Strong enhancement of the valley splitting in a 2D electron system in silicon

Using magnetocapacitance data, we directly determine the chemical potential jump in a strongly correlated 2D electron system in silicon when the filling factor traverses the valley gap at \nu=1 and \nu=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.