Session E25: Superconductivity: Vortex matter

A quantitative model for flux flow resistivity and Nernst effect of vortex fluid in high-temperature superconductors

Transport properties of vortex fluid in high-temperature superconductors have been described in terms of viscous dynamics of magnetic and thermal vortices. We have constructed a quantitative model by extending the Bardeen-Stephen model of damping viscosity to include the contributions of flux pinning in low temperature and vortex-vortex interaction in high magnetic field. A uniformly accurate description of flux flow resistivity and Nernst signal is achieved for empirical data over a wide range of temperature and magnetic field strength. A discrepancy of three orders of magnitude between data and Anderson model of Nernst signal is pointed out, suggesting the existence of anomalous transport in high-temperature superconductor beyond mere quantum and thermal fluctuations. The model enables to derive a set of physical parameters characterizing the vortex dynamics from the Nernst signal, as we illustrate with an analysis of six samples of Bi$_{\mathrm{2}}$Sr$_{\mathrm{2-y}}$La$_{\mathrm{y}}$CuO$_{\mathrm{6}}$ and Bi$_{\mathrm{2}}$Sr$_{\mathrm{2}}$CaCu$_{\mathrm{2}}$O$_{\mathrm{8+\delta }}$.   

In-plane electronic anisotropy from core states of tilted vortices.

Magnetic field enters type II superconductors in form of quantized vortices. Each vortex has a core with the superconducting wavefunction vanishing at its center. Quasiparticles at the vortex core form bound states whose radial extension depends on the superconducting gap value and Fermi surface shape. In the layered superconductor 2H-NbSe2 vortex cores have been studied using scanning tunneling microscopy (STM) mostly with magnetic fields applied perpendicular to the layers. It is found that vortices have a six-fold star shape due to the in-plane anisotropy of the superconducting gap and of the electronic density of states. Here we study vortex core states with the magnetic field applied parallel to the layers. We find that the vortex cores change their shape depending on the angle of the tilted magnetic field with respect to the in-plane crystalline directions, providing a lateral view of the electronic structure.   

Characterization of vortex pinning through the Campbell length

Vortex pinning is decisive in establishing dissipation-free current flow in a type-II superconductor; knowledge and optimization of the pinning landscape (pinscape) is of major importance for applications. The $ac$ magnetic response, characterized by the Campbell penetration depth $\lambda_C$ [1], provides valuable information on the pinscape, besides the critical current density $j_c$. While microscopic derivations of $j_c$ are available both in the weak and strong pinning limits, this is not the case for the Campbell length, whose understanding has remained on a phenomenological level so far. Based on the microscopic theory of strong pinning, we have established a proper link between the Campbell length and the pinscape parameters. This new quantitative formalism [2] captures all experimentally observed signatures [3], among which are the dependence of $\lambda_C$ on the vortex state preparation and the hysteresis in $\lambda_C$ upon thermal cycling the field-cooled state. [1] A.M. Campbell, J Phys C: Solid State Physics 2, 1492 (1969), ibid. 4, 3186 (1971) [2] R. Willa, V.B. Geshkenbein, and G. Blatter, PRB 92, 134501 (2015), R. Willa, V.B. Geshkenbein, R. Prozorov and G. Blatter, PRL in press [3] R. Prozorov et al., PRB 67, 184501 (2003), H. Kim et al., PRB 87, 094515 (2013)   

Observation of RF-induced flux lattice annealing (RIFLA) in cuprate high temperature superconductors

We report the annealing of a strained flux lattice (FL) in cuprate high temperature superconductors, by the RF pulses used to obtain the NMR spin-echo signal and by a series of RF pulses that are input into the sample coil in a tuned NMR probe circuit. The strained FL is prepared by changing the alignment and/or magnitude of the applied magnetic field at temperatures well below the superconducting transition temperature, which leaves the FL pinned in a non-equilibrium configuration. We provide a very sensitive measure of the phenomenon. This new observation enriches the phenomenon of FL, and indicates that shaking the flux lattice by the applied RF pulses (including both the spin-echo pulses and the pulses input to the sample coil circuit) progressively causes the flux lattice to change to a lower free energy configuration. Supported by NSF China grant #: 61474096   

