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 sup
erconducting 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.
The geometric, kinetic, and total inductances and the attenuation constant are theoretically analyzed for a thin-film superconducting coplanar waveguide (CPW) resonator consisting of a current-carrying central conductor, adjacent slots, and ground pl
anes that return the current. The analysis focuses on films of thickness $d$ obeying $d < 2lambda$ ($lambda$ is the London penetration depth), for which the material properties are characterized by the two-dimensional screening length $Lambda = 2 lambda^2/d$. Introducing a cut-off procedure that guarantees that the magnitudes of the currents in the central conductor and the ground planes are equal, new and simpler results are obtained for the kinetic inductance and the attenuation constant for small $Lambda$. Exact results for arbitrary $Lambda$ are presented for the geometric, kinetic, and total inductances in the limit of tiny slot widths, and approximate results are presented for arbitrary slot widths.
We use both Eilenberger-Usadel and Ginzburg-Landau (GL) theory to calculate the superfluids temperature-dependent kinetic inductance for all currents up to the depairing current in thin and narrow superconducting films. The calculations apply to BCS
weak-coupling superconductors with isotropic gaps and transport mean-free paths much less than the BCS coherence length. The kinetic inductance is calculated for the response to a small alternating current when the film is carrying a dc bias current. In the slow-experiment/fast-relaxation limit, in which the superconducting order parameter quasistatically follows the time-dependent current, the kinetic inductance diverges as the bias current approaches the depairing value. However, in the fast-experiment/slow-relaxiation limit, in which the the superconducting order parameter remains fixed at a value corresponding to the dc bias current, the kinetic inductance rises to a finite value at the depairing current. We then use time-dependent GL theory to calculate the kinetic impedance of the superfluid, which includes not only the kinetic reactance but also the kinetic resistance of the superfluid arising from dissipation due to order-parameter relaxation. The kinetic resistance is largest for angular frequencies $omega$ obeying $omega tau_s > 1$, where $tau_s$ is the order-parameter relaxation time, and for bias currents close to the depairing current. We also include the normal fluids contribution to dissipation in deriving an expression for the total kinetic impedance. The Appendices contain many details about the temperature-dependent behavior of superconductors carrying current up to the depairing value.
The critical current of a thin superconducting strip of width $W$ much larger than the Ginzburg-Landau coherence length $xi$ but much smaller than the Pearl length $Lambda = 2 lambda^2/d$ is maximized when the strip is straight with defect-free edges
. When a perpendicular magnetic field is applied to a long straight strip, the critical current initially decreases linearly with $H$ but then decreases more slowly with $H$ when vortices or antivortices are forced into the strip. However, in a superconducting strip containing sharp 90-degree or 180-degree turns, the zero-field critical current at H=0 is reduced because vortices or antivortices are preferentially nucleated at the inner corners of the turns, where current crowding occurs. Using both analytic London-model calculations and time-dependent Ginzburg-Landau simulations, we predict that in such asymmetric strips the resulting critical current can be {it increased} by applying a perpendicular magnetic field that induces a current-density contribution opposing the applied current density at the inner corners. This effect should apply to all turns that bend in the same direction.
In this paper we calculate the critical currents in thin superconducting strips with sharp right-angle turns, 180-degree turnarounds, and more complicated geometries, where all the line widths are much smaller than the Pearl length $Lambda = 2 lambda
^2/d$. We define the critical current as the current that reduces the Gibbs free-energy barrier to zero. We show that current crowding, which occurs whenever the current rounds a sharp turn, tends to reduce the critical current, but we also show that when the radius of curvature is less than the coherence length this effect is partially compensated by a radius-of-curvature effect. We propose several patterns with rounded corners to avoid critical-current reduction due to current crowding. These results are relevant to superconducting nanowire single-photon detectors, where they suggest a means of improving the bias conditions and reducing dark counts. These results also have relevance to normal-metal nanocircuits, as these patterns can reduce the electrical resistance, electromigration, and hot spots caused by nonuniform heating.
