  Using atomistic simulations, we have investigated the transport and
annihilation of skyrmions interacting with a funnel array under a current
applied perpendicular to the funnel axis. We find that transport without
annihilation is possible at low currents, when the motion is dominated by
skyrmion-skyrmion interactions and skyrmions push each other through the funnel
opening. Skyrmion annihilation occurs for higher currents when skyrmions in the
upper half of the sample exert pressure on skyrmions in the bottom half of the
sample due to the external current. Upon interacting with the funnel wall, the
skyrmions undergo a size reduction that makes it easier for them to pass
through the funnel opening. We find five phases as a function of the applied
current and the size of the funnel opening: (i) pinned, (ii) transport without
annihilation, (iii) transport with annihilation, (iv) complete annihilation,
and (v) a reentrant pinning phase that only occurs for very narrow openings.
Our findings provide insight into how to control skyrmion transport using
funnel arrays by delineating regimes in which transport of skyrmions is
possible as well as the conditions under which annihilation occurs.
