Session D40: Superconductivity: Vortices

Non-linear flux vortex dynamics in MoGe

In the limit of small magnetic and electric fields, and low current densities, free flux flow in the mixed state leads to an Ohmic response. A number of interesting non-linearities can arise during free flux flow when it is pushed to high values of these parameters, because of changes in the quasiparticle distribution function or temperature (principally at high electric fields), and pair breaking due to the current or magnetic field. Usually pinning obscures these regimes so that the current density and magnetic field required to overcome pinning is such that the system is already out of the linear response range. MoGe has an uncommonly low level of pinning, which allows one to clearly observe the linear response regime without invoking near pair-breaking magnitudes of the parameters. We have studied the vortex stability in this system and also observe a superlinear magnetic field dependence that seems to arise from magnetic pair breaking.   

Using large scale 2D modeling to explain driven vortex motion observed by STM

We studied vortex matter in NbSe$_2$, a type II superconductor, at magnetic fields of 0.25 - 0.75 T and temperatures of 4.2 K. At these fields the vortices form an Abrikosov lattice. Due to a small residual resistance in our superconducting magnet the applied magnetic field slowly decayed, driving the vortex lattice. The velocity was low enough to allow acquiring highly resolved time series using a low temperature scanning tunneling microscopy (STM). From the images we where able to extract the lattice constant as well as time series of the average vortex position (path) and velocity. The data was compared to a large scale 2D molecular dynamic type model of over 10000 vortices. Different configurations were examined to match the observed behaviour concerning vortex tracks, velociy vs. time and lattice constant vs. time. The data is detailed enough two distinguish small loops in the vortex tracks most likely caused by lattice dislocations. The focus of this presentation lies in matching simulation to the observed time evolution of the average velocity and lattice constant. We would like to thank Eva Andrej and Helmut Berger for providing NbSe$_2$ samples.   

Logarithmic flux flow resistivity across the cuprate phase diagram

The microwave response of vortices in high quality YBa$_2$Cu$_3$O$_{6+x}$ and Tl$_2$Ba$_2$CuO$_{6+x}$ samples has been studied using high resolution microwave spectroscopy in applied magnetic field. Measurements of the flux flow resistivity and vortex viscosity probe dissipation from electronic states near the vortex cores. These quantities have been accurately measured at temperatures far below $T_c$, at applied fields far below $B_{c2}$, and at a number of dopings that span the entire superconducting region of the cuprate phase diagram. Here we report the first observation of a universal logarithmic temperature dependence of the flux-flow resistivity, in the highest quality samples, across the cuprate phase diagram. The behaviour bears a strong resemblance to the ``normal-state'' resistivity of the underdoped cuprates first observed by Ando and Boebinger. Our measurements shows that the effect persists to the highly overdoped side, where the resistivity is metallic and the normal state is a Fermi liquid. We show that the resistivity upturns are an intrinsic property of $d$-wave quasiparticles and discuss the implications of this for the nature of the underdoped cuprate normal state.   

Vortex-induced dissipation in narrow current-biased thin-film superconducting strips

We consider a vortex crossing a narrow superconducting strip from one edge to the other, perpendicular to a bias current, as the dominant mechanism for dissipation in thin-film superconductors of thickness $d$ of order of the coherence length $\xi$. The width $w$ of the strip is much narrower than the Pearl length $\Lambda=2\lambda^2/d$, with $\Lambda\gg w\gg\xi$. Every crossing of a vortex results in a detectable voltage pulse. We derive the rate of vortex crossings and the rate of pulses using the general theory of transition rates between metastable states. For the first time, we account for the renormalization of the vortex crossing rate by superconducting fluctuations and estimate the amplitude of voltage pulses and their consequences for the $I$-$V$ characteristics. We find ohmic $I$-$V$ behavior at low bias currents, power laws at intermediate currents, and exponential dependence close to the critical current $I_c$. We argue that pulse rate measurements may provide crucial information on the thermal and quantum dynamic nature of fluctuations, vortices, and the superconducting state. Finally, we discuss the impact of vortex-induced dissipation on the fundamental limitations for dark counts in superconducting nanowire single-photon detectors.   

