect of scattering centers created by proton irradiation. Using results of previous irradiation work, one could control the extent of normal state scattering while monitoring effects on FFF. Questions also exist concerning vortex motion in channels with widths approaching that of individual vortices -- as determined solely by inter-vortex interactions. Studies have suggested that flux flow through constrictions could imitate ``jamming'' in the collective motion of \textit{grains}: Under certain conditions, it is possible for grains to form a barrier, blocking flow. More than just qualitatively comparing flux flow and granular flow to find evidence of jamming, we propose a new experiment for quantitatively modeling flux jamming by realizing the flux flow equivalent of granular jamming in a ``hopper''. In the same way, we also propose a FFF equivalent of another granular-flow phenomenon, ``non-Newtonian'' fluids, where rapid shear causes jamming.   

Vortex core size due to the quasiparticle interference effect in cuprate superconductors

We investigate the vortex core properties by solving the Bogoliubov de-Gennes equations for the t-t'-U-V Hamiltonian. The double peaks structure of the local density of states at the vortex core center characterizes the vortex core state. The local density of states maps have been numerically obtained near the slightly underdoping for the energy at the vortex core state. It is found that the field induced spin-density wave would cause the vortex core shrinking as the magnetic increases. We also found that the quasiparticle interference effect would affect the vortex core shrinking that the core size is independent the strength of the applied magnetic field.   

Field-induced Dirac fermions and Fermi-surface resonance-scattering in the vortex-lattice cores of strongly type-II superconductors

A remarkable relationship between the formation of Dirac fermions in the vortex lattice of a clean 2D strongly type-II superconductor at high magnetic fields and a peculiar magneto-quantum oscillations effect is revealed. It is shown that at the magnetic fields where the low-lying BdG quasi-particle dispersion has a Dirac cone structure, dHvA oscillations amplitude is sharply modified due to Fermi-surface resonance-scatterings occurring in core regions of the vortex lattice. A Dirac cone is created at each vortex core in the reciprocal vortex lattice at magnetic fields where the effective Zeeman spin-splitting vanishes and the chemical potential is in the middle of a Landau band (M.R.Norman and A.H.MacDonald, Phys.Rev. B54 4239 (1996); Z.Tesanovic and P.Sacramento, Phys.Rev.Lett.80 1521 (1998); T.Maniv, et al., Rev.Mod.Phys.73 867 (2001)). Under these resonance conditions coherent BdG quasi-particle scatterings are singularly enhanced leading to ``erratic,'' quasi-periodic modulation of the dHvA oscillation amplitude as a function of 1/B (V.Zhuravlev and T.Maniv, Phys.Rev. B85 104528 (2012)). For a spin-triplet superconductor in the presence of commensurate arrays of pinning centers, an ``exotic'' possibility of field-induced sub-lattices of bound Majorana fermions is discussed.   

Theory of de Haas van Alphen Oscillations in Superconductors with Preformed Pair

We address recent observations of quantum oscillatory behavior in high temperature superconductors within a preformed pair theory of the pseudogap phase. These non condensed pairs, present in the normal and superconducting phases are shown to be reflective of a slightly distorted vortex lattice phase $^1$. Importantly they contribute a separate additive (``bosonic") component to the field dependent thermodynamics in addition to that arising from fermions. In this talk we report our findings that the bosonic component appears to display the same Lifshitz-Kosevich oscillation frequencies as also found in the mixed state of conventional superconductors (associated with gapless fermionic states). We explore the different amplitude weighting factors for the bosonic and fermionic contributions and the effects of varying the pairing symmetry from $s$ to $d$-wave. For the latter and for many properties, the bosonic component is most strongly associated with the anti-node, while the fermionic contribution comes from the node. Ref.1. Pseudogap Effects in Fermi Gases in the Presence of a Strong Effective Magnetic Field, P. Scherpelz, Dan Wulin, K. Levin and A. K. Rajagopal, ArXiv 1207.4826   

Quantum oscillations in d-wave superconductors with loop current order

Coexistence of $d$-wave superconductivity and Fermi pockets in underdoped high temperature cuprate superconductors has been suggested by recent quantum oscillation experiments. The origin of Fermi pockets in the superconducting state has been under debate. Here we report numerical results of quantum oscillations of the specific heat in the vortex state of a $d$-wave superconductor in the presence of loop current order, which gives rise to Fermi pockets coexisting with nodal $d$-wave superconductivity. First, we calculate the specific heat within a lattice tight-binding model, varying the loop current order and the external magnetic field. Second, we investigate the same problem in the continuum linearized limit, performing Franz-Tesanovic transformation, and find that the Bogoliubov Dirac quasiparticles also couple to a vector-like potential which corresponds to a highly nonuniform magnetic field. The results thus found are consistent with the tight-binding calculation. While the energy spectrum is qualitatively different from Landau levels, we find oscillations of the specific heat that in an intermediate temperature range approximately follow Onsager relation.   

Oscillations of the Magnetoresistance and the Critical Current in MoGe Thin Films with Hole-arrays in Square Vortex-ice Geometry

Resistivity measurements on MoGe thin films containing hole-arrays in square vortex-ice configuration were carried out to study the formation of a frustrated vortex state. MoGe thin films of 20 nm thick were prepared by sputter-deposition and holes with spacings of 200 nm - 400 nm and diameters from 100 nm to 300 nm were introduced into them using focused-ion-beam milling. We observed unusual matching effects: depending on the hole-hole spacing and the experimental temperature, the pinning enhancement at the half matching field can be stronger than that at the first matching field, as divulged by the deeper dip in the magnetoresistance and the higher peak in the critical current. Computer simulations within the nonlinear time-dependant Ginzburg-Landau theory reveal an origin of vortex jamming in the square vortex-ice state, indicating the first experimental realization of a square vortex-ice.   

