Universality of electron mobility in LaAlO₃/SrTiO₃ and bulk SrTiO₃

Metallic LaAlO₃/SrTiO₃ (LAO/STO) interfaces attract enormous attention, but the relationship between the electron mobility and the sheet electron density, n_s, is poorly understood. Here, we derive a simple expression for the three-dimensional electron density near the interface, n_3D, as a function of n_s and find that the mobility for LAO/STO-based interfaces depends on n_3D in the same way as it does for bulk doped STO. It is known that undoped bulk STO is strongly compensated with N similar or equal to 5 x 10¹⁸ cm^-3 background donors and acceptors. In intentionally doped bulk STO with a concentration of electrons n_3D < N, background impurities determine the electron scattering. Thus, when n_3D < N, it is natural to see in LAO/STO the same mobility as in the bulk. On the other hand, in the bulk samples with n_3D > N, the mobility collapses because scattering happens on n_3D intentionally introduced donors. For LAO/STO, the polar catastrophe which provides electrons is not supposed to provide an equal number of random donors and thus the mobility should be larger. The fact that the mobility is still the same implies that for the LAO/STO, the polar catastrophe model should be revisited.