Magnetometry on quantum Hall systems: Thermodynamic energy gaps and the density of states distribution

Abstract

AbstractWe review experiments on the de Haas–van Alphen (dHvA) effect, i.e., the quantum oscillatory behavior of the magnetization M, in modulation‐doped AlGaAs/GaAs heterostructures at low temperature T. In particular we focus on the thermodynamic energy gaps and the density of states (DOS) of two‐dimensional electron systems (2DES's) in the integer quantum Hall regime. M as a thermodynamic quantity yields direct access to both quantities. Energy gaps due to Landau quantization at even integer filling factors ν are extracted from different samples that cover a wide range of electronic parameters. They are varied by heterostructure growth parameters. For the quantitative analysis we simulate the magnetization starting from a single‐particle model DOS. We find that a DOS consisting of, both, levels with a Gaussian broadening and a background that increases linearly with ν is essential to model magnetization data for the different heterostructures over a wide range of ns and T. In particular we discuss the correlation of the Landau level broadening with the specific sample parameters. Oscillations in M at odd filling factors resulting from the spin splitting of Landau levels are investigated as a function of magnetic field and electron density ns. We recalculate the exchange‐energy contribution to the spin splitting and find a disagreement with Hartree–Fock calculations. However, our results are consistent with previously published magnetocapacitance measurements. In the sample exhibiting the lowest level broadening we observe discontinuous jumps of M at even ν. This specific feature of the 2DES magnetization was predicted more than 70 years ago by Peierls but never reported for dHvA effect studies before. Both, the significant improvements of the measurement technique and the optimization of heterostructure growth during recent years have allowed us to observe such discontinuities in M. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)