Strong enhancement of the valley splitting in a two-dimensional electron system in silicon

Using magnetocapacitance data, we directly determine the chemical potential jump in a strongly correlated two-dimensional electron system in silicon when the filling factor traverses the valley gap at ν=1 and ν=3. The data yield a valley gap that is strongly enhanced compared to the single-particle value and increases linearly with magnetic field. This result has not been explained by existing theories.