Phase slips in submicrometer $\mathrm{Y}\mathrm{Ba}{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ bridges

We have measured the resistance vs temperature, $R\left(T\right)$, and current vs voltage, $I\left(V\right)$, for a series of submicrometer $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ tracks. We find that superconductivity is suppressed when the room temperature resistance is greater than the superconducting resistance quantum, $R_q=h∕4e^2$. In addition, we observe regular steps in the $I\left(V\right)$ characteristics of some bridges, which we associate with phase slip centers. For one bridge, with resistance just below the resistance quantum, $R_q$, we find a gradual entry into the superconducting state which is well fit by theoretical predictions for thermally activated phase slips in a superconducting wire.

Figure 1

Scanning electron microscope image of a submicrometer bridge produced by focused ion beam lithography. The central light region is the YBCO bridge. Two successive milling processes have reduced the bridge width to $500\mathrm{nm}$.

Figure 2

Temperature dependence of the resistance of five YBCO bridges. The dashed line is the quantum of resistance $R_q=h∕4e^2\approx 6.45\mathrm{k}\Omega$. The bridge widths are (1) $50\mathrm{nm}$, (2) $100\mathrm{nm}$, (3) $500\mathrm{nm}$, (4) $100\mathrm{nm}$, (5) $3\mu \mathrm{m}$. Bridge $4a$ is bridge 4 after thermal cycling (see text). Bridges 1–4 have thickness $150\mathrm{nm}$, while bridge 5 has thickness $300\mathrm{nm}$.

Figure 3

Current-voltage characteristics of the $100\mathrm{nm}$ wide bridge 4 at temperatures: (1) $84.4\mathrm{K}$, (2) $82.7\mathrm{K}$, (3) $80.9\mathrm{K}$, (4) $79\mathrm{K}$. The voltage steps represent the nucleation of successive phase slip centers. Each step is associated with an increase in the differential resistance, as expected for an extra phase slip center, although these increments are not identical. Hysteresis at the highest temperature is negligible, but increases as the temperature is reduced. The approximately linear regions between the voltage steps are nonhysteretic, until the current is increased beyond some critical point, as shown for curve 4. Note that the negative slope of parts of the characteristics are due to the finite source resistance of our current supply.

Figure 4

Resistance vs temperature for the $500\text{−}\mathrm{nm}$-wide bridge 3. The open circles are the experimental data. The solid line is a fit to the LAMH theory for thermally activated phase slips as given in Eq. (2).