Geometric background charge: dislocations on capillary bridges

Recent experiments have shown that colloidal crystals confined to weakly curved capillary bridges introduce groups of dislocations organized into 'pleats' as means to relieve the stress caused by the Gaussian curvature of the surface. We consider the onset of this curvature-screening mechanism, by examining the energetics of isolated dislocations and interstitials on capillary bridges with free boundaries. The boundary provides an essential contribution to the problem, akin to a background charge that neutralizes the unbalanced integrated curvature of the surface. This makes it favorable for topologically neutral dislocations and groups of dislocations - rather than topologically charged disclinations and scars - to relieve the stress caused by the unbalanced Gaussian curvature of the surface. This effect applies to any crystal on a surface with non-vanishing integrated Gaussian curvature and stress-free boundary conditions. We corroborate the analytic results by numerically computing the energetics of a defective lattice of springs confined to surfaces with weak positive and negative curvatures.