Two-dimensional density of states in the extreme quantum limit

We have measured the density of states of a two-dimensional electron gas from the weak-field limit to the extreme quantum limit and obtained quantitative information about the density of states at filling factors of frac13; and frac23;. Our magnetocapacitance measurements were made at magnetic field strengths up to 29 T at temperatures between 0.4 and 4.2 K using modulation-doped $\mathrm{GaAs}-{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures on conducting substrates.