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1. Artificial Pinning Centers in (Y,RE)-Ba-Cu-O Superconductors: Recent Progress and Future Perspective

   https://doi.org/1088/1361-6668/ab4ccd  

   Timothy J. Haugan, Teresa Puig ( October 2019 , Superconductor science technology)

   A microscopic understanding of vortex pinning in type II superconductors began with the theoretical discovery of magnetic vortices by Abrikosov, which received the 2003 Nobel Prize in Physics [1, 2]. When type II superconductors are exposed to magnetic fields (H), the magnetic field enters as quantized vortices, each with a fundamental flux j0 = 2.07 × 10−11 T cm−2 , or 2.07 × 10−15 Wb. The vortex core size on the order of the superconducting coherence length can be very small, e.g. ∼1–2 nm for the cuprate family of high-temperature superconductors (HTSs). The vortices electrically interact with each other by repelling, and act collectively together as a flux lattice that is affected by the intrinsic crystal lattice properties and microstructure defects. For superconducting power applications where applied magnetic fields are in the range of 0.1 T to >30 T, the areal number density of the vortices can reach incredibly high values. For example, for an applied magnetic field of 5 T, the vortex areal density is around 2.5 × 1011 cm−2 , which translates to inter-vortex spacing of about 20 nm (assuming a square lattice for vortices). Somewhat surprisingly, if the crystal lattice for type II superconductors, such as HTS cuprates [3] is nearly perfect without any defects to pin vortices, the vortices can move collectively and almost freely in an applied magnetic field due to Lorentz forces, which results in electrical resistance at a fairly low critical current density Jc(H, T) at an applied magnetic field (H) and temperature (T). In order to realize useful critical current densities in type II superconductors, imperfections and defects must be added to the crystal lattice to effectively pin vortices. The simplest example of this was achieved in the (Y, RE)Ba2Cu3O7 (where RE is rare earth elements) family by depositing thin films, in which high densities of dislocations and other growth defects are added into the film microstructure and dramatically increase the critical current density Jc(77 K, H//c-axis) > 106 A cm−2 compared to Jc (77 K) < 103 A cm−2 for single crystals [4–6] 

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2. Driven responses of periodically patterned superconducting films

   Al Luhaibi, A. ; Glatz, A ; Ketterson, J. B. ( December 2024 , Physical Review B: Solid state)

   We simulate the motion of a commensurate vortex lattice in a periodic lattice of artificial circular pinning sites having different diameters, pinning strengths, and spacings using the time-dependent Ginzburg-Landau formalism. Above some critical DC current density Jc, the vortices depin, and the resulting steady-state motion then induces an oscillatory electric field E (t) with a defect "hopping" frequency f0, which depends on the applied current density and the pinning landscape characteristics. The frequency generated can be locked to an applied AC current density over some range of frequencies, which depends on the amplitude of the DC as well as the AC current densities. Both synchronous and asynchronous collective hopping behaviors are studied as a function of the supercell size of the simulated system and the (asymptotic) synchronization threshold current densities determined. 

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3. Superdiffusion of quantized vortices uncovering scaling laws in quantum turbulence

   https://doi.org/10.1073/pnas.2021957118  

   Tang, Yuan ; Bao, Shiran ; Guo, Wei ( February 2021 , Proceedings of the National Academy of Sciences)

   Generic scaling laws, such as Kolmogorov’s 5/3 law, are milestone achievements of turbulence research in classical fluids. For quantum fluids such as atomic Bose–Einstein condensates, superfluid helium, and superfluid neutron stars, turbulence can also exist in the presence of a chaotic tangle of evolving quantized vortex lines. However, due to the lack of suitable experimental tools to directly probe the vortex-tangle motion, so far little is known about possible scaling laws that characterize the velocity correlations and trajectory statistics of the vortices in quantum-fluid turbulence, i.e., quantum turbulence (QT). Acquiring such knowledge could greatly benefit the development of advanced statistical models of QT. Here we report an experiment where a tangle of vortices in superfluid⁴He are decorated with solidified deuterium tracer particles. Under experimental conditions where these tracers follow the motion of the vortices, we observed an apparent superdiffusion of the vortices. Our analysis shows that this superdiffusion is not due to Lévy flights, i.e., long-distance hops that are known to be responsible for superdiffusion of random walkers. Instead, a previously unknown power-law scaling of the vortex–velocity temporal correlation is uncovered as the cause. This finding may motivate future research on hidden scaling laws in QT.

    

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4. Imaging quantized vortex rings in superfluid helium to evaluate quantum dissipation

   https://doi.org/10.1038/s41467-023-38787-w  

   Tang, Yuan ; Guo, Wei ; Kobayashi, Hiromichi ; Yui, Satoshi ; Tsubota, Makoto ; Kanai, Toshiaki ( May 2023 , Nature Communications)

   The motion of quantized vortices is responsible for many intriguing phenomena in diverse quantum-fluid systems. Having a theoretical model to reliably predict the vortex motion therefore promises a broad significance. But a grand challenge in developing such a model is to evaluate the dissipative force caused by thermal quasiparticles in the quantum fluids scattering off the vortex cores. Various models have been proposed, but it remains unclear which model describes reality due to the lack of comparative experimental data. Here we report a visualization study of quantized vortex rings propagating in superfluid helium. By examining how the vortex rings spontaneously decay, we provide decisive data to identify the model that best reproduces observations. This study helps to eliminate ambiguities about the dissipative force acting on vortices, which could have implications for research in various quantum-fluid systems that also involve similar forces, such as superfluid neutron stars and gravity-mapped holographic superfluids.

    

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5. Ginzburg-Landau approach to the vortex–domain wall interaction in superconductors with nematic order

   https://doi.org/10.1103/PhysRevB.109.094513  

   Severino, R. S. ; Mininni, P. D. ; Fradkin, E. ; Bekeris, V. ; Pasquini, G. ; Lozano, G. S. ( March 2024 , Physical Review B)

   In this work, we study the interaction between vortices and nematic domain walls within the framework of a Ginzburg-Landau approach. The free energy of the system is written in terms of a complex order parameter characteristic of s-wave superconductivity and a real (Ising-type) order parameter associated with nematicity. The interaction between both order parameters is described by a biquadratic and a trilinear derivative term. To study the effects of these interactions, we solve the time-dependent dissipative Ginzburg-Landau equations using a highly effective pseudospectral method by which we calculate the trajectories of a vortex that, for different coupling parameters, is either attracted or repelled by a wall, as well as of the wall dynamics. We show that despite its simplicity, this theory displays many phenomena observed experimentally in Fe-based superconductors. In particular, we find that the sign of the biquadratic term determines the attractive (pinning) or repulsive (antipinning) character of the interaction, as observed in FeSe and BaFeCoAs compounds, respectively. The trilinear term is responsible for the elliptical shape of vortex cores as well as the orientation of the axes of the ellipses and vortex trajectories with respect to the axes of the structural lattice. For the case of pinning, we show that the vortex core is well described by a heart-shaped structure in agreement with scanning tunneling microscopy experiments performed in FeSe. 

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