Dynamic and Structural Studies of Metastable Vortex Lattice Domains in MgB$_2$

Small-angle neutron scattering (SANS) studies of the vortex lattice (VL) in the type-II superconductor MgB$_2$ have revealed an unprecedented degree of metastability that is demonstrably not due to vortex pinning, [C. Rastovski $et$ $al.$, Phys. Rev. Lett. {\bf 111}, 107002 (2013)]. The VL can be driven to the GS through successive application of an AC magnetic field. Here we report on detailed studies of the transition kinetics and structure of the VL domains. Stroboscopic studies of the transition revealed a stretched exponential decrease of the metastable volume fraction as a function of the number of applied AC cycles, with subtle differences depending on whether the AC field is oriented parallel or perpendicular to the DC field used to create the VL. We speculate the slower transition kinetics for the transverse AC field may be due to vortex cutting. Spatial studies include scanning SANS measurements showing the VL domain distribution within the MgB$_2$ single crystal as well as measurements of VL correlation lengths.   

Enhancement of long-range correlations in a 2D vortex lattice by an incommensurate 1D disorder potential

In two dimensional (2D) systems, theory has proposed that random disorder destroys long range correlations driving a transition to a glassy state. Here, I will discuss new insights into this issue obtained through the direct visualization of the critical behaviour of a 2D superconducting vortex lattice formed in a thin film with a smooth 1D thickness modulation [1]. Using scanning tunneling microscopy at 0.1K, we have tracked the modification in the 2D vortex arrangements induced by the 1D thickness modulation while increasing the vortex density by three orders of magnitude. Upon increasing the field, we observed a two-step order-disorder transition in the 2D vortex lattice mediated by the appearance of dislocations and disclinations and accompanied by an increase in the local vortex density fluctuations. Through a detailed analysis of correlation functions, we find that the transition is driven by the incommensurate 1D thickness modulation. We calculate the critical points and exponents and find that they are well above theoretical expectation for random disorder. Our results show that long range 1D correlations in random potentials enhance the stability range of the ordered phase in a 2D vortex lattice. [1] I. Guillamon et al., Nature Physics 10, 851–856 (2014)   

Study of vortex states and dynamics in mesoscopic superconducting samples with MFM

Vortex states in superconducting (SC) structures, their dynamics and ways to manipulate them are topics of great interest. We report a new method of magnetic force microscopy (MFM) that allows the study of vortex states in mesoscopic SC samples. For the case of a SC ring, which is biased to a half-integer flux quantum, the flux modulation through the ring caused by the motion of the magnetic tip drives the ring between two consecutive fluxoid states. The corresponding current switching in the ring produces strong position-dependent forces on the cantilever. In the regime where the frequency of the thermally activated jumps between fluxoid states is close to the frequency of the cantilever, large changes in the cantilever frequency and dissipation are observed. This effect may be understood as a stochastic resonance (SR) process. These changes in the cantilever’s mechanical properties are used to “image” the barrier energies between fluxoid states. Additionally, SR imaging of the barrier energies are used to study the effect of the locally applied magnetic field from the MFM tip on the barrier heights. We report the results of measurements for Al rings. Further, the same imaging technique can be applied to more sophisticated SC structures such as arrays of Josephson junctions.   

History Dependence of the Vortex Lattice Rotation in the B-phase of UPt$_3$ with ${\bf H} \parallel {\bf c}$

The unconventional superconductor UPt$_3$ is widely believed to be a triplet superconductor, where the low temperature superconducting B-phase is a chiral state. We have performed small angle neutron scattering (SANS) from the vortex lattice (VL) in UPt$_3$ at the Paul Scherrer Institute with the magnetic field parallel to the hexagonal $c$-axis in the 0.5 T to 0.9 T range. The diffraction pattern of the VL rotates away from a high symmetry direction producing two domains of different orientation. Our field dependent measurements show a subtle magnetic field history dependence of this orientation; VLs prepared with the magnetic field parallel or anti-parallel with respect to the angular momentum from the circulating screening currents show different field-history dependence. These results suggest a coupling of a chiral superconducting order parameter with the applied magnetic field.   

Vortex matter in superconductors: solid or gas?

We will report on results of our recent study of the equilibrium magnetic properties of the mixed state in type-II superconductors performed with high purity bulk and film niobium samples in parallel and perpendicular magnetic fields using dc magnetometry and scanning Hall-probe microscopy. Equilibrium magnetization data for the perpendicular geometry were obtained for the first time. It was found that none of the existing theories is consistent with these new data. To address this problem a theoretical model is developed and verified experimentally. The new model describes the magnetic properties of the mixed state in an averaged limit, i.e. without detailing the samples' magnetic structure and therefore ignoring interactions between the structural units (vortices). Nevertheless, it is quantitatively consistent with the data obtained in a perpendicular field. At low values of the Ginzburg-Landau parameter, the model converts to that of Peierls and London for the intermediate state in type-I superconductors, valid in the limit of non-interacting normal domains. We will show that description of the vortex matter in type-II superconductors in terms of a 2D gas is more appropriate than the frequently used crystal- and glass-like scenarios.   

