| Abstract: | Competition or cooperation between different electronic orders with similar energy scales often gives rise to new or unexpected behaviors. Detecting traces of such orders requires versatile probes, which can probe different aspects of the system, such as conductivity, superconductivity and magnetism. In my talk, I will describe two systems where our local view uncovered surprising mesoscopic effects. In the oxide interface LaAlO3/SrTiO3, we imaged the current flow close to a metal-insulator transition. We found that the critical behavior is controlled by structural domain patterns in the substrate, rather than by universal scaling laws. In the transition metal dichalcogenide 4Hb-TaS2 we show that the superconducting state hosts a spontaneous vortex phase, where vortices appear in the absence of an external field. I will show evidence that this spontaneous vortex phase is caused by unconventional magnetism in the normal state. |