Observation by resonant angle-resolved photoemission of a critical thickness for 2-dimensional electron gas formation in SrTiO$_3$ embedded in GdTiO$_3$

For certain conditions of layer thickness, the interface between GdTiO$_3$ (GTO) and SrTiO$_3$ (STO) in multilayer samples has been found to form a two-dimensional electron gas (2DEG) with very interesting properties including high mobilities and ferromagnetism. We have here studied two trilayer samples of the form [2 nm GTO/1.0 or 1.5 unit cells STO/10 nm GTO] as grown on (001) (LaAlO$_3$)$_{0.3}$(Sr$_2$AlTaO$_6$)$_{0.7}$ (LSAT), with the STO layer thicknesses being at what has been suggested is the critical thickness for 2DEG formation. We have studied these with Ti-resonant angle-resolved (ARPES) and angle-integrated photoemission and find that the spectral feature in the spectra associated with the 2DEG is present in the 1.5 unit cell sample, but not in the 1.0 unit cell sample. We also observe through core-level spectra additional states in Ti and Sr, with the strength of a low-binding-energy state for Sr being associated with the appearance of the 2DEG, and we suggest it to have an origin in final-state core-hole screening.