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Register a new userEquilibrium intermediate-state patterns in a type-I superconducting slab in an arbitrarily oriented applied magnetic field
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The equilibrium topology of superconducting and normal domains in flat type-I superconductors is investigated. Important improvements with respect to previous work are: (1) the energy of the external magnetic field, as deformed by the presence of superconducting domains, is calculated in the same way for three different topologies, and (2) calculations are made for arbitrary orientation of the applied field. A phase diagram is presented for the minimum-energy topology as a function of applied field magnitude and angle. For small (large) applied fields normal (superconducting) tubes are found, while for intermediate fields parallel domains have a lower energy. The range of field magnitudes for which the superconducting-tubes structure is favored shrinks when the field is more in-plane oriented.
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To address unsolved fundamental problems of the intermediate state (IS), the equilibrium magnetic flux structure and the critical field in a high purity type-I superconductor (indium film) are investigated using magneto-optical imaging with a 3D vector magnet and electrical transport measurements. The least expected observation is that the critical field in the IS can be as small as nearly 40% of the thermodynamic critical field $H_c$. This indicates that the flux density in the textit{bulk} of normal domains can be textit{considerably} less than $H_c$, in apparent contradiction with the long established paradigm, stating that the normal phase is unstable below $H_c$. Here we present a novel theoretical model consistently describing this and textit{all} other properties of the IS. Moreover, our model, based the rigorous thermodynamic treatment of observed laminar flux structure in a tilted field, allows for a textit{quantitative} determination of the domain-wall parameter and the coherence length, and provides new insight into the properties of all superconductors.
Normal state bubble patterns in Type I superconducting Indium and Lead slabs are studied by the high resolution magneto-optical imaging technique. The size of bubbles is found to be almost independent of the long-range interaction between the normal state domains. Under bubble diameter and slab thickness proper scaling, the results gather onto a single master curve. On this basis, in the framework of the current-loop model [R.E. Goldstein, D.P. Jackson and A.T. Dorsey, Phys. Rev. Lett. 76, 3818 (1996)], we calculate the equilibrium diameter of an isolated bubble resulting from the competition between the Biot-and-Savart interaction of the Meissner current encircling the bubble and the superconductor-normal interface energy. A good quantitative agreement with the master curve is found over two decades of the magnetic Bond number. The isolation of each bubble in the superconducting matrix and the existence of a positive interface energy are shown to preclude any continuous size variation of the bubbles after their formation, contrary to the prediction of mean-field models.
Magnetometry measurements in high quality LiFeAs single-crystals reveal a change in the sign of the magnetic hysteresis in the vicinity of the upper critical field $H_{c2}$, from a clear diamagnetic response dominated by the pinning of vortices, to a considerably smaller net hysteretic response of opposite sign, which emph{disappears} at $H_{c2}$. If the diamagnetic response at high fields results from pinned vortices and associated screening super-currents, this sign change must result from currents circulating in the opposite sense, which give rise to a small field-dependent magnetic moment emph{below} $H_{c2}$. This behavior seems to be extremely sensitive to the sample quality or stoichiometry, as we have observed it only in a few fresh crystals, which also display the de Haas van Alphen-effect. We provide arguments against the surface superconductivity, the flux compression, and the random $pi$ junction scenarios, which have been previously put forward to explain a paramagnetic Meissner effect, below the lower critical field $H_{c1}$. The observed anomalous hysteresis at high fields will be compatible with the existence of chiral gap wave-functions, which possess a field dependent magnetic moment. Within a Landau-Ginzburg framework, we demonstrate how a $(d_{x^2 - y^2} + id_{xy})$ or a $(p_x+ip_y)$ chiral superconducting component can be stabilized in the mixed state of $s_{pm}$ superconductor, due to the combined effects of the magnetic field and the presence of competing pairing channels. The realization of a particular chiral pairing depends on the microscopic details of the strengths of the competing pairing channels.
The importance of accounting for the inhomogeneity of the magnetic field distribution and roundness of domain walls near the surface of type-I superconductors in the intermediate state for forming the equilibrium flux structure was predicted by Landau eight decades ago. Further studies confirmed this prediction and extended it to all equilibrium properties of this state. Here we report on direct depth-resolved measurements of the field distribution and shape of domains near the surface of high-purity type-I (indium) films in a perpendicular field using Low-Energy Muon Spin Rotation spectroscopy. We find that at low applied fields (in about half of the field range of the intermediate state) the field distribution and domains shape agrees with that proposed by Tinkham. However, for high fields our data suggest that reality differs from theoretical expectations. In particular, the width of the superconducting laminae can expand near the surface leading to formation of a maximum in the static magnetic field in the current-free space outside the sample. A possible interpretation of these experimental results is discussed.
Dissipative-free electric current flow is one of the most fascinating and practically important property of superconductors. Theoretical consideration of the charge carriers flow in infinitely long rectangular slab of superconductor in the absence of external magnetic field (so called, self-field) is based on an assumption that the charge carriers have rectilinear trajectories in the direction of the current flow whereas the current density and magnetic flux density are decaying towards superconducting slab with London penetration depth as characteristic length. Here, we calculate charge particle trajectories (as single electron/hole, as Cooper pair) at self-field conditions and find that charge carriers do not follow intuitive rectilinear trajectories along the slab surface, but instead ones have meander shape trajectories which cross the whole thickness of the slab. Moreover, if the particle velocity is below some value, the charge moves in opposite direction to nominal current flow. This disturbance of the canonical magnetic flux density distribution and backward movement of Cooper pairs can be entire mechanism for power dissipation in superconductors.
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