Electronic subbands in the a−LaAlO3/KTaO3 interface revealed by quantum oscillations in high magnetic fields

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 ($a$)-${\mathrm{LaAlO}}_{3}/{\mathrm{KTaO}}_{3}$ 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 charge carriers extending deep into the ${\mathrm{KTaO}}_{3}$. The SdH oscillations measured in magnetic fields perpendicular to the interface show four frequencies corresponding to four 2D subbands with different effective masses ($0.20\phantom{\rule{0.16em}{0ex}}{m}_{e}\ensuremath{-}0.55\phantom{\rule{0.16em}{0ex}}{m}_{e}$). The single-frequency oscillations originating from 3D electrons yields a larger effective mass of $\ensuremath{\sim}0.70\phantom{\rule{0.16em}{0ex}}{m}_{e}$. Overall, the inferred subbands are in good agreement with the theoretical calculations and angle-resolved photoemission spectroscopy studies on 2DEG at ${\mathrm{KTaO}}_{3}$ surface.