Lankhorst, M.

Poccia, N.

Journal of Physics Condensed Matter

English

M Lankhorst

N Poccia

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Symmetric dynamic behaviour of a superconducting proximity array with respect to field reversal

As the complexity of strongly correlated systems and high temperature superconductors increases, so does also the essential complexity of defects found in these materials and the complexity of the supercurrent pathways. It can be therefore convenient to realize a solid-state system with regular supercurrent pathways and without the disguising effects of disorder in order to capture the essential characteristics of a collective dynamics. Using a square array of superconducting islands placed on a normal metal, we observe a state in which magnetic field-induced vortices are frozen in the dimples of the egg crate potential by their strong repulsion interaction. In this system a dynamic vortex Mott insulator transition has been previously observed. In this work, we will show the symmetric dynamic behaviour with respect to field reversal and we will compare it with the asymmetric behaviour observed at the dynamic vortex Mott transition.</p

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Journal of Physics: Condensed MatterPAPERSymmetric dynamic behaviour of asuperconducting proximity array with respect tofield reversalTo cite this article: M Lankhorst and N Poccia 2017 J. Phys.: Condens. Matter 29 024003 View the article online for updates and enhancements.Related contentProximity coupling in superconductor-graphene heterostructuresGil-Ho Lee and Hu-Jong Lee-Proximity-induced superconductivity inbismuth nanostripesSoraya Sangiao, Laura Casado, LuisMorellón et al.-Coulomb interaction effects on theMajorana states in quantum wiresA Manolescu, D C Marinescu and T DStanescu-This content was downloaded from IP address 130.89.46.45 on 05/06/2019 at 12:471 © 2016 IOP Publishing Ltd Printed in the UK1. IntroductionIn spatially inhomogeneous systems carriers create com-plex spatial pathways and their band-structure becomes more difficult to connect with the physical properties of the material [1, 2]. High temperature superconductors belong to this latter class of materials where a non-Fermi liquid is observed [3].Most of the manifestations of non-Fermi liquid behaviour occurs in material with a very high degree of inhomogeneity which is quite difficult to control [4, 5]. Although disorder and inhomogeneities in strongly correlated electron systems could be considered an annoyance, it seems on the other hand that they are unavoidable as shown in several experiments with atomic scale resolution [6–10].In prototypical cuprate superconductors, x-ray images have considered that correlated disorder could be actually benefi-cial [11, 12]. It has been experimentally observed that nano-structures of the quenched disorder within the spacer layer are anti-correlated with the charge density puddles accompanied by local lattice distortions of the active layer [13–15] [17] [18]. Moreover, the tuning of the superconducting properties in the active layers is inseparably given by the properties of the spacer layers that can also be controlled through a con-tinuous light illumination [16]. As a result of the tuning, an optimal mix of anti-correlated fractal nanostructures between the active and the spacer layer has been suggested to deter-mine an optimal spatial pathways for supercurrents [14, 18].However, the morphology of these spatial pathways of supercurrents and their collective behaviour is considered an open problem [19]. In superconducting networks the supercon-ducting critical temperature is dependent on the geometrical Journal of Physics: Condensed MatterSymmetric dynamic behaviour  of a superconducting proximity array  with respect to field reversalM Lankhorst1 and N Poccia1,2,31 MESA+  Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands2 NEST Istituto Nanoscienze-CNR, Scuola Normale Superiore, Pisa, ItalyE-mail: n.poccia@utwente.nlReceived 31 July 2016, revised 21 September 2016Accepted for publication 26 September 2016Published 14 November 2016AbstractAs the complexity of strongly correlated systems and high temperature superconductors increases, so does also the essential complexity of defects found in these materials and the complexity of the supercurrent pathways. It can be therefore convenient to realize a solid-state system with regular supercurrent pathways and without the disguising effects of disorder in order to capture the essential characteristics of a collective dynamics. Using a square array of superconducting islands placed on a normal metal, we observe a state in which magnetic field-induced vortices are frozen in the dimples of the egg crate potential by their strong repulsion interaction. In this system a dynamic vortex Mott insulator transition has been previously observed. In this work, we will show the symmetric dynamic behaviour with respect to field reversal and we will compare it with the asymmetric behaviour observed at the dynamic vortex Mott transition.Keywords: superconductivity, vortex, critical dynamics, supercurrent pathways, Mott physics(Some figures may appear in colour only in the online journal)M Lankhorst and N PocciaSymmetric dynamic behaviour of a superconducting proximity array with respect to field reversalPrinted in the UK024003JCOMEL© 2016 IOP Publishing Ltd29J. Phys.: Condens. MatterCM0953-898410.1088/0953-8984/29/2/024003Paper2Journal of Physics: Condensed MatterIOP3 This article belongs to the special issue: Emerging Leaders, which features invited work from the best early-career researchers working within the scope of Journal of Physics: Condensed Matter. This project is part of the Journal of Physics series’ 50th anniversary celebrations in 2017. Nicola Poccia was selected by the Editorial Board of Journal of Physics: Condensed Matter as an Emerging Leader.20170953-8984/17/024003+4$33.00doi:10.1088/0953-8984/29/2/024003J. Phys.: Condens. Matter 29 (2017) 024003 (4pp)M Lankhorst and N Poccia 2parameters of the network [20–23]. The relevance of the geom-etry for the spatial pathways of supercurrents is shown by a recent experiment on an artificial man-made superconducting proximity array where supercurrents can flow in regular and well controlled pathways [24]. In this array of supercon-ducting islands, the supercurrents pathways form vortices that are trapped between the islands in the areas of weaker prox-imity-induced