Vortex-slip transitions in superconducting $a\text{−}\mathrm{NbGe}$ mesoscopic channels

Intriguing and novel physical aspects related to the vortex flow dynamics have been recently observed in mesoscopic channel devices of $a\text{−}\mathrm{NbGe}$ with $\mathrm{NbN}$ channel edges. In this work we have systematically studied the flow properties of vortices confined in such mesoscopic channels as a function of the magnetic field history, using dc-transport and mode-locking (ML) measurements. As opposed to the field-down situation, in the field-up case a kink anomaly in the dc $I\text{−}V$ curves is detected. The mode-locking measurements reveal that this anomaly is, in fact, a flow induced vortex slip transition: by increasing the external drive (either dc or ac) a sudden change occurs from $n$ to $n+2$ moving vortex rows in the channel. The observed features can be explained in terms of an interplay between field focusing due to screening currents and a change in the predominant pinning mechanism.

Figure 1

Comparison between the critical current $I_c$ measured in FU and FD at $1.9\mathrm{K}$. Both data show commensurate-incommensurate oscillations but below $0.5\mathrm{T}$ they behave differently. The insets show schematic drawings of the channel sample: cross-section perpendicular to channels and top-view indicating the vortex structure in the channels and channel edges. The drawings are not on scale. The arrows show the direction of the applied current.

Figure 2

dc $I\text{−}V$ curves at $T=1.9\mathrm{K}$ and ${\mu }_{0}H=0.08\mathrm{T}$ for FU and FD cases. For the FU curve the two mobility regimes are characterized by two different critical currents, $I_{c1}$ and $I_{c2}$, defined from the linear extrapolations (the dashed lines). The inset shows the calculated differential resistance $R_d=dV∕dI$ vs current for the FU case.

Figure 3

(a) History dependent behavior of the critical current at small fields $H<H^{*}$: $I_{c1}$ is small and oscillates smoothly, whereas $I_{c2}$ shows similar commensurate oscillations as $I_{c,FD}$. (b) The number of coherently moving rows is determined from ML experiments over $\approx 200$ channels for the FU case [they are also indicated on the plots around the minima in (a) in order to compare to the FD case].

Figure 4

(a) Schematic illustration of the flux line configuration around a channel in increasing and decreasing fields. The thick lines (FU case) are bent down from the straight broken lines (FD case) due to the field focusing effect of the screening currents along the channel edges; (b) scanning electron microscopy (SEM) picture after magnetic decoration of a sample with $w=1.5\mathrm{\mu }\mathrm{m}$ (at $0.05\mathrm{T}$, FU). The screening currents flowing in the $\mathrm{NbN}$ islands are also indicated.

Figure 5

dc $I\text{−}V$ curves measured at $0.08\mathrm{T}$ in the FU case with and without a superimposed $30\mathrm{MHz}$ ac current. ML interference steps are observed for the fundamental voltage [$(p∕q=1∕1)$ and harmonics (2/1, 3/1)] in the high-mobility branch. The inset shows $dI∕dV$ vs $V$ in the low-mobility regime measured when a $6\mathrm{MHz}$ ac current is superimposed. Subharmonic ML peaks at $p∕q=1∕3$, 1/2 as well as the fundamental peak (1/1) are observed.

Figure 6

The dependence of (a) the fundamental ML voltage and (b) the width of ML current step on the dc-drive at ${\mu }_{0}H=0.08\mathrm{T}$ in the FU case.

Figure 7

ac-driven vortex slip transition at ${\mu }_{0}H=0.08\mathrm{T}$ and for $f=6\mathrm{MHz}$. Increasing $I_{rf}$ a jump from $n=3$ to $n=5$ occurs. Just above the transition $V_{1∕1}$ shows an anomalous dependence on the rf amplitude.

Figure 8

Field dependence of the flux-flow resistance $\left(R_f\right)$ at small fields $H<0.25\mathrm{T}$, as determined from the dc $I\text{−}V$ curves. The experimental data (circles for low mobility, and squares for high mobility) are shown together with their best fits of $\propto \sqrt{H}$ for $H<H^{*}$ and linear dependence $H$ for $H>H^{*}$. Around $50\mathrm{mT}$ jumps in $R_f$ occur due to the change in the number of moving rows from $n$ to $n+1$.