Electric field effect on magneto-thermopower in oxide interface LaAlO$_{3}$/SrTiO$_{3}$

Oxide interface LaAlO$_{3}$/SrTiO$_{3}$ has been attracting huge interest as it shows 2-dimensional electron liquid behavior, negative compressibility and coexistence of magnetism and superconductivity. In this study we measured the magneto-thermoelectric effect and report the observation of the quantum oscillation in the thermopower. Backing gating through SrTiO$_3$ tunes the carrier density and the oscillation pattern in the thermoelectric signal. At low carrier density, the oscillation frequency decreases when more electrons are populated, which directly indicates the negative capacitance. At high carrier density regime, both of magneto-thermopower and Nernst effect show the nonlinear behavior which suggests a Lifshitz transition. These results point to the unique multiband electronic structure of oxide interface.