We have investigated the valley splitting of two-dimensional electrons in high-quality $\mathrm{Si}∕{\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ heterostructures under tilted magnetic fields. For all the samples in our study, the valley splitting at filling factor $\nu =3$ $\left({\Delta }_3\right)$ is significantly different before and after the coincidence angle, at which energy levels cross at the Fermi level. On both sides of the coincidence, a linear dependence of ${\Delta }_3$ on the electron density was observed, while the slope of these two configurations differs by more than a factor of 2. We argue that screening of the Coulomb interaction from the low-lying filled levels, which also explains the observed spin-dependent resistivity, is responsible for the large difference of ${\Delta }_3$ before and after the coincidence.

• Received 27 January 2006

DOI:https://doi.org/10.1103/PhysRevB.73.161301