Conduction-band edge and Shubnikov–de Haas effect in low-electron-density SrTiO${}_3$

The Shubnikov–de Haas effect is used to explore the conduction-band edge of high mobility SrTiO${}_3$ films doped with La. The results largely confirm the earlier measurements by Uwe et al. [Jpn. J. Appl. Phys. 24 (Suppl. 24-2), 335 (1985)]. The band edge dispersion differs significantly from the predictions of ab initio electronic structure theory.

Figure 1

(a) Dispersion at the conduction-band edge using parameters from Uwe et al. (Ref. 22) in a model that includes relatively strong spin-orbit interaction and an electron density of $7.5\times {10}^{17}$ cm${}^{-3}$; $k$ is expressed in units of π/$a$, where $a$ is the length of the cubic SrTiO${}_3$ unit cell. $k_z$ is directed along the tetragonal $c$ axis. (b) Corresponding Fermi surface for the lowest state split off by the tetragonal distortion and (c) corresponding Fermi surface for the higher lying state.

Figure 2

Shubnikov–de Haas oscillations with the magnetic field aligned along [111] for sample 1. (a) The quantum oscillations are exhausted at the quantum limit, ∼15 T. (b) Features persist down to 2 T.

Figure 3

Sample 1. The relative maxima in Fig. 2, plotted vs 1/$B$. Near the quantum limit a splitting appears. The slope of the line corresponds to an extremal area of 17.5 T.

Figure 4

Sample 2. Shubnikov–de Haas oscillations with the magnetic field aligned along [001]. (a) Spin splitting is apparent at the highest field. At low fields a weak, low frequency oscillation is observed (arrows) and assigned to the strain-induced split-off band.

Figure 5

Sample 2. Indexed relative maxima for two sets of quantum oscillations in Fig. 4, corresponding to extremal cross sections of 55.2 and 9.55 T.

Figure 6

Sample 2. Angle dependence of measured extremal area (solid squares). A comparison with parameters from Uwe et al. (Ref. 22) is also shown (open and solid circles, respectively). Open circles assume that the tetragonal $c$ axis is normal to the surface, and solid circles assume the tetragonal $c$ axis is in the plane of the sample.

Figure 7

Temperature dependence of the Shubnikov–de Haas oscillations for sample 2. (a) Measured with the magnetic field along the [110] direction. (b) Model calculation with an effective mass of 1.41$m_e$.

Figure 8

Fermi surface area vs angle, measured (solid) and fit (open), using the parameters in the text.