High-frequency vortex ratchet effect in a superconducting film with a nanoengineered array of asymmetric pinning sites

Vortex ratchet effect is investigated experimentally in the frequency range between 0.5 MHz and 2 GHz. The ratchet potential is provided by an array of about a quarter of a million nanoengineered asymmetric antidots in a Pb film. A square vortex lattice is stabilized at the first matching field, when each asymmetric antidot is occupied by a single vortex. We have found that (1) the transition from adiabatic to nonadiabatic cases occurring at about 1 MHz, above which the ratchet windows shift upwards with the applied frequency due to the fact that the time for a vortex to escape from the pinning potential is comparable to the period of the applied rf driving current $I_{\text{rf}}$; (2) a sudden $V_{\text{dc}}$ reversal at large $I_{\text{rf}}$, which can be attributed to inertia effect; (3) the collective step-motor behavior in the MHz region, i.e., the vortex lattice moves forward by an integer number of the period of pinning array at each cycle of $I_{\text{rf}}$; and (4) very weak ratchet effect at several GHz, indicating the possibility of stronger inertia effects in the vortex motion at such high frequencies. These results reveal rich physics information in the nonadiabatic ratchet system and are of particular importance for particle separation and molecular motor in biology.

Figure 1

(Color online) (a) The schematic illustration of the sample and the measurement setup; (b) the photograph of sample-mounted copper box.

Figure 2

(Color online) Total transmission loss versus the frequency without (black square) and with resistors (red circle) in the voltage branches.

Figure 3

(Color online) The rectified dc voltage $V_{\text{dc}}$ dependence on the input rf current $I_{\text{rf}}$ at 0.5, 1, 2, 20, and 50 MHz. $I_{\text{c}1}$ and $I_{\text{c}2}$ represent two critical currents where $V_{\text{dc}}$ occurs and reverses. The shift of $I_{\text{c}1}$ and $I_{\text{c}2}$ is clearly seen from the figure.

Figure 4

(Color online) The frequency dependence of the $I_{\text{c}1}$ and $I_{\text{c}2}$ for the asymmetric pinning potentials. The blue dash lines represent the fit to the results at and above 20 MHz. The horizontal red dot line represents a rough separation between low and high-frequency regimes.

Figure 5

(Color online) The loss during the rectification as a function of $I_{\text{rf}}$ at 0.5, 1, 2, 20, and 50 MHz, respectively.

Figure 6

(Color online) The temperature dependence of the received power by the spectrum analyzer. Here, the measured frequency is about 0.5 MHz with the input power of $-10\text{dBm}$ and $B=0$.

Figure 7

Simulation result of $V_{\text{dc}}$ dependence on the ac drive amplitude. Here the period P of the ac drive is 2250 ${\tau }_0$ and $M=1$.

Figure 8

(Color online) The $V_{\text{dc}}$ dependence on the input rf current at 5, 10 and 30 MHz. The phase locking voltage steps are clearly observed (see the vertical arrows).

Figure 9

(Color online) The rectified dc voltage $V_{\text{dc}}$ (positive parts)dependence on the input power at 100, 250, 500 MHz, 1, and 2 GHz. The ratchet effect becomes weak in GHz region.