K·p subband structure of the LaAlO₃/SrTiO₃ interface

Heterostructures made of transition metal oxides are new tailor-made materials which are attracting much attention. We have constructed a six-band k·p Hamiltonian and used it within the envelope function method to calculate the subband structure of a variety of LaAlO₃/SrTiO ₃ heterostructures. By use of density functional calculations, we determine the k·p parameters describing the conduction band edge of SrTiO₃: the three effective mass parameters L=0.6104eVÅ2, M=9.73eVÅ2, N=-1.616eVÅ2, the spin orbit splitting Δ_SO=28.5 meV, and the low temperature tetragonal distortion energy splitting Δ_T=2.1 meV. For confined systems we find strongly anisotropic nonparabolic subbands. As an application we calculate bands, density of states, and magnetic energy levels and compare the results to Shubnikov-de Haas quantum oscillations observed in high magnetic fields. For typical heterostructures we find that electric field strength at the interface of F=0.1 meV/Å for a carrier density of 7.2×1012 cm^-2 results in a subband structure that is similar to experimental results.