Electronic Energy Bands in Strontium Titanate

Abstract

A theoretical examination of the electronic energy bands of cubic strontium titanate has been performed by application of the LCAO (linear combination of atomic orbitals) method. Diagonal energies were determined from ionization potentials and crystalline fields based on a point-charge model for the ions. The ionic charges were adjusted to give agreement with the observed energy gap. Overlap integrals were estimated from free-ion wave functions. For the crystals studied, the calculations led to filled valence bands derived primarily from oxygen $2p$ orbitals and empty conduction bands derived predominantly from titanium $3d$ orbitals. In cubic strontium and barium titanates, there are six lowest-conduction-band ellipsoids lying along $〈100〉$ directions of $k$ space with minima probably at the edges of the Brillouin zone. The longitudinal mass is about $20\ensuremath{-}50 {m}_{0}$ and the transverse mass about $1 {m}_{0}$. Spin-orbit splitting removes degeneracy at $k=0$ and leads to additional conduction bands several hundredths of an eV above the lowest conduction band. Comparison is made with experimental data on conductivity, Hall effect, thermoelectric power, reflectivity, and soft x-ray emission. Results are in substantial agreement with experiment.