Unconventional quantum oscillations in mesoscopic rings of spin-triplet superconductor Sr$_2$RuO$_4$

Spin-triplet superconductor Sr$_2$RuO$_4$ has been found to feature exotic vortex physics including the formation of vortex lattices at low fields and most recently, evidence for half-flux quanta trapped in a doubly connected sample. We carried out the magnetoresistance measurements in mesoscopic ring samples of Sr$_2$RuO$_4$ fabricated on mechanically exfoliated single crystals of Sr$_2$RuO$_4$ by photolithography and focused ion beam. With the magnetic field applied perpendicular to the in-plane direction, thin-wall rings of Sr$_2$RuO$_4$ were found to exhibit a large number of full-flux quantum oscillations with pronounced amplitudes unexpected from the conventional Little-Parks effect. Furthermore, in thick-wall rings, two distinct periods were observed in both resistance and critical current oscillations, which we attribute to the effect of vortices, namely, the ``lock-in" effect of a vortex lattice in Sr$_2$RuO$_4$. No evidence for half-flux-quantum oscillations were identified in any sample measured so far without the presence of an in-plane field. The measurements with an in-plane field are being pursued.