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 ± 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.