Onset, evolution, and magnetic braking of vortex lattice instabilities in nanostructured superconducting films

In 1976, Larkin and Ovchinnikov [Zh. Eksp. Teor. Fiz. 68, 1915 (1975) [Sov. Phys.–JETP 41, 960 (1976)]] predicted that vortex matter in superconductors driven by an electrical current can undergo an abrupt dynamic transition from a flux-flow regime to a more dissipative state at sufficiently high vortex velocities. Typically, this transition manifests itself as a large voltage jump at a particular current density, so-called instability current density $J^{*}$, which is smaller than the depairing current. By tuning the effective pinning strength in Al films, using an artificial periodic pinning array of triangular holes, we show that a unique and well-defined instability current density exists if the pinning is strong, whereas a series of multiple voltage transitions appear in the relatively weaker pinning regime. This behavior is consistent with time-dependent Ginzburg-Landau simulations, where the multiple-step transition can be unambiguously attributed to the progressive development of vortex chains and subsequently phase-slip lines. In addition, we explore experimentally the magnetic braking effects, caused by a thick Cu layer deposited on top of the superconductor, on the instabilities and the vortex ratchet effect.

Figure 1

Upper panel: sketch of the transport bridge with the corresponding dimensions. Lower panels: scanning electron microscopy images of the Al samples with the triangular array of triangular antidots.

Figure 2

(a) Experimental current-voltage characteristics for sample Tr1 obtained at $T=0.97T_c$ and for several applied magnetic fields. The magnetic field $H=0.8$ mT is above the upper critical field and the curve corresponds to the Ohmic response in the normal state. (b) Zoom-in of the low-voltage regime. The onset of different dynamic phases is indicated by arrows.

Figure 3

(a) Simulated current-voltage characteristics for sample Tr2 at $T=0.97T_c$ and for several applied magnetic fields. (b) Zoom-in of the low-voltage regime. The onset of different dynamic phases is indicated by arrows. The right column shows four contour plots of the Cooper-pair density for different values of the applied current flowing from left to right at a magnetic field $H\approx 0.2H_{c2}$. In these images, vortices cross the bridge from top to bottom. In the lower right panel, the contacts between which the voltage is measured are indicated.

Figure 4

Dynamic vortex phases as a function of applied current ($J$) and magnetic field ($H$) for samples (a) Tr1, (b) Tr2 experimental, and (c) Tr2 simulated. $J_c$ is the depinning current, $J_1$ and $J_T$ indicate the current densities at which the first and last voltage jumps occur, respectively, and $J_N$ is the current needed to reach the normal state. In panel (a), the open circles indicate the end point of the first current-density plateau $J_2$.

Figure 5

Voltage of the first instability point $V_1$ as a function of the magnetic field for the two samples Tr1 and Tr2 at $T=0.97T_c$ (a) and for the simulated system (b).

Figure 6

(a) Voltage versus current for the sample Tr2b with and without a 500-nm-thick Cu layer on top. Panel (b) shows a low-voltage zoom-in of the panel (a) evidencing the same instability point $J_1$ with and without Cu. The inset in panel (b) shows the rectified voltage $V_{\text{dc}}$ versus magnetic field when applying an alternative current of 1 mA and frequency of 33 kHz at $T/T_c$ = 0.94.

Figure 7

Contour plot of the magnetic field and temperature dependence of the measured dc voltage $V_{\text{dc}}$ with an ac current of 1 mA and frequency 33 kHz applied to sample Tr2b (a) without Cu layer and (b) covered with a Cu layer.