Thermal Hall effect in the underdoped cuprate superconductor YBa$_2$Cu$_3$O$_{6.5}$

The thermal Hall conductivity $\kappa_{xy}$ (Righi-Leduc effect) is tailor-made to probe the transport properties of Bogolyubov quasiparticles (QPs) in a superconductor because neither the phonons nor vortices contribute to the off-diagonal response. We report measurements of $\kappa_{xy}$ in untwinned crystals of underdoped YBa$_2$Cu$_3$O$_{6.5}$, extending from 100 K to 15 K in fields $H$ up to 14 T. Several key features will be described. At all temperatures $T$, the QPs are hole-like. However, there is a small negative contribution that appears just below $T_c$. Below 30 K, the curve of $\kappa_{xy}/T$ vs. $H$ approaches an apparent universal step-like profile that may reflect the behavior of long-lived Dirac excitations confined to orbits around the gap nodes in an intense magnetic field. Measurements to much lower $T$ and higher $H$ ($\sim$ 32 T) are planned.   

Zero field Hall effect in chiral p-wave superconductors near the Kosterlitz-Thouless transition

A theory of vortex dynamics developed by Ambegaokar, Halperin, Nelson, and Siggia is employed to study two-dimensional chiral $p$-wave superconducting systems. Due to unequal values of drag coefficients of opposite vorticity specific to chiral $p$-wave cases, we find that a ``convective'' term, in addition to diffusivity, should enter the dynamical equations governing vortex pair unbinding process. As a consequence, we find a matrix form dielectric function and a new contribution to Hall conductance $\sigma_{xy}$ automatically follows even in zero magnetic field. We predict both the Hall conductance and power dissipation show a peak across the Kosterlitz-Thouless transition temperature. Their frequency dependence is also discussed. It is found that a set of frequency-dependent length scales, which controls the truncation of renormalization process, depends on both the convective and diffusive motion of vortices.   

Domain Wall and Reverse Domain Superconductivity in Superconducting/Ferromagnet Hybrid Structures

We have investigated the effect of inhomogeneous stray fields of a ferromagnet on the nucleation of the superconducting order parameter in superconductor/ferromagnet (S/F) systems magnetically coupled. Low-temperature scanning tunneling microscopy and spectroscopy measurements were performed on a Pb/[Co/Pd] system, which has a nontrivial H-T phase diagram under externally applied magnetic fields. Conductance maps and tunneling spectroscopy of these systems show clear indications of domain wall and reverse domain superconductivity. Close to the transition temperature (T$_{c}$) and in zero applied field, we visualized the emergence of superconductivity in regions above the separation between adjacent magnetic domains on length scales of the order of the coherence length. We also find an increase in T$_{c}$ for certain values of applied field above magnetic domains of the opposite polarity.   

Vortex confinement by magnetic domains in superconductor-ferromagnet bilayers

We use a line of miniature Hall sensors to study the effect of magnetic-domain-induced vortex confinement on the flux dynamics in a superconductor/ferromagnet bilayer. A single tunable bilayer is built of a ferromagnetic Co/Pt multilayer with perpendicular magnetic anisotropy and a superconducting Nb layer, with the insulating layer in between to avoid proximity effect. The magnetic domain patterns of various geometries are reversibly predefined in the Co/Pt multilayer using the appropriate magnetization procedure. The magnetic domain geometry strongly affects vortex dynamics, leading to geometry-dependent trapping of vortices at the sample edge, nonuniform flux penetration, and strongly nonuniform critical current density. With the decreasing temperature the magnetic pinning increases but this increase is substantially weaker than that of the intrinsic pinning. The analysis of the initial flux penetration suggests that vortices may form various vortex structures, including disordered Abrikosov lattice or single and double vortex chains, in which minimal vortex-vortex distance is comparable to the magnetic penetration depth.   

Magnetic decoration imaging of a superconductor-ferromagnet bilayer

Magnetic decoration imaging technique is used to study flux distribution and local vortex order in a superconducting Nb film deposited on a ferromagnetic yttrium-iron garnet substrate. Ambient field-cooled decoration patterns reveal concentration of vortices in the Nb along the labyrinthine magnetic domains of the garnet. Re-magnetization cycles result in a formation of the complex ``vortex foam'' structure due to a coupled magnetic dynamics of the superconductor-ferromagnet (S/F) bilayer system. We analyze density variations and spatial distribution of vortices in these structures. Flux exit patterns obtained upon removal of an external magnetic field show large-scale inhomogeneity of the vortex flow. Results are compared to the recent theoretical predictions and reported studies of S/F systems by other imaging methods.   

Vortex coalescence and type-1.5 superconductivity in Sr2RuO4

Recently vortex coalescence was reported in superconducting Sr2RuO4 by several experimental groups for fields applied along the c-axis. We argue that Sr2RuO4 is a type-1.5 superconductor with long-range attractive, short-range repulsive intervortex interaction. The type-1.5 behavior stems from an interplay of the two orbital degrees of freedom describing this chiral superconductor together with the multiband nature of the superconductivity. These multiple degrees of freedom give rise to multiple coherence lengths, some of which are larger and some smaller than the magnetic field penetration length, resulting in nonmonotonic intervortex forces. The talk is based on Phys. Rev. B 86, 060513(R) (2012)   

Heirarchical mesophases of vortex matter in layered and multi-component superconductors

Based on several models for Type-1.5 and hybrid Type-1/Type-2 layered superconductors, we examine the zero temperature properties of vortices with Langevin dynamics and Monte Carlo simulations. We demonstrate that inter-vortex forces with multiple length scales can result in unusual mesophases of vortex structures, such as clusters of clusters, concentric rings, clusters in a ring, and stripes in a cluster.