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Using numerical simulations, we investigate vortex configurations and pinningin superconductors with honeycomb and kagome pinning arrays. We find that avariety of novel vortex crystal states can be stabilized at integer andfractional matching field densities. The honeycomb and kagome pinning arraysproduce considerably more pronounced commensuration peaks in the criticaldepinning force than triangular pinning arrays, and also cause additional peaksat noninteger matching fields where a portion of the vortices are located inthe large interstitial regions of the pinning lattices. For the honeycombpinning array, we find matching effects of equal strength at most fillingsB/B_\phi=n/2 for n>2, where n is an integer, in agreement with recentexperiments. For kagome pinning arrays, pronounced matching effects generallyoccur at B/B_\phi=n/3 for n>3, while for triangular pinning arrays pronouncedmatching effects are observed only at integer fillings B/B_\phi=n. At thenoninteger matching field peaks in the honeycomb and kagome pinning arrays, theinterstitial vortices are arranged in dimer, trimer, and higher order n-merstates that have an overall orientational order. We call these n-mer states"vortex molecular crystals" and "vortex plastic crystals" since they aresimilar to the states recently observed in colloidal molecular crystal systems.We argue that the vortex molecular crystals have properties in common withcertain spin systems such as Ising and n-state Potts models. We show thatkagome and honeycomb pinning arrays can be useful for increasing the criticalcurrent above that of purely triangular pinning arrays.

Vortex Molecular Crystal and Vortex Plastic Crystal States in Honeycomb and Kagome Pinning Arrays