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Register a new userEffect of nearby Pearl vortices upon the $I_c$ vs $B$ characteristics of planar Josephson junctions in thin and narrow superconducting strips
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John R. Clem
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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.
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We study the field dependence of the maximum supercurrent in narrow edge-type thin-film Josephson junctions. It is assumed that the junction extends across thin-film strip of width W that is much less than the Pearl length; the film thickness is much less than the London penetration depth. We calculate the maximum supercurrent within nonlocal Josephson electrodynamics, which takes into account the stray fields affecting tunneling currents. In the case when W is much less than the thin-film Josephson length, the phase difference along the junction depends only on the junction geometry and the applied field, but is independent of the Josephson critical current density, i.e., it is universal. Zeros of the maximum supercurrent are equidistant only in large fields (unlike the case of junctions with bulk banks); they are spaced by a field that is much smaller than the one of bulk junctions. Peaks of the maximum supercurrent decrease inversely proportional to the square root of the applied field, i.e., slower than 1/H for the bulk.
The phase difference between the banks of an edge-type planar Josephson junction crossing the narrow thin-film strip depends on wether or not vortices are present in the junction banks. For a vortex close to the junction this effect has been seen by Golod, Rydh, and Krasnov, prl {bf 104}, 227003 (2010), who showed that the vortex may turn the junction into $pi$-type. It is shown here that even if the vortex is far away from the junction, it still changes the 0-junction to $pi$-junction when situated close to the strip edges. Within the approximation used, the latter effect is independent of the vortex-junction separation, a manifestation of topology of the vortex phase which extends to macroscopic distances of superconducting coherence.
Josephson junctions based on three-dimensional topological insulators offer intriguing possibilities to realize unconventional $p$-wave pairing and Majorana modes. Here, we provide a detailed study of the effect of a uniform magnetization in the normal region: We show how the interplay between the spin-momentum locking of the topological insulator and an in-plane magnetization parallel to the direction of phase bias leads to an asymmetry of the Andreev spectrum with respect to transverse momenta. If sufficiently large, this asymmetry induces a transition from a regime of gapless, counterpropagating Majorana modes to a regime with unprotected modes that are unidirectional at small transverse momenta. Intriguingly, the magnetization-induced asymmetry of the Andreev spectrum also gives rise to a Josephson Hall effect, that is, the appearance of a transverse Josephson current. The amplitude and current phase relation of the Josephson Hall current are studied in detail. In particular, we show how magnetic control and gating of the normal region can enable sizable Josephson Hall currents compared to the longitudinal Josephson current. Finally, we also propose in-plane magnetic fields as an alternative to the magnetization in the normal region and discuss how the planar Josephson Hall effect could be observed in experiments.
It is shown that a vortex trapped in one of the banks of a planar edge-type Josephson junction in a narrow thin-film superconducting strip can change drastically the field dependence of the junction critical current $I_c(H)$. When the vortex is trapped at certain positions in the strip middle, the pattern $I_c(H)$ has zero at $H=0$ instead of the traditional maximum of 0-type junctions. The number of these positions is equal to the number of vortices trapped at the same location. When the junction-vortex separation exceeds approximately $2W$, $I_c(H)$ is no longer sensitive to the vortex presence.
We have made current-voltage (IV) measurements of artificially layered high-$T_c$ thin-film bridges. Scanning SQUID microscopy of these films provides values for the Pearl lengths $Lambda$ that exceed the bridge width, and shows that the current distributions are uniform across the bridges. At high temperatures and high currents the voltages follow the power law $V propto I^n$, with $n=Phi_0^2/8pi^2Lambda k_B T+1$, and at high temperatures and low-currents the resistance is exponential in temperature, in good agreement with the predictions for thermally activated vortex motion. At low temperatures, the IVs are better fit by $ln V$ linear in $I^{-2}$. This is expected if the low temperature dissipation is dominated by quantum tunneling of Pearl vortices.
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