Origins of conducting channel at LaAlO$_{\mathrm{3}}$/SrTiO$_{\mathrm{3}}$ heterointerface investigated by \textit{in situ} ARPES

The high-mobility conducting interface (CI) between LaAlO$_{\mathrm{3}}$ (LAO) and SrTiO$_{\mathrm{3}}$ (STO) has revealed many fascinating phenomena. But the formation mechanism of the CI has not been conclusively explained. Here, we investigated the CI formation between LAO and STO by \textit{in situ} angle-resolved photoemission spectroscopy. By directly imaging the LAO polarity-induced built-in potential (V$_{\mathrm{i}})$ at each step of the LAO growth, we demonstrated that the V$_{\mathrm{i}}$ is proportional to the LAO thickness and the conducting interface is appeared above 3 unit cells of LAO. However, we found that the V$_{\mathrm{i}}$ and the critical thickness are strongly dependent on the amount of the surface oxygen vacancies controlled by the synchrotron ultraviolet-irradiation and the oxygen gas exposure. This indicates that the only polar catastrophe, theorized to explain the CI formation above a critical thickness, is not adequate. Instead, our results point to a decisive role played by the oxygen vacancy, and explain why the V$_{\mathrm{i}}$ and the critical thickness as reported in several works show some variation, rather than being a universal quantity.