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1

service), SpringerLink (Online, ed. Scanning SQUID Microscope for Studying Vortex Matter in Type-II Superconductors. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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2

Rabinovich, B. I. Vortex processes and solid body dynamics: The dynamic problems of spacecrafts and magnetic levitation systems. Dordrecht: Kluwer Academic, 1994.

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3

G, Lebedev V., and Mytarev Alexander I, eds. Vikhrevye prot͡s︡essy i dinamika tverdogo tela: Zadachi dinamiki kosmicheskikh apparatov i sistem na magnitnoĭ podveske. Moskva: "Nauka," Glav. red. fiziko-matematicheskoĭ lit-ry, 1992.

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4

Antos, R., and Y. Otani. The dynamics of magnetic vortices and skyrmions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198787075.003.0022.

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This chapter argues that control of magnetic domains and domain wall structures is one of the most important issues from the viewpoint of both applied and basic research in magnetism. Its discussion is however limited to static and dynamic properties of magnetic vortex structures. It has been revealed both theoretically and experimentally that for particular ranges of dimensions of cylindrical and other magnetic elements, a curling in-plane spin configuration is energetically favored, with a small region of the out-of-plane magnetization appearing at the core of the vortex. Such a system, which is sometimes referred to as a magnetic soliton, is characterized by two binary properties: A chirality and a polarity, each of which suggests an independent bit of information in future high-density nonvolatile recording media.
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5

Kokubo, N., S. Okayasu, and K. Kadowaki. Multi-Vortex States in Mesoscopic Superconductors. Edited by A. V. Narlikar. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780198738169.013.3.

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This article investigates multi-vortex states in mesoscopic amorphous superconductors with different geometries by means of scanning SQUID microscopy. It first describes the setup of the scanning SQUID microscope used in magnetic imaging of superconducting vortices before discussing the physical properties of amorphous superconducting thin films. It then presents the results of experiments showing the formation of multi-vortex states in mesoscopic dots of weak pinning, amorphous MoGe thin films, along with the formation of vortex polygons and concentric vortex rings in mesoscopic disks. It also considers the concept of multiple vortex shells and its applicability to vortex patterns observed in mesoscopic circle and square dots. The article highlights some of the key features of mesoscopic superconducting dots, including commensurability effect, multiple shell structures, repeated packing sequences, inclusion structural hierarchy, and pinning effect.
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6

Scanning Squid Microscope for Studying Vortex Matter in TypeII Superconductors Springer Theses. Springer, 2012.

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7

Ono, T. Spin-transfer torque in nonuniform magnetic structures. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198787075.003.0023.

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This chapter defines a magnetic domain wall (DW) as the transition region where the direction of magnetic moments gradually change between two neighbouring domains. It has been pointed out that ferromagnetic materials are not necessarily magnetized to saturation in the absence of an external magnetic field. Instead, they have magnetic domains, within each of which magnetic moments align. The formation of the magnetic domains is energetically favourable because this structure can lower the magnetostatic energy originating from the dipole–dipole interaction. A magnetic vortex realized in a ferromagnetic disk is a typical example of nonuniform magnetic structure. In very small ferromagnetic systems, where a curling spin configuration has been proposed to occur in place of domains, the formation of DWs is not energetically favored.
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8

Finkler, Amit. Scanning SQUID Microscope for Studying Vortex Matter in Type-II Superconductors. Springer, 2014.

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9

Finkler, Amit. Scanning SQUID Microscope for Studying Vortex Matter in Type-II Superconductors. Springer, 2012.

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10

Narlikar, Anant V. Vortex Physics And Flux Pinning: Studies of High Temperature Superconductors. Nova Science Publishers, 2005.

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11

Motta, M., A. V. Silhanek, and W. A. Ortiz. Magnetic Flux Avalanches in Superconducting Films with Mesoscopic Artificial Patterns. Edited by A. V. Narlikar. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780198738169.013.13.

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This article examines the practical problem of thermally driven high-speed flux avalanches occurring in superconducting thin films with mesoscopic artificial patterns. The thin films are synthesized with artificial pins in the form of sub-micrometric antidots (ADs). The article first provides an overview of magnetic flux avalanches in superconductors, with particular emphasis on thermally driven avalanches, before discussing the occurrence and morphology of flux avalanches in superconducting thin films comprised of AD arrays. It analyses the influence of lattice symmetry and different AD geometries on the guidance and consequently the branching of flux avalanches. It also explores how artificial pinning centers inserted in superconducting films affect vortex dynamics.
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12

Roberts, Jeanette Marie. Critical scaling of thin-film YBaCuO and NdCeCuO resistivity-current isotherms: Implications for vortex phase transitions and universality. 1995.

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13

Roberts, Jeanette Marie. Critical scaling of thin-film YBaCuO and NdCeCuO resistivity-current isotherms: Implications for vortex phase transitions and universality. 1995.

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14

Brown, Brandon R. Neutron irradiation and dc transport in YBaCuO single crystals: A study of vortex depinning. 1997.

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15

Claisse, John Richard. Vortex density motion in a cylindrical type II superconductor subject to a transverse applied magnetic field. 2001.

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16

Rabinovich, B., A. I. Lebedev, and A. I. Mytarev. Vortex Processes and Solid Body Dynamics: The Dynamic Problems of Spacecrafts and Magnetic Levitation Systems (Fluid Mechanics and Its Applications). Springer, 2012.

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17

Narlikar, A. V. Small Superconductors—Introduction. Edited by A. V. Narlikar. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780198738169.013.1.

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This article provides an overview of small superconductors, including some of the basic definitions, prominent characteristics, and important effects manifested by such materials. In particular, it discusses size effects, surface effects, electron-mean-free-path effects, phase slips, unusual vortex states, and proximity effects. The article first considers the two characteristic length scales of superconductors, namely the magnetic penetration depth and coherence length, before proceeding with an analysis of two size effects that account for how superconductivity responds when the bulk sample is made smaller and smaller in the nano range: the small size effects and the quantum size effects. It then examines other phenomena associated with small superconductors such as quantum fluctuations, Anderson limit, parity and shell effects, along with the behaviour of nanowires and ultra-thin fims. It also describes some of the experimental techniques commonly used in the synthesis of small superconductors.
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18

Narlikar, A. V., ed. The Oxford Handbook of Small Superconductors. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780198738169.001.0001.

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This handbook examines cutting-edge developments in research and applications of small or mesoscopic superconductors, offering a glimpse of what might emerge as a giga world of nano superconductors. Contributors, who are eminent frontrunners in the field, share their insights on the current status and great promise of small superconductors in the theoretical, experimental, and technological spheres. They discuss the novel and intriguing features and theoretical underpinnings of the phenomenon of mesoscopic superconductivity, the latest fabrication methods and characterization tools, and the opportunities and challenges associated with technological advances. The book is organized into three parts. Part I deals with developments in basic research of small superconductors, including local-scale spectroscopic studies of vortex organization in such materials, Andreev reflection and related studies in low-dimensional superconducting systems, and research on surface and interface superconductivity. Part II covers the materials aspects of small superconductors, including mesoscopic effects in superconductor–ferromagnet hybrids, micromagnetic measurements on electrochemically grown mesoscopic superconductors, and magnetic flux avalanches in superconducting films with mesoscopic artificial patterns. Part III reviews the current progress in the device technology of small superconductors, focusing on superconducting spintronics and devices, barriers in Josephson junctions, hybrid superconducting devices based on quantum wires, superconducting nanodevices, superconducting quantum bits of information, and the use of nanoSQUIDs in the investigation of small magnetic systems.
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19

Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.

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Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.
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