Density and strain dependence of ν=1 energy gap in a valley-degenerate AlAs quantum well

In an AlAs quantum well where two-dimensional electrons occupy two conduction-band valleys with anisotropic Fermi contours, we tune the valley splitting energy via the application of strain and measure the energy gaps for the quantum-Hall state at filling factor ν=1. At zero valley splitting energy (strain), there is a sizeable energy gap which increases linearly with density. At a fixed density, the gap rises with increasing strain much faster than the single-particle picture predicts. Interpreting the rapid rise of the gap as a signature of valley Skyrmions, we find that their size grows as the electron density increases.