The search for spontaneous edge currents in Sr2RuO4 mesa structures with controlled geometrical shapes

Scanning Hall microscopy has been used to search for spontaneous edge fields in geometrically shaped mesa structures etched into the ab surface of Sr2RuO4 single crystals in order to test recent theories of the direction of edge current flow as a function of facet orientation and band filling. We find no evidence for spontaneous edge fields in any of our mesa structures above our experimental noise floor of & PLUSMN; 25 mG. We do, however, observe pronounced vortex clustering at low fields and temperatures, consistent with the established semi-Meissner scenario whereby a long range attractive component to the vortex-vortex interaction arises due, for example, to the multiband nature of the superconductivity. We also see clear evidence for the formation of a square vortex lattice inside square mesa structures above 1.3 K. Our results are discussed in terms of recent relevant experimental results and theoretical predictions.