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Register a new userA Classroom Demonstration of Levitation and Suspension of a Superconductor over a Magnetic Track
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Matthew C. Sullivan
Publication date
2008
fields
Physics
and research's language is
English
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The suspension and levitation of superconductors by permanent magnets is one of the most fascinating consequences of superconductivity, and a wonderful instrument for generating interest in low temperature physics and electrodynamics. We present a novel classroom demonstration of the levitation/suspension of a superconductor over a magnetic track that maximizes levitation/suspension time, separation distance between the magnetic track and superconductor and also insulator aesthetics. The demonstration as described is both inexpensive and easy to construct.
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We describe and discuss an experimental set-up which allows undergraduate and graduate students to view and study magnetic levitation on a type-I superconductor. The demonstration can be repeated many times using one readily available 25 liter liquid helium dewar. We study the equilibrium position of a magnet that levitates over a lead bowl immersed in a liquid hand-held helium cryostat. We combine the measurement of the position of the magnet with simple analytical calculations. This provides a vivid visualization of magnetic levitation from the balance between pure flux expulsion and gravitation. The experiment contrasts and illustrates the case of magnetic levitation with high temperature type-II superconductors using liquid nitrogen, where levitation results from partial flux expulsion and vortex physics.
A current-carrying superconducting strip partly penetrated by magnetic flux and surrounded by a bulk magnet of high permeability is considered. Two types of samples are studied: those with critical current controlled by an edge barrier dominating over the pinning, and those with high pinning-mediated critical current masking the edge barrier.It is shown for both cases that the current distribution in a central flux-free part of the strip is strongly affected by the actual shape of the magnetic surroundings. Explicit analytical solutions for the sheet current and self-field distributions are obtained which show that, depending on the geometry, the effect may suppress the total loss-free transport current of the strip or enhance it by orders of magnitude. The effect depends strongly on the shape of the magnet and its distance to the superconductor but only weakly on the magnetic permeability.
The topological state of a two-dimensional triplet superconductor may be changed by an appropriate addition of magnetic impurities. A ferromagnetic magnetic chain at the surface of a superconductor with spin-orbit coupling may eliminate the edge states of a finite system giving rise to localized zero modes at the edges of the chain. The coexistence/competition between the two types of zero modes is considered. The reduction of the system to an effective $1d$ system gives partial information on the topological properties but the study of the two sets of zero modes requires a two-dimensional treatment. Increasing the impurity density from a magnetic chain to magnetic islands leads to a finite Chern number. At half-filling small concentrations are enough to induce chiral modes.
Self-consistent solutions of microscopic Eilenberger theory are presented for a two-dimensional model of a superconducting channel with a geometric constriction. Magnetic fields, external ones as well as those caused by the supercurrents, are included and the relevant equations are solved numerically without further assumptions. Results concerning the influence of temperature, geometric parameters, of $kappa=lambda_L/xi_0$ and of external magnetic fields on the Andreev bound states in the weak link and on the current-phase relation are presented. We find that the Andreev bound states within the junction obtain peculiar substructure when a finite supercurrent flows. As long as the London penetration depth is comparable to or bigger than the extension of the constriction, the Josephson effect is independent of $kappa$. Furthermore, the weak link is very insensitive to external magnetic fields. Features restricted to a self-consistent calculation are discussed.
We study the magnetic and electronic phases of a 1D magnetic adatom chain on a 2D superconductor. In particular, we confirm the existence of a `self-organized 1D topologically non-trivial superconducting phase within the set of subgap Yu-Shiba-Rusinov (YSR) states formed along the magnetic chain. This phase is stabilized by incommensurate spiral correlations within the magnetic chain that arise from the competition between short-range ferromagnetic and long-range antiferromagnetic electron-induced exchange interactions, similar to a recent study for a 3D superconductor [M. Schecter et al. Phys. Rev. B 93, 140503(R) 2016]. The exchange interaction along diagonal directions are also considered and found to display behavior similar to a 1D substrate when close to half filling. We show that the topological phase diagram is robust against local superconducting order parameter suppression and weak substrate spin-orbit coupling. Lastly, we study the effect of a direct ferromagnetic exchange coupling between the adatoms, and find the region of spiral order in the phase diagram to be significantly enlarged in a wide range of the direct exchange coupling.
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