Investigating Shubnikov-de Haas (SdH) oscillations in high magnetic fields, we experimentally infer the electronic band structure of the quasi-two-dimensional electron gas (2DEG) at the ionic-liquid gated amorphous (a)-LaAlO 3 /KTaO 3 interface. The angular dependence of SdH oscillations indicates a 2D confinement of a majority of electrons at the interface. However, additional SdH oscillations with an angle-independent frequency observed at high tilt angles indicate the coexistence of 3D

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... carriers extending deep into the KTaO 3 . The SdH oscillations measured in magnetic fields perpendicular to the interface show four frequencies corresponding to four 2D subbands with different effective masses (0.20 m e −0.55 m e ). The single-frequency oscillations originating from 3D electrons yields a larger effective mass of ∼0.70 m e . Overall, the inferred subbands are in good agreement with the theoretical calculations and angle-resolved photoemission spectroscopy studies on 2DEG at KTaO 3 surface.