Depinning and dynamics of vortices confined in mesoscopic flow channels

We study the behavior of vortex matter in artificial flow channels confined by pinned vortices in the channel edges (CEs). The critical current $J_s$ is governed by the interaction with static vortices in the CEs. We study structural changes associated with (in)commensurability between the channel width $w$ and the natural row spacing $b_0$, and their effect on $J_s$. The behavior depends crucially on the presence of disorder in the CE arrays. For ordered CEs, maxima in $J_s$ occur at matching $w=nb_0$ ($n$ integer), while for $w eq nb_0$ defects along the CEs cause a vanishing $J_s$. For weak CE disorder, the sharp peaks in $J_s$ at $w=nb_0$ become smeared via nucleation and pinning of defects. The corresponding quasi-1D $n$ row configurations can be described by a (disordered)sine-Gordon model. For larger disorder and $wsimeq nb_0$, $J_s$ levels at $sim 30 %$ of the ideal lattice strength $J_s^0$. Around half filling ($w/b_0 simeq npm 1/2$), disorder causes new features, namely {it misaligned} defects and coexistence of $n$ and $n pm 1$ rows in the channel. This causes a {it maximum} in $J_s$ around mismatch, while $J_s$ smoothly decreases towards matching due to annealing of the misaligned regions. We study the evolution of static and dynamic structures on changing $w/b_0$, the relation between modulations of $J_s$ and transverse fluctuations and dynamic ordering of the arrays. The numerical results at strong disorder show good qualitative agreement with recent mode-locking experiments.