Vortex frequency locking and Shapiro steps in superconductor open nanotubes

The movement of magnetic flux quanta (Abrikosov vortices) in superconductors leads to dissipation and is influenced by various ordering effects arising from vortex-vortex, vortex-defect, and vortex-edge interactions. Under combined dc and ac stimuli, when the distance traveled by fluxons during an ac cycle corresponds to an integer multiple of the vortex lattice period, the superconductor's current-voltage (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>I</a:mi><a:mtext>−</a:mtext><a:mi>V</a:mi></a:mrow></a:math>) curve displays synchronization (Shapiro) steps. However, in planar constrictions, frequency-locking effects rely on a perfectly ordered vortex lattice and are typically observed when periodic vortex pinning arrays dominate over intrinsic uncorrelated disorder. Here, we propose 3D superconducting open nanotubes as systems free of periodic disorder, where the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>I</b:mi><b:mtext>−</b:mtext><b:mi>V</b:mi></b:mrow></b:math> curves are expected to display pronounced Shapiro steps. Using the time-dependent Ginzburg-Landau equation, we attribute the predicted effect to a reduction in the dimensionality of vortex motion. Namely, rolling a planar film into a tube causes the 2D vortex array, which initially moves throughout the film, to evolve into quasi-1D vortex chains that are restricted to areas where the normal component of the magnetic field is near its maximum. The discussed effects are relevant for superconducting devices, where vortex nucleation frequency and voltage stabilization by an external ac stimulus can enhance their operation.