In this paper I show how to calculate the effect of a nearby Pearl vortex or antivortex upon the critical current $I_c(B)$ when a perpendicular magnetic induction $B$ is applied to a planar Josephson junction in a long, thin superconducting strip of
width $W$ much less than the Pearl length $Lambda = 2lambda^2/d$, where $lambda$ is the London penetration depth and $d$ is the thickness ($d < lambda$). The theoretical results provide a qualitative explanation of unusual features recently observed experimentally by Golod {it et al.}cite{Golod10} in a device with a similar geometry.
We discuss predictions of five proposed theories for the critical state of type-II superconductors accounting for both flux cutting and flux transport (depinning). The theories predict different behaviours for the ratio $E_y/E_z$ of the transverse an
d parallel components of the in-plane electric field produced just above the critical current of a type-II superconducting slab as a function of the angle of an in-plane applied magnetic field. We present experimental results measured using an epitaxially grown YBCO thin film favoring one of the five theories: the extended elliptic critical-state model. We conclude that when the current density $bm J$ is neither parallel nor perpendicular to the local magnetic flux density $bm B$, both flux cutting and flux transport occur simultaneously when $J$ exceeds the critical current density $J_c$, indicating an intimate relationship between flux cutting and depinning. We also conclude that the dynamical properties of the superconductor when $J$ exceeds $J_c$ depend in detail upon two nonlinear effective resistivities for flux cutting ($rho_c$) and flux flow ($rho_f$) and their ratio $r= rho_c/rho_f$.
I introduce a critical-state theory incorporating both flux cutting and flux transport to calculate the magnetic-field and current-density distributions inside a type-II superconducting cylinder at its critical current in a longitudinal applied magne
tic field. The theory is an extension of the elliptic critical-state model introduced by Romero-Salazar and Perez-Rodriguez. The vortex dynamics depend in detail upon two nonlinear effective resistivities for flux cutting (rho_parallel) and flux flow (rho_perp), and their ratio r = rho_parallel/rho_perp. When r < 1, the low relative efficiency of flux cutting in reducing the magnitude of the internal magnetic-flux density leads to a paramagnetic longitudinal magnetic moment. As a model for understanding the experimentally observed interrelationship between the critical currents for flux cutting and depinning, I calculate the forces on a helical vortex arc stretched between two pinning centers when the vortex is subjected to a current density of arbitrary angle phi. Simultaneous initiation of flux cutting and flux transport occurs at the critical current density J_c(phi) that makes the vortex arc unstable.
I consider a Corbino-geometry SNS (superconducting-normal-superconducting) Josephson weak link in a thin superconducting film, in which current enters at the origin, flows outward, passes through an annular Josephson weak link, and leaves radially. I
n contrast to sandwich-type annular Josephson junctions, in which the gauge-invariant phase difference obeys the sine-Gordon equation, here the gauge-invariant phase difference obeys an integral equation. I present exact solutions for the gauge-invariant phase difference across the weak link when it contains an integral number N of Josephson vortices and the current is zero. I then study the dynamics when a current is applied, and I derive the effective resistance and the viscous drag coefficient; I compare these results with those in sandwich-type junctions. I also calculate the critical current when there is no Josephson vortex in the weak link but there is a Pearl vortex nearby.
We theoretically investigate the response of a superconducting film to line currents flowing in linear wires placed above the film, and we present analytic expressions for the magnetic-field and current distributions based on the critical state model
. The behavior of the superconducting film is characterized by the sheet-current density $K_z$, whose magnitude cannot exceed the critical value $j_cd$, where $j_c$ is the critical current density and $d$ is the thickness of the film. When the transport current $I_0$ flowing in the wire is small enough, $|K_z|$ is smaller than $j_cd$ and the magnetic field is shielded below the film. When $I_0$ exceeds a threshold value $I_{c0}propto j_cd$, on the other hand, $|K_z|$ reaches $j_cd$ and the magnetic field penetrates below the film. We also calculate the ac response of the film when an ac transport current flows in the linear wires.
