L. W. van Heeringen, G. A. de Wijs, A. McCollam, J. C. Maan, A. Fasolino
Heterostructures made of transition metal oxides are new tailor-made materials which are attracting much attention. We have constructed a 6-band $\bm{k}\cdot\bm{p}$ Hamiltonian and used it within the envelope function method to calculate the subband structure of the LaAlO$_3$/SrTiO$_3$ interface, modeled by an electric field that we treat as a parameter. By use of density functional calculations, we determine the $\bm{k}\cdot\bm{p}$ parameters describing the conduction band edge of SrTiO$_3$: the three effective mass parameters, $L=0.6104 \text{eV\AA}^2$, $M=9.73 \text{eV\AA}^2$, $N=-1.616 \text{eV\AA}^2$, the spin orbit splitting $\Delta_{SO}=28.5 $meV and the low temperature tetragonal distortion energy splitting $\Delta_T=2.1 $meV. We find strongly anisotropic non-parabolic subbands. Through quasiclassical quantization for a given density, this model allows a direct comparison to the frequency of the Shubnikov-de Haas quantum oscillations recently observed in high magnetic fields. Our results are in very good agreement with the experiments for an electric field strength $F = 0.1$ meV/\AA{} and a charge density of $7.2 \times 10^{12}$ cm$^{-2}$.
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http://arxiv.org/abs/1303.7095
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