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The simultaneous occurrence of electric-field controlled superconductivityand spin-orbit interaction makes two-dimensional electron systems (2DES)constructed from perovskite transition metal oxides promising candidates forthe next generation of spintronics and quantum computing. It is, however,essential to understand the electronic bands thoroughly and verify thepredicted electronic states experimentally in these 2DES to advancetechnological applications. Here, we present novel insights into the electronicstates of the 2DES at oxide interfaces through comprehensive investigations ofShubnikov-de Haas oscillations in two different systems: EuO/KTaO$_3$ (EuO/KTO)and LaAlO$_3$/SrTiO$_3$ (LAO/STO). To accurately resolve these oscillations, weconducted transport measurements in high magnetic fields up to 60 T and lowtemperatures down to 100 mK. For 2D confined electrons at both interfaces, weobserved a progressive increase of oscillations frequency and cyclotron masswith the magnetic field. We interpret these intriguing findings by consideringthe existence of non-trivial electronic bands, for which the $E-k$ dispersionincorporates both linear and parabolic dispersion relations. In addition toproviding experimental evidence for topological-like electronic states inKTO-2DES and STO-2DES, the unconventional oscillations presented in this studyestablish a new paradigm for quantum oscillations in 2DES based on perovskitetransition metal oxides, where the oscillations frequency exhibits quadraticdependence on the magnetic field.

Unconventional quantum oscillations and evidence of non-trivial  electronic states in quasi-two-dimensional electron system at complex oxide  interfaces