Phase diagram in a Nb/[Co/Pt]$_{n}$ bilayer with tunable domain width

Exploiting the stripe domain pattern in ferromagnets with perpendicular magnetic anisotropy (PMA), we investigate the influence of domain width in the [Co/Pt]$_{n}$ multilayer with PMA on the nucleation of superconductivity in the Nb film, where a thin insulating layer separates the Nb and the [Co/Pt]$_{n}$ to avoid proximity effects. We employ a novel demagnetization procedure on a single Nb/[Co/Pt]$_{n}$ multilayer to reversibly tune the domain width. This allows us to explore the phase diagram using only one sample without the unavoidable variations when multiple samples are involved. We find that tuning the domain width in [Co/Pt]$_{n}$ dramatically alters the dependence of the critical temperature T$_{c}$ on the external magnetic field H$_{ext}$ in the Nb layer. By tuning the domain width, we observe a continuous evolution of the phase boundary T$_{c}$(H), from a non-linear dependence with a single maximum at H$_{ext}$= 0 for small domain widths, to an reentrant phase boundary line with multiple T$_{c}$ peaks for wider domains. Our results provide an experimental confirmation of the theoretical predictions of strong dependence of superconductivity nucleation on the magnetic domain size [1]. We demonstrate a unique method to determine the superconducting phase diagram by reversibly tuning the characteristics of a single sample. [1] A. Yu. Aladyshkin et al., Phys. Rev. B 68, 184508 (2003).   

Local probing of the vortex-antivortex dynamics in superconductor/ferromagnet hybrid structures.

In-plane ferromagnetic bars, parallel to each other and arranged to form a linear array underneath a superconducting bridge, create two types of vortex chains of opposite polarity inside the superconductor. The time-dependent Ginzburg-Landau approach is applied to investigate the dynamics of these vortex chains and the critical current densities, which correspond to the onset of vortex propagation along each chain. As a function of an external magnetic field, the calculated critical currents are strongly asymmetric and manifest pronounced oscillations, which strongly correlate with the field-induced changes in the number of vortices in a chain. The results of modeling are used to interpret the performed local transport measurements, which probe the dynamics of individual vortex channels. This combined theoretical and experimental investigation allows us to explain the most relevant properties of the dynamics of these superconductor-ferromagnet hybrid systems..   

Combined domain structures in superconducting/ferromagnetic hybrids

Combined domain (CD) structures of superconducting (SC) vortices strongly coupled to magnetic domains are studied using direct magneto-optical imaging in a bilayer of type II SC Nb film on a RE - iron garnet film. In a bare garnet film the domain width D increases with decreasing temperature and is substantially larger that the film thickness h. Below the SC Tc the CDs are formed which become much narrower than normal state domains after application of the AC fields in contrast with thermodynamic predictions for D$>>$h. A model is proposed explaining the observed effect by emergence of a transitional nonequilibrium state of the CD in the AC field. The studied CD structure defined by both SC and magnetic properties of the hybrid yields a novel electromagnetic response similar to that of a type I SC where the magnetization goes through the domain wall motion. The system acquires an enhanced pinning due to the coupled vortex/domain dynamics. The mobility of vortices reduces resulting in the suppression of thermo-magnetic avalanches at low temperatures and increased critical currents at T $\sim $ Tc.   

Experimental determination of the structure factor of a Bragg glass phase coexisting with a dirty edge state using slicing neutron diffraction

We use a slicing neutron diffraction technique, employing neutron reflectometry in the diffraction mode, to study the structure factor of a Bragg glass phase. We found that the ordered center region of the vortex matter gives a distinct cusp line shape in the Bragg peak. We will report our analysis using the Bragg glass model.   

Slicing through a bulk vortex matter using neutron reflectometry: observation of a vortex crystal (Bragg glass) with dirty edge states.

It is now widely accepted that the ground state of the vortex matter in weak-pinning type-II superconductors is a topologically ordered Bragg Glass (BrG) phase. An unresolved issue is how to access the equilibrium state of the BrG phase. For example, in some samples, the ZFC (zero-field-cooled) states are more ordered than that of the FC (field-cooled) states, while in seemingly similar samples, the opposite is true. In this work, we use neutron reflectometry in the diffraction mode to measure thin slices of the bulk vortex state prepared under various thermal-magnetic history. We found that in a sample with disordered ZFC states, but more ordered FC states, the vortex matter is highly inhomogeneous. We found that after repeated thermal annealing, a large domain of the BrG phase exists in the center of the sample, while the edge vortex matter remains disordered. Our results also provide additional insight into the disappearance of the peak effect.   

The Dynamics of Multi-Shell Vortex Matter in Mesoscopic Superconducting Corbino Disks

The discrete shell structure of vortex matter strongly influences the flux dynamics in mesoscopic superconducting Corbino disks. While the dynamical behavior is well understood in large and in very small disks [1], in the intermediate-size regime it occurs to be much more complex and unusual, due to (in)commensurability between the vortex shells. We demonstrate [2] unconventional vortex dynamics (inversion of shell velocities with respect to the gradient driving force) and angular melting (propagating from the boundary where the shear stress is minimum, towards the center) in mesoscopic Corbino disks. We show that intra- and inter-shell defects in shell structures can lead, correspondingly, to the inversion and hysteresis in the angular velocities of the shells [3]. [1] V.R. Misko and F.M. Peeters, Phys. Rev. B {\bf 74}, 174507 (2006). [2] N.S. Lin, V.R. Misko, and F.M. Peeters, Phys. Rev. Lett. {\bf 102}, 197003 (2009). [3] N.S. Lin, V.R. Misko, and F.M. Peeters, unpublished.   

