Ab initio low-energy model of transition-metal-oxide heterostructure LaAlO ₃/SrTiO ₃

We develop a multiscale ab initio scheme for correlated electrons (MACE) for transition-metal-oxide heterostructures, and determine the parameters of the low-energy effective model. By separating Ti t2g bands near the Fermi level from the global Kohn-Sham (KS) bands of LaAlO ₃ (LAO)/SrTiO ₃ (STO), which are highly entangled with each other, we are able to calculate the parameters of the low-energy effective model of the interface with the help of constrained random phase approximation (cRPA). The on-site energies of the Ti t _2g orbitals in the 1st layer is about 650 meV lower than those in the second layer. In the 1st layer, the transfer integral of the Ti t2g orbital is nearly the same as that of bulk STO, while the effective screened Coulomb interaction becomes about 10% larger than that of bulk STO. The differences in the parameters from bulk STO decrease rapidly with increasing distance from the interface. Our present versatile method enables us to derive effective ab initio low-energy models and to study interfaces of strongly correlated electron systems from first principles.