Formation and observation of a quasi-two-dimensional $d_{xy}$ electron liquid in epitaxially stabilized Sr$_{2-x}$La$_{x}$TiO$_{4}$ thin films

We report the formation and observation of an electron liquid in Sr$_{2-x}$La$_{x}$TiO$_4$, the quasi-two-dimensional counterpart of SrTiO$_3$, through reactive molecular-beam epitaxy and {\it in situ} angle-resolved photoemission spectroscopy. The lowest lying states are found to be comprised of Ti 3$d_{xy}$ orbitals, analogous to the LaAlO$_3$/SrTiO$_3$ interface and exhibit unusually broad features characterized by quantized energy levels and a reduced Luttinger volume. Using model calculations, we explain these characteristics through an interplay of disorder and electron-phonon coupling acting co-operatively at similar energy scales, which provides a possible mechanism for explaining the low free carrier concentrations observed at various oxide heterostructures such as the LaAlO$_3$/SrTiO$_3$ interface.