Density-functional modelling of electron energy-loss spectra for LaAlO$_{\mathrm{3}}$/SrTiO$_{\mathrm{3}}$ quantum well

LaAlO$_{\mathrm{3}}$/SrTiO$_{\mathrm{3}}$ quantum wells (QW) are grown S by molecular beam epitaxy (MBE). The conduction band alignment is investigated using electron energy loss spectroscopy (EELS). We model the EELS spectrum using first-principle calculations. To account for the core-hole effect, the Z$+$1 approximationis adopted. Site-projected unoccupied p and d densities of states (pDOS) are extracted and compared with the experimental O K and Ti L edges that correspond to 1s to 2p and 2p to 3d transitions, respectively. Results fro bulk LaAlO$_{\mathrm{3\thinspace }}$(LAO) and$_{\mathrm{\thinspace }}$SrTiO$_{\mathrm{3\thinspace }}$(STO) are discussed first and then the quantum well case is analyzed. We investigate the orbital character of the conduction band states in a QW. We find that in LAO/STO QW, there are evanescent Ti-originated states in the LAO layer and elate them with the peak at EELS front edge.