Valley splitting of Si/SiGe heterostructures in tilted magnetic fields

TL;DR

This study investigates how valley splitting in high-quality Si/SiGe heterostructures varies with electron density and magnetic field orientation, revealing significant differences before and after the coincidence angle due to Coulomb screening effects.

Contribution

It provides new insights into the behavior of valley splitting under tilted magnetic fields and highlights the role of Coulomb screening in these phenomena.

Findings

Valley splitting at filling factor ν=3 differs significantly before and after the coincidence angle.

Linear dependence of valley splitting on electron density observed on both sides of the coincidence.

Screening effects from filled levels explain the large difference in valley splitting.

Abstract

We have investigated the valley splitting of two-dimensional electrons in high quality Si/Si$_{1-x}$Ge$_x$ heterostructures under tilted magnetic fields. For all the samples in our study, the valley splitting at filling factor $\nu=3$ ($\Delta_3$) 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 density dependence of $\Delta_3$ on the electron density was observed, while the slope of these two configurations differs by more than a factor of two. 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.