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Register a new userMagnetic-field and current-density distributions in thin-film superconducting rings and disks
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We show how to calculate the magnetic-field and sheet-current distributions for a thin-film superconducting annular ring (inner radius a, outer radius b, and thickness d<<a) when either the penetration depth obeys lambda < d/2 or, if lambda > d/2, the two-dimensional screening length obeys Lambda = 2 lambda^2/d << a for the following cases: (a) magnetic flux trapped in the hole in the absence of an applied magnetic field, (b) zero magnetic flux in the hole when the ring is subjected to an applied magnetic field, and (c) focusing of magnetic flux into the hole when a magnetic field is applied but no net current flows around the ring. We use a similar method to calculate the magnetic-field and sheet-current distributions and magnetization loops for a thin, bulk-pinning-free superconducting disk (radius b) containing a dome of magnetic flux of radius a when flux entry is impeded by a geometrical barrier.
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We have measured the dynamics of individual magnetic fluxoids entering and leaving photolithographically patterned thin film rings of the underdoped high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$, using a variable sample temperature scanning SQUID microscope. These results can be qualitatively described using a model in which the fluxoid number changes by thermally activated nucleation of a Pearl vortex in, and transport of the Pearl vortex across, the ring wall.
The discovery of superconductivity at 39 K in magnesium diboride offers the possibility of a new class of low-cost, high-performance superconducting materials for magnets and electronic applications. With twice the critical temperature of Nb_3Sn and four times that of Nb-Ti alloy, MgB_2 has the potential to reach much higher fields and current densities than either of these technological superconductors. A vital prerequisite, strongly linked current flow, has already been demonstrated even at this early stage. One possible drawback is the observation that the field at which superconductivity is destroyed is modest. Further, the field which limits the range of practical applications, the irreversibility field H*(T), is ~7 T at liquid helium temperature (4.2 K), significantly lower than ~10 T for Nb-Ti and ~20 T for Nb_3Sn. Here we show that MgB_2 thin films can exhibit a much steeper temperature dependence of H*(T) than is observed in bulk materials, yielding H*(4.2 K) above 14 T. In addition, very high critical current densities at 4.2 K, 1 MA/cm_2 at 1 T and 10_5 A/cm_2 at 10 T, are possible. These data demonstrate that MgB_2 has credible potential for high-field superconducting applications.
We have observed spontaneous fluxoid generation in thin-film rings of the amorphous superconductor Mo$_3$Si, cooled through the normal-superconducting transition, as a function of quench rate and externally applied magnetic field, using a variable sample temperature scanning SQUID microscope. Our results can be explained using a model of freezout of thermally activated fluxoids, mediated by the transport of bulk vortices across the ring walls. This mechanism is complementary to a mechanism proposed by Kibble and Zurek, which only relies on causality to produce a freezout of order parameter fluctuations.
A vortex crossing a thin-film superconducting strip from one edge to the other, perpendicular to the bias current, is the dominant mechanism of dissipation for films of thickness d on the order of the coherence length XI; and of width w much narrower than the Pearl length LAMBDA >> w >> XI. At high bias currents, I* < I < Ic, the heat released by the crossing of a single vortex suffices to create a belt-like normal-state region across the strip, resulting in a detectable voltage pulse. Here Ic is the critical current at which the energy barrier vanishes for a single vortex crossing. The belt forms along the vortex path and causes a transition of the entire strip into the normal state. We estimate I* to be roughly Ic/3. Further, we argue that such hot vortex crossings are the origin of dark counts in photon detectors, which operate in the regime of metastable superconductivity at currents between I* and Ic. We estimate the rate of vortex crossings and compare it with recent experimental data for dark counts. For currents below I*, i.e., in the stable superconducting but resistive regime, we estimate the amplitude and duration of voltage pulses induced by a single vortex crossing.
For any practical superconductor the magnitude of the critical current density, $J_textrm{c}$, is crucially important. It sets the upper limit for current in the conductor. Usually $J_textrm{c}$ falls rapidly with increasing external magnetic field but even in zero external field the current flowing in the conductor generates a self-field which limits $J_textrm{c}$. Here we show for thin films of thickness less than the London penetration depth, $lambda$, this limiting $J_textrm{c}$ adopts a universal value for all superconductors - metals, oxides, cuprates, pnictides, borocarbides and heavy Fermions. For type I superconductors, it is $H_{textrm{c}}/lambda$ where $H_textrm{c}$ is the thermodynamic critical field. But surprisingly for type II superconductors we find the self-field $J_textrm{c}$ is $H_{textrm{c}1}/lambda$ where $H_{textrm{c}1}$ is the lower critical field. $J_textrm{c}$ is thus fundamentally determined and this provides a simple means to extract absolute values of $lambda(T)$ and, from its temperature dependence, the symmetry and magnitude of the superconducting gap.
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