Heat-capacity study of two-dimensional electrons in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As multiple-quantum-well structures in high magnetic fields: Spin-split Landau levels

Using an earlier developed ac calorimetric technique, we measure the heat capacity of the two-dimensional electron system (2D ES) in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As multiple-quantum-well structures with relatively low density and high mobility (${\mathit{n}}_{2\mathrm{D}}$∼2×${10}^{11}$/${\mathrm{cm}}^2$; μ∼5×${10}^5$ ${\mathrm{cm}}^2$/V s). Sweeping the magnetic field B up to ∼10 T below 1 K, we have observed the heat capacity, and thereby the equilibrium density of states (DOS) of a 2D ES in the spin-split lowest Landau levels. Analyzing the 2D ES DOS derived from our data, we find that many-body interactions within the 2D ES must be considered in order to explain the B dependence of both the spin splitting and broadening of the Landau levels. In optimal fits to our data, the g factor of Landau-level spin splitting is enhanced more than 10 times over the value at B=0, in agreement with results from analyses of the 2D ES transport. The Landau-level broadening oscillates versus 1/B, consistent with earlier results for the heat capacity of higher-density 2D ES samples.