  The two-dimensional electron gas formed at interfaces between SrTiO$_3$ and
other materials has attracted much attention since extremely efficient
spin-to-charge current conversion has been recently observed at these
interfaces. This has been attributed to their complicated quantized
multi-orbital structures with a topological feature. However, there are few
reports quantitatively comparing the conversion efficiency values between
experiments and theoretical calculations at these interfaces. In this study, we
theoretically explain the experimental temperature dependence of the
spin-to-charge current conversion efficiency using an 8x8 effective
tight-binding model considering the second $d_{xy}$ subband, revealing the
vital role of the quantization of the multi-band structure.
