Large energy dissipation due to vortex dynamics in mesoscopic Al disks

We present systematic resistance measurements of mesoscopic Al disk samples with three different sizes and compare them with those of an Al-wire sample. When a magnetic field is applied perpendicular to the disks, a large excess resistance, which is approximately six times larger than the normal-state resistance $\left(R_{\text{n}}\right)$, appears near the critical field of the Al leads connected to the disks. In the low-field region of the large excess resistance, successive resistant peaks are observed. These peaks are ascribed to the transitions of the vortex states in the disk. Remarkably, some of the resistance peaks are significantly larger than $R_{\text{n}}$, indicating that the Al disks are superconducting in the excess resistance state. Such behavior has never been observed in the case of a wire sample. These results suggest that the vortices in the mesoscopic disks cause anomalously large energy dissipation when they are driven by the sample current. The superconducting current leads connected to the disks also play a crucial role in the occurrence of the large excess resistance.

Figure 1

(Color online) Magnetic field dependence of resistance at various temperatures for three sizes of Al disks with (a) 1.0, (b) 0.7, and (c) $0.4\mu \text{m}$ in diameter, and (d) for an Al wire with $0.4\mu \text{m}$ in length, respectively. The dashed lines indicate the position of the small resistance peaks, where the vorticity $L$ transits as $L\to L+1$ $\left(L=0,1,2,\dots \right)$. The insets show the SEM images of the samples.

Figure 2

(Color online) (a) Schematic plot of the free energy with vorticity $L$ vs the magnetic field. Each curve corresponds to the free energy for each $L$. (b) Normalized field interval between the $L\text{th}$ and the $\left(L+1\right)\text{th}$ peaks, $\Delta H_{\text{L}}S/{\Phi }_0$ as a function of $L$. (c) $R$ vs $H$ plot at various temperatures in a low-field region for the Al disk with $0.7\mu \text{m}$ in diameter. Some of the successive resistance peaks are larger than $R_{\text{n}}$.

Figure 3

(Color online) Magnetic field dependence of $T_{\text{onset}}$ (open symbols) and $T_{\text{zero}}$ (solid symbols) for the Al disks with 1.0 (circles), 0.7 (triangles), and $0.4\mu \text{m}$ (squares) in diameter, and $T_{\text{c}}$ for the Al wire with $0.4\mu \text{m}$ (solid diamonds) in length. The solid curve is calculated by the formula $H=\sqrt{3}{\Phi }_0/\pi w\xi \left(T\right)$ with $w=0.1\mu \text{m}$, ${\xi }_{\text{GL}}=0.13\mu \text{m}$, and $T_{\text{c}}=1.28\text{K}$.

Figure 4

(Color online) (a) Temperature dependence of resistance at $H=0$ and 283 Oe for the Al disk with $0.7\mu \text{m}$ in diameter. $T_{\text{onset}}$, $T_{\text{zero}}$, and $T_{\text{peak}}$ are defined at $H\ne 0$, as indicated by the arrows. (b) Resistance contour plots for $R=R_{\text{n}}$, $1.5\times R_{\text{n}}$, $2\times R_{\text{n}}$, and $3\times R_{\text{n}}$ along with $T_{\text{peak}}$, $T_{\text{onset}}$, and $T_{\text{zero}}$. The transitions of the vorticity $L$ are also indicated by dotted lines.

Figure 5

(Color online) Magnetic field dependence of the resistance with various ac at $T=1.23\text{K}$ for (a) the disk with $0.7\mu \text{m}$ in diameter and (b) the Al wire with $0.4\mu \text{m}$ in length.

Figure 6

(Color online) $R_{\text{peak}}/R_{\text{n}}$ vs $HS/{\Phi }_0$ for the three sizes of the Al disks. The vorticity transition lines are indicated by solid lines for all samples.