Abstract
We have measured the magnetization oscillations---i.e., the de Haas--van Alphen (dHvA) effect---of high-mobility two-dimensional electron systems (2DES's) in modulation-doped $\mathrm{AlGaAs}∕\mathrm{GaAs}$ heterostructures. In the sample exhibiting the highest oscillation amplitude of $2{\ensuremath{\mu}}_{B}^{*}$ per electron we observe discontinuous jumps in the magnetization when an even integer number of Landau levels (LLs) is filled. This specific feature of the 2DES magnetization was predicted by Peierls more than 70 years ago but never observed in the experiments. Numerical simulations assuming no states between LLs remodel the jumps quantitatively. Measurements on samples with lower mobility reveal a finite background density of states between LLs that depends systematically on the filling factor.
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