Removing vortices from a SC using an asymmetric potential.
(a)
The potential necessary to remove vortices from the SC. Using the
simulation method described in Fig.2, we investigated a
system consisting of N=5 teeth oriented to the left and the same
number oriented to the right, as shown in the figure, the parameters of
each tooth being identical to that described in Fig.1c. To
mimic the pressure generated by the external magnetic field, which acts
to push vortices into the SC, on the two sides we attached two
reservoirs, that have a constant vortex density rho_0 at all times.
Thus, vortices can leave the SC for the reservoir, or new vortices can
enter from the reservoir. In thin SC films, due to the Meissner
current, there is a geometrical barrier that acts to trap the vortices
inside the SC. Since most applications of SC's involve
thin films, we included in the simulations this geometrical barrier,
that creates a force f_in(x)=-H*Phi_0*x/2pi/sqrt(w^2-x^2) for
-w+d/2 < x < w-d/2, and f_edge = 2*epsilon_0-(H*Phi_0/2pi)*sqrt(4w/d-1) for x > w-d/2, and -f_edge for x < -w+d/2. Thus the geometrical barrier opposes
the entry of the vortices at the edge of the SC, but once they move
inside, it moves them towards the center of the SC. For successful
vortex removal the ratchet effect has to be strong enough to move the
vortices against f_in(x). (b) The (f_L,T)
diagram describing the effectiveness of the ratchet effect as a
function of the parameters characterizing the driving current, f_L. The color code corresponds to the the relative vortex
densit rho/rho_0, where rho_0 is the initial vortex density
corresponding to H=1G and rho is the final vortex density
after the application of the ac current. As the color code indicates,
there is a region where vortex removal is complete, the vortex density
being equal to zero. The dashed lines correspond to the T_1 and T_2
boundaries, that are calculated analytically (see text) and separate
the three main regimes: I: complete vortex removal in the
majority of the regime, rho=0; II: partial vortex removal, 0
< rho < rho_0; and III: no change in the vortex density,
rho=rho_0. The thin white lines denote the boundaries of the regions where vortex trapping due to periodic orbits occurs. These boundaries correctly
reflect the structure of the fingers, but slightly deviate from the
results of the numerical simulation, because the
analytical calculation assumed an array of identical teeth.