Valley splitting of Si Si1-x Gex heterostructures in tilted magnetic fields

We have investigated the valley splitting of two-dimensional electrons in high-quality Si Si1-x Gex heterostructures under tilted magnetic fields. For all the samples in our study, the valley splitting at filling factor ν=3 (Δ3) 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 Δ3 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 Δ3 before and after the coincidence.