Orientational Ordering, Buckling, and Dynamic Transitions for Vortices Interacting with a Periodic Quasi-One Dimensional Substrate

We examine the statics and dynamics of vortices in the presence of a periodic quasi-one dimensional substrate, focusing on the limit where the vortex lattice constant is smaller than the substrate lattice period. As a function of the substrate strength and filling factor, within the pinned state we observe a series of order-disorder transitions associated with buckling phenomena in which the number of vortex rows that fit between neighboring substrate maxima increases. These transitions coincide with steps in the depinning threshold, jumps in the density of topological defects, and changes in the structure factor. For weaker substrate strengths we find that the vortices retain triangular ordering but can show changes in the orientation of the triangular lattice with respect to the substrate. Under an applied drive the system exhibits a rich variety of distinct dynamical phases, including plastic flow, a density-modulated moving crystal, and moving floating solid phases. We also discuss how these results are related to recent experiments by I. Guilamon et al, Nature Physics 10, 751 (2014), for vortices interacting on quasi-one-dimensional periodic modulated substrates.   

The dynamics and pinning of single vortices in type-II superconductors investigated using a scanning SQUID-on-tip microscope

The electromagnetic properties of superconductors, particularly their ability to carry non-dissipative currents, are governed by the dynamics of quantized magnetic vortices and their pinning due to material defects. Despite recent advances in the understanding of the complex physics of vortex matter, the behavior of vortices driven by current through a potential created in an actual material is still not well understood, mostly due to the scarcity of adequate experimental tools. Using a novel scanning SQUID-on-tip microscope we have investigated the controlled dynamics of vortices in Pb films with sub-Angstrom sensitivity to vortex displacement. Using the ability to trace vortex trajectories on nanometer scales, we measured, for the first time, the fundamental dependence of the elementary pinning force of multiple defects on the vortex displacement, revealing a far more complex behavior than has previously been recognized. Our results indicate the importance of thermal fluctuations even at 4.2 K, and of the vital role of small and seemingly un-important ripples in the pinning potential. These give new insights into the mechanisms of magnetic relaxation and electromagnetic response of superconductors.   

Dissipative vortex dynamics in overdamped superconducting arrays

We study 2D superconductor-normal-superconductor (SNS) arrays consisting of regularly spaced Nb islands on Au films, measuring the current-driven voltage response. SNS arrays provide a highly tunable platform for studying classical vortex behavior and we are able to access a number of vortex regimes, including edge pinning and site pinning regimes at low fields and commensurate vortex lattice behavior at higher fillings. Focusing on the low vortex filling regime, we study the current driven transition from pinned vortices to flux flow, finding that the differential resistance peak predicted by current driven vortex models is absent in our arrays. While the absence of a differential resistance peak is typically associated with finite temperature effects, this explanation is not consistent with our data. Instead, we find that the dynamic behavior of our system is consistent with the presence of time delayed dissipative forces in an overdamped array.   

$^{93}$Nb NMR investigation of vortex- glass transition in layered NbSe$_{2}$

We report a detailed low temperature investigation of vortex glass transition in layered superconducting compound NbSe$_{2}$ using $^{93}$Nb NMR at fields below H$_{c2}$. Preliminary measurements show that spin-lattice relaxation rate 1/$T_{1}$ demonstrates a classic Korringa behavior 1/$T_{1\, }$\textasciitilde $T$ above the superconducting transition $T_{c}$ , consistent with previous measurements on this compound. However, for field $H$ perpendicular to the layers, we observed that 1/$T_{1}$ exhibits an anomalous plateau between $T_{c}$ ($H=$0) and $T_{c}(H)$ and a suppression of the superconducting enhancement expected below $T_{c}$. Instead, a power law behavior, 1/$T_{1}$ \textasciitilde $T^{1.2}$ below $T_{c}$ down to 360mK was observed which suggests a strong anisotropy in the low energy excitations. However, the possibility of enhancement in 1/$T_{1}$ due to vortex fluctuations which competes with electronic mechanisms cannot be excluded. The implications of these results with regards to vortex-glass transition will be discussed.