Probing Confined Vortices with a Superconducting Nanobridge

M. Foltyn, K. Norowski, M.J. Wyszyński, A.S. de Arruda, M.V. Milošević, and M. Zgirski

Phys. Rev. Applied 19, 044073 – Published 24 April 2023

Abstract

We realize a superconducting nanodevice in which vortex traps in the form of an aluminum square are integrated with a Dayem nanobridge. We perform field cooling of the traps arriving to different vortex configurations, dependent on the applied magnetic field, to demonstrate that the switching current of the bridge is highly sensitive to the presence and location of vortices in the trap. Our measurements exhibit unprecedented precision and ability to detect the first and successive vortex entries into all fabricated traps, from few hundred nm to $2 μ m$ in size. The experimental results are corroborated by Ginzburg-Landau simulations, which reveal the subtle yet crucial changes in the density of the superconducting condensate in the vicinity of the bridge with every additional vortex entry and relocation inside the trap. An ease of integration and simplicity make our design a convenient platform for studying dynamics of vortices in strongly confining geometries, involving a promise to manipulate vortex states electronically with simultaneous in situ control and monitoring.

Received 25 November 2022
Revised 27 February 2023
Accepted 28 February 2023

DOI:https://doi.org/10.1103/PhysRevApplied.19.044073

Physics Subject Headings (PhySH)

Critical current Metrology Vortices in superconductors

Devices for digital logic, storage & processing Low-temperature superconductors Nanostructures Solid-state detectors Weak links

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Foltyn^1,*, K. Norowski¹, M.J. Wyszyński ², A.S. de Arruda³, M.V. Milošević^2,3,†, and M. Zgirski ^1,‡

¹Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, Warsaw PL 02668, Poland
²Department of Physics & NANOlab Center of Excellence, University of Antwerp, Groenenborgerlaan 171, Antwerp B-2020, Belgium
³Instituto de Física, Universidade Federal de Mato Grosso, Cuiabá, Mato Grosso 78060-900, Brazil

^*foltyn@ifpan.edu.pl
^†milorad.milosevic@uantwerpen.be
^‡zgirski@ifpan.edu.pl

Article Text (Subscription Required)

Click to Expand

Multimedia (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 19, Iss. 4 — April 2023

Subject Areas

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Sample layout and measurement protocol. (a) The sample consists of the square vortex traps connected via a short Dayem nanobridge. The traps are connected to the contact pads through approximately 100- $μ m$ -long and 300-nm-wide leads. Electric signal is applied to one of the contact pads, while the other pad is grounded. Insets show SEM images of the typical aluminum structures of the single and double vortex traps. (b) We send a train of $N$ pulses to the nanobridge in order to determine its switching probability $P$ . For a certain current amplitude of the testing pulses ( $I_{0.5}$ ) the nanobridge switches to the normal state around $N / 2$ times. (c) In each cycle we send an additional pulse before every testing of the nanobridge, which acts as a “reset.” The annealing pulse always switches the nanobridge to the normal state and overheats the vortex trap above $T_{c}$ . In our experiment the real probing pulse is more complex and consists of a short part of higher amplitude intended to test the junction (so-called testing pulse), and much longer, typically $5 μ s$ long, sustain part, enabling the readout of the state of the bridge with a low-pass-filtered line.
Reuse & Permissions
Figure 2
Normalized nanobridge switching currents versus the perpendicular magnetic field $B_{⊥}$ for a series of vortex traps (samples $A$ – $D$ , sizes indicated in the panels) and reference nanostripes (samples $E$ and $F$ ), measured at bath temperature $T_{0} = 400 mK$ . Up to the first vortex entry $I_{sw}$ decreases monotonously with magnetic field (Meissner state) and changes abruptly at $B_{0}$ . Samples $A$ and $B$ , in double and single trap configuration, respectively, both with the side of the trap $W = 860 nm$ , exhibit the same threshold magnetic field values for successive vortex entries into the trap (marked with vertical dashed lines in the top-left panel) although $I_{sw}$ decreases faster with the field for the sample with a double vortex trap. Nanostripes $E$ and $F$ lack the two-dimensional confining effect on vortices, and above $B_{0}$ exhibit irregular, but fully reproducible pattern of $I_{sw} (B_{⊥})$ .
Reuse & Permissions
Figure 3
Vortex penetration field $B_{0}$ for different considered vortex boxes and stripes. Experimental data (full symbols) for single, double boxes, and nanowires, extracted from Fig. 2, as well as the simulated data points (hollow symbols), follow the analytical expression for metastable equilibrium of the vortex in the superconducting strip [Eq. (3)], up to a multiplying constant $β = 2.45$ for traps, and $β = 1.7$ for stripes. For visual comparison, the dashed line shows the values of $B_{0}$ for $β = 1$ .
Reuse & Permissions
Figure 4
Normalized critical current of sample $A$ , calculated by TDGL simulations (red points). Solid line shows experimental data. Each simulated point is calculated independently for the fixed value of the applied magnetic field. It is obtained as a result of successive equilibrations at step-increasing values of the applied current. The switching current is defined as the one corresponding to the onset of the phase-slip process in the bridge or, at higher fields, in the leads. The color bars denote the total number of trapped vortices $n_{v} (B_{⊥})$ at the given applied magnetic field. This number is stochastic: it is possible to obtain a different number of trapped vortices when repeating the simulation starting from randomized initial conditions (simulating nucleation from the quasinormal state). The trapping stochasticity is at the root of not sharp transitions between vortex configurations, i.e., reentrant behavior is observed whenever we see a decrease in $v (B_{⊥})$ although $B_{⊥}$ is increased. The stochasticity may explain occasional rounding of the experimental curves since they result from measurements performed over $N = 1000$ realizations for each field. Noteworthy, the simulated points are grouped according to own vortex number. Those families are marked with broken lines in the plot to provide a convenient guide for an eye. For some magnetic field values, simulation predicts expulsion and entry of the vortex during testing pulse before the switching current of the nanobridge is reached (visible as a two-color bar, where the change of color marks the current for which vortex is expelled or has entered). At a field of approximately $27 mT$ vortices start to enter into leads giving rise to an irregular pattern of $I_{SW} (B_{⊥})$ (cf. Fig. 5).
Reuse & Permissions
Figure 5
$I_{SW} (B_{⊥})$ characteristics of sample $E$ , calculated using TDGL simulations (red dots) in comparison with experimental data (blue line). The bars show the range of fields and currents for which the vortex row exists in the nanowire. At the onset of the vortex entry, the row is unstable at higher applied currents and it is expelled from the sample (such an event is marked as the termination of the bar before the switching current is reached). The inset shows the comparison of the simulation presented in the main panel to the simulated critical current of the nanostripe of the same size, but without any nanobridge. Noteworthy, in the latter case, the $I_{sw}$ shows nonmonotonous behavior attributed to the changes in the edge currents and the order parameter after vortex row enters into the stripe.
Reuse & Permissions
Figure 6
Switching current versus the perpendicular magnetic field $B_{⊥}$ (sample $A$ ) for the nanobridge connecting two vortex traps, both with side of $W = 860 nm$ (see inset), measured at bath temperature $T_{0} = 400 mK$ , with enlarged transitions to the next vorticity level.
Reuse & Permissions

Physical Review Applied