Vortex molecular crystal and vortex plastic crystal states in honeycomb and kagomé pinning arrays

Abstract

Using numerical simulations, we investigate vortex configurations and pinning in superconductors with honeycomb and kagom\'e pinning arrays. We find that a variety of vortex crystal states can be stabilized at integer and fractional matching field densities. The honeycomb and kagom\'e pinning arrays produce considerably more pronounced commensuration peaks in the critical depinning force than triangular pinning arrays, and also cause additional peaks at noninteger matching fields where a portion of the vortices are located in the large interstitial regions of the pinning lattices. For the honeycomb pinning array, we find matching effects of equal strength at most fillings $B∕{B}_{\ensuremath{\phi}}=n∕2$ for $ng2$, where $n$ is an integer, in agreement with recent experiments. For kagom\'e pinning arrays, pronounced matching effects generally occur at $B∕{B}_{\ensuremath{\phi}}=n∕3$ for $ng3$, while for triangular pinning arrays pronounced matching effects are observed only at integer fillings $B∕{B}_{\ensuremath{\phi}}=n$. At the noninteger matching field peaks in the honeycomb and kagom\'e pinning arrays, the interstitial vortices are arranged in dimer, trimer, and higher order $n$-mer states that have an overall orientational order. We call these $n$-mer states ``vortex molecular crystals'' and ``vortex plastic crystals'' since they are similar to the states recently observed in colloidal molecular crystal systems. We argue that the vortex molecular crystals have properties in common with certain spin systems such as Ising and $n$-state Potts models. We show that kagom\'e and honeycomb pinning arrays can be useful for increasing the critical current above that of purely triangular pinning arrays.