Valley effects on the fractions in an ultrahigh mobility SiGe/Si/SiGe two-dimensional electron system

Abstract

We observe minima of the longitudinal resistance corresponding to the quantum Hall effect of composite fermions at quantum numbers $p=1$, 2, 3, 4, and 6 in an ultraclean strongly interacting bivalley SiGe/Si/SiGe two-dimensional electron system. The minima at $p=3$ disappear below a certain electron density, although the surrounding minima at $p=2$ and $p=4$ survive at significantly lower densities. Furthermore, the onset for the resistance minimum at a filling factor $\nu=3/5$ is found to be independent of the tilt angle of the magnetic field. These surprising results indicate the intersection or merging of the quantum levels of composite fermions with different valley indices, which reveals the valley effect on fractions.