Flow of a Single Magnetic Vortex in a Submicron-Size Superconducting Al Disk Controlled by Radio-Frequency Currents

We report the first observation of a single-vortex flow in a mesoscopic superconductor. A flow of a single vortex is successfully controlled by an rf current superimposed on a dc current, evidence of which is provided by voltage steps in current-voltage ($I\mathrm{\text{−}}V$) characteristics. Irrespective of the number of vortices confined to the disk, we unambiguously observe that when a single vortex inside the disk is driven out of the disk, another vortex enters the disk similarly to two balls colliding in billiards: only one vortex passes through the Al disk at the same time in mesoscopic systems.

Figure 1

(a) Contour plot of the resistance measured with a low-frequency ac current ($I_{\mathrm{ac}}=50\mathrm{nA}$) for a mesoscopic Al disk of $0.7\mu \mathrm{m}$ diameter. The dashed lines indicate the vorticity ($L$) transitions in the $R=0$ region. The inset shows an SEM image of the sample. (b)–(d) $I\mathrm{\text{−}}V$ characteristics of the disk in the absence of an rf current under various magnetic fields at $T=0.8\mathrm{K}$. The solid lines indicate the linear dependence $V=R_{n}I$, where $R_n$ is the normal-state resistance.

Figure 2

(a) $I\mathrm{\text{−}}V$ characteristics of an Al disk with and without a superimposed rf current ($I_{\mathrm{rf}}$) of $f=420\mathrm{MHz}$ for $L=1$. The superimposition of $I_{\mathrm{rf}}$ on the dc current ($I_{\mathrm{dc}}$) induces equidistant voltage steps ($V_n$). The inset shows $dI/dV$ vs $V$ with the superimposed $I_{\mathrm{rf}}$. The dashed lines indicate $V_n=n{\varphi }_{0}f$ for $f=420\mathrm{MHz}$. (b) $I\mathrm{\text{−}}V$ characteristics of the Al disk with superimposed $I_{\mathrm{rf}}$ of $f=340$ and 820 MHz. (c) Frequency ($f$) dependence of $V_n$ ($n=1$, 2, 3, 4) for $L=1$. The solid lines show $V_n=n{\varphi }_{0}f$. (d) Schematic diagram of a single vortex in a mesoscopic Al disk at $I_{\mathrm{dc}}$, $I_{\mathrm{rf}}=0$ (left) and $I_{\mathrm{dc}}$, $I_{\mathrm{rf}}\ne 0$ (right). The number of times ($n$) that the vortex passes through the disk within the period $1/f$ is controlled by the rf current. The voltage steps appear when the flow rate is locked by the rf current.

Figure 3

(a) $I\mathrm{\text{−}}V$ characteristics with various rf powers ($P$) for $f=420\mathrm{MHz}$ when $L=1$. The dashed lines and the dot-dashed line indicate the voltage steps and $V=R_{n}I$, respectively. (b) $I_{\mathrm{rf}}$ dependence of $\Delta I_n$ ($n=0$, 1, 2, 3, 4). The values of $I_{\mathrm{rf}}$ are obtained from $I_{\mathrm{rf}}\propto \sqrt{P}$, and $\Delta I_n$ is determined in the voltage range of $\Delta V=\pm 0.05\mu \mathrm{V}$ at each voltage step (inset). The solid lines are the theoretical curves calculated using $\Delta I_n=\alpha |{\mathcal{J}}_n(\beta I_{\mathrm{rf}})|$, where $\alpha =0.45\mu \mathrm{A}$ and $\beta =21$.

Figure 4

(a) $I\mathrm{\text{−}}V$ characteristics of the Al disk with and without the superimposed $f=420\mathrm{MHz}$ $I_{\mathrm{rf}}$ for $L=1$, 2, 3, and 4. Irrespective of the value of $L$ in the Al disk, voltage plateaus appear at $n{\varphi }_{0}f$ (dashed lines). (b) Illustration of vortex billiards for the $L=4$ state. The detailed configuration of the three vortices inside the disk cannot be specified.