Vortex matter in two-band mesoscopic superconductors

Using two-band Ginzburg-Landau theory, we discuss the effect of Josephson coupling and the mutual drag between two interacting superconducting condensates in mesoscopic samples exposed to a homogeneous magnetic field. We show that drag between condensates in combination with order parameter coupling strongly affects the interband vortex-vortex interaction. This leads to a unique set of possible vortex configurations, comprising {\it asymmetric}, {\it non-composite}, and {\it dynamic} vortex states. We also calculate the demagnetization properties of the samples, and show how latter exotic vortex states can be detected by magnetometry. Finally we introduce the magnetic coupling between condensates, and study in particular the case where one band is type II and the other type I, i.e. the sample is effectively of I.x type. Both the found vortex states and the calculated $M(H)$ loops show a clear signature of the mixed type of superconductivity, which we find to be strongly affected by the ratio of coherence lengths in two condensates.   

Spin Density Modulation Near the Vortex Cores of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$

Spatially resolved NMR spin-lattice (T$_1$) and spin-spin (T$_2$) measurements are used to probe the microscopic structure of the vortex lattice in the highly anisotropic High Temperature Superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. Results, differing from similar measurements in YB$_2$Cu$_3$O$_7$[1], are interpreted in the context of a long range spin density modulation in and outside the vortex core in accordance with previous LDOS ``checkerboard'' patterns found by STM[2]. Our model includes a checkerboard pattern of a Gaussian cosine decay from the vortex core, characterized by a amplitude and decay length, in addition to the diamagnetic contribution from vortices. Fitting this model to our data, we find that the amplitude increases and the decay length decreases with increasing external field and with this model we can also account for experimental T$_1$ relaxation rates.[1]Mitrovi\'c, V.F. \textit {et.al.} Nature \textbf{413}, 501(2001) [2] Hoffman, J.E. \textit{et al.} Science \textbf{295}, 466 (2002)   

Properties of superconducting Pb/Bi films modulated by a periodic magnetic stripe pattern

Rectangular Pb/Bi patterns with four contact leads were defined on Si wafers by e-beam lithography. Pb/Bi films with thickness $\sim $ 100 nm were deposited by evaporation with the substrates held at liquid nitrogen temperature. Ge layers of thickness $\sim $ 20 nm were then deposited as a spacer layer. Parallel Ni stripes were patterned by e-beam lithography and deposited by e-beam evaporation on the top of the Ge spacer layer. The width of the stripes was 120 nm and the spacing was 500 nm. The thickness of Ni layer was 120 nm. Electron transport properties were investigated in two types of samples, with the current applied parallel (the parallel samples) or perpendicular (the perpendicular samples) to the Ni stripes. Hysteretic superconducting properties under a magnetic field were observed in both types of samples. An anomalous magneto-resistance exceeding the normal state resistance was observed in the perpendicular samples at certain temperature and magnetic field range. A strong enhancement in critical current was observed in the parallel samples at higher temperatures. The experimental data was compared with the recent theories of magnet-superconductor hybrids. This work was supported by DOE No. DE-FG02-07ER46450, NSF CHE-0809651, the Robert A. Welch Foundation A-0514 and A-1688, and NHARP under grant {\#} 010366-0039-2007.   

A case for superconducting stripes in cuprates

Existence of charge-spin stripe states has been demonstrated in several families of cuprate superconductors; however, their relationship to superconductivity has remained enigmatic. The evidence of stripes, which is particularly clear in the underdoped regime, appears to go hand in hand with the anomalously broad superconducting fluctuation regime above Tc, as evidenced by the Nernst, diamagnetism, and ac-conductivity measurements. We therefore examine a phenomenological model of strongly inhomogeneous -striped - superconductor. We estimate the magnitude of the Nernst and the diamagnetic responses, and determine the trends as a function of doping and temperature. Our estimates are qualitatively consistent with the experimental results in the anomalous fluctuation regime, lending support to the view that spin-charge stripes can well coexist, or possibly promote, superconductivity.   

Mixed State of a Striped d-Wave Superconductor

A model of anti-phase modulated d-wave superconductor has been proposed to describe the decoupling between Cu-O planes in $1/8$ doped La$_{2-x}$Ba$_{x}$CuO$_{4}$. Unlike a uniform d-wave superconductor, this model exhibits an extended Fermi surface. We study the possibility of the existence of quantum oscillations in the mixed state of this model and compare it to the case of a uniform d-wave superconductor. Within Bogoliubov-deGennes theory, employing the Franz-Tesanovic transformation, we find a periodic structure of low-energy density of states with a frequency that is linear in $1/B$.