Figure 1

A schematic view (left) and a scanning electron micrograph (right) of the sample. Two Cu leads are connected to an Al asymmetric ring through highly resistive small tunnel junctions (shaded areas). An Al drain is directly connected to the widest part of the ring. This structure was fabricated using $e$-beam lithography followed by double-angle evaporation of Al and Cu. After the Al film was deposited, its surface was slightly oxidized to provide a tunnel barrier.Reuse & Permissions

Figure 2

(Color online) Magnetic field dependence of the junction voltage (current of $0.3\mathrm{nA}$ is applied) for the junction at the narrowest part of the ring at (a) $0.9\mathrm{K}$, (b) $1.05\mathrm{K}$, and (c) $1.2\mathrm{K}$, and (d) for the junction at the widest part at $1.2\mathrm{K}$. The origin and the scale of the ordinate are shifted for clarity. The arrows [blue (red) is for sweep up (down)] indicate the sweep direction of the magnetic field. [(c) and (d)] At $1.2\mathrm{K}$, data obtained by sweeping up and down the magnetic field coincide within the accuracy of the measurement. (The error is mainly due to the offset shift of the voltage amplifier.)Reuse & Permissions

Figure 3

(Color online) (a) Fluxoid-state transition fields for several temperatures. Open (blue) and closed (red) squares correspond to transition fields for increasing and decreasing magnetic fields, respectively, and the diamonds (green) to the transitions without hysteresis. The solid (red) and dashed (blue) curves correspond to the theoretical expulsion and penetration fields obtained within the framework of the nonlinear Ginzburg-Landau theory. The best agreement with the experimental data was obtained for a system with dimensions 5% smaller than the experimental sample and for the coherence length ${\xi }_{\mathrm{num}}\left(0\right)=120\mathrm{nm}$. Contour plots of the calculated Cooper-pair density in linear scale are shown for the middle of the (b) first and (d) third continuous transitions. The temperatures are 1.2 and $1.0\mathrm{K}$, respectively. Red (blue) regions correspond to high (low) Cooper-pair density. At the white region, the Cooper-pair density is less than ${10}^{-3}$ of the $B=0$ value. (c) A close-up of the narrow part of the ring in (b) but now in logarithmic scale. The white and blue regions correspond to Cooper-pair densities which are less than ${10}^{-5}$ and ${10}^{-4}$ of the $B=0$ value, respectively.Reuse & Permissions

Figure 4

(Color online) [(a)–(d)] Temperature dependence of the zero-bias junction resistance $R$ normalized by its normal state value $R_n$ for junctions attached to the widest part [closed (red) circle] and the narrowest part [open (blue) square] of the ring for applied magnetic fields of (a) 0, (b) $4.5\mathrm{mT}$, (c) $13.4\mathrm{mT}$, and (d) $20.0\mathrm{mT}$. The magnetic field values for (b)–(d) are close to those of the fluxoid-state transitions without hysteresis. The resistance was obtained from a linear fit of the $I\text{−}V$ curve at $\mid V\mid <50\mu \mathrm{V}$. In (a), the theoretical $R∕R_n$ ratio [Eq. (15)] is also shown (solid curve). (e) Temperature where the resistance ratio $R∕R_n$ reaches 1.05 is plotted as a function of the applied magnetic field.Reuse & Permissions

Figure 5

(Color online) The calculated average of the order parameter over the junction area for the magnetic field of the first continuous transition. The junctions are placed at the center of the narrowest part of the ring and at a distance of $0.09\mu \mathrm{m}$ from the outer boundary of the widest part. Squares indicate the results for infinitesimal junction area, and circles for the junction area of $0.1\times 0.1\mu {\mathrm{m}}^2$. The insets show the Cooper-pair density at $1.2\mathrm{K}$. The hatched squares in the left inset and the dots in the right inset indicate the junctions.Reuse & Permissions