superconductivity. Since the Feyman pathways interpretation of quantum mechanics [25] and of continuous quantum phase transitions [26], this system can be mapped to a Mott insulating state that forms when the particle concentra-tion matches the density of the regular potential minima [27]. Via the vortex-particle mapping, in fact, the vortices sitting at the sites between the islands take the role of electrons in an electronic Mott insulator. With the application of an electric field, a collective dynamic phase transition between a vortex-Mott-insulator and a vortex-metal is observed [24].In this weakly coupled superconducting proximity array, a classical critical dynamics of the vortex lattices is observed. We will show the transition upon magnetic field reversal, dis-cussing the symmetrical aspects in comparison with its asym-metric counterpart observed at integer fillings of the vortex lattice.2. Experimental methodA square array of 270-by-270 Nb islands was grown on a 40 nm thin layer of gold on top of a Si substrate. The gold layer was fabricated with photolithography and DC sputtering. The Nb islands were fabricated with e-beam lithography and DC sputtering. The islands have a diameter of 180 nm and the array has a lattice constant of 250 nm. A four-point probe measurement was done to obtain the voltage and differential resistance as a function of a transverse magnetic field. The Figure 1. Comparison of the critical behavior around f  =  0 and f  =  1. The upper left panel shows the differential resistance, /V Id d , around f  =  0. The lower left panel shows the corresponding resistance around f  =  0. The upper right panel shows the differential resistance, /V Id d , around f  =  1. The lower center panel shows the corresponding resistance around f  =  1. The color bar shows the external current, and the resistance panels have the same current range as their respective /V Id d  panel. The lower right panel shows the SEM image of a portion of the superconducting proximity array. The scale bar is 1 μm.J. Phys.: Condens. Matter 29 (2017) 024003M Lankhorst and N Poccia 3transport measurements were done in a liquid helium bath cryostat at 4.14 K.3. Results and discussionVortices occur in superconductors because the phase of the superconducting order parameter around a closed loop can pick up an integer times π2 . In contrast to Abrikosov vortices, where this loop encircles a normal core, the loop contains the weak links between the superconducting islands. If one forms a closed path between four such links along the Josephson junctions, the sum of the phase difference picked up in the junctions must add up to an integer times π2 . This integer counts the number of Josephson vortices.The number of Josephson vortices in the square array is proportional to the perpendicular external magnetic field. The magnetic field at which the number of vortices matches the traps in our square array is /= ΦB a0 0 2, with /πΦ =  e0  being the magnetic flux quantum [28]. The vortex filling fraction is defined as f  =  B/B0. This means that f  =  1 corresponds to one vortex per lattice cell. The vortices repel each other, and the in the ground state the vortices form a periodic pattern. If the filling factor is a rational value p/q, the ground state vortex configuration is a q by q superlattice. The ground state energy energy versus f is described by the Harper equation [29]. The minima in the magnetoresistance as described in [24] are resulting from a Hofstadter-type energy spectrum [30]. In this experiment, we apply an external current and measure the regime where a finite voltage is measured, so phase slips occur and the Josephson vortices are not stationary.Figure 1 shows a scanning electron microscopy image (SEM) of the superconducting array of Nb islands, the meas-urements done around f  =  0 and f  =  1 for comparison upon the application of a current. The resistances corresponding to the differential resistance, /V Id d  are shown. The resist-ance around f  =  0 and f  =  1 show pronounced dips indicating strong pinning at rational f. The minima remains even at the currents where /V Id d  shows profound maxima. The vortex phase pinned around f  =  1 is a vortex Mott insulator [31], and the transition is a dynamic vortex Mott transition [24].In this superconducting proximity array the dip to peak reversal for f  =  0 occurs in the range of 80 to 160 μA. Visual inspection of the shape of this current driven transition shows a symmetry around the magnetic field reversal. The nature of this symmetry is further shown in figure 2. Here the two side of the transition are plotted one on the top of each other. The superposition shows the symmetric behaviour. Around f  =  1, this mirror symmetry around f  =  fc is clearly broken. In the analogy with the electronic Mott insulator proposed in [24], the asymmetry is explained by noting that the f  <  1 regime corresponds to a hole doped Mott insulator, while the f  >  1 regime corresponds to an electron doped, which need not have the same physical behaviour.In conclusion, we have showed the differential resist-ance in a superconducting proximity array and compared its symmetric behaviour at f  =  0 with the dynamic vortex Mott insulator to metal transition, observed at f  =  1. Further exper-imental and theoretical investigations are under way to deter-mine the origin of this difference and its implication for the strongly correlated electronic systems.AcknowledgmentsThe work was supported by the Dutch FOM and NWO foundations and the Italian Ministry for Education and Research.References	 [1]	 Dagotto E 2005 Complexity in strongly correlated electronic systems Science 309 257–62	 [2]	 Shengelaya A and Muller K A 2015 The intrinsic heterogeneity of superconductivity in the cuprates Europhys. Lett. 109 27001	 [3]	 Keimer B, Kivelson S A, Norman M R, Uchida S and Zaanen J 2015 From quantum matter to high-temperature superconductivity in copper oxides Nature 518 179–86	 [4]	 Phillips J C, Saxena A and Bishop A R 2003 Pseudogaps, dopants, and strong disorder in cuprate high-temperature superconductors Rep. Prog. Phys. 66 2111–82	 [5]	 Kresin V, Ovchinnikov Y and Wolf S 2006 Inhomogeneous superconductivity and the pseudogap state of novel superconductors Phys. 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Symmetric dynamic behaviour of a superconducting proximity array with respect to field reversal

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