No abstract

No abstract

We present de Haas-van Alphen ͑dHvA͒ measurements on high-mobility two-dimensional electron systems formed in modulation-doped Si/ SiGe ͑100͒ quantum wells and demonstrate directly the manifestation of the valley splitting in the magnetization. We resolve sawtoothlike magnetization oscillations at even filling factors which reflect the Landau quantization and the spin splitting of Landau levels in the electronic energy spectrum. At odd filling factors we observe the lifting of the valley degeneracy in Si at high magnetic field. The magnetization is a thermodynamic quantity that at low temperature reflects the ground-state energy of the interacting electron system. We can thus determine quantitatively the energetic splitting of the two occupied conduction-band valleys directly from the oscillation amplitude. Both valley and spin splitting are found to be enhanced by electron-electron interactions. The energy gap due to valley splitting is found to be ജ0.8 meV at high perpendicular field B Ќ . From studies in tilted magnetic fields we find that the valley splitting is governed solely by B Ќ . From the spin splitting we recalculate an enhanced g factor g * = 2.9 at = 2 including the influence of disorder. This is significantly larger than the band-structure g factor of 2 in Si. We have successfully applied the coincidence technique for the dHvA effect and thus obtained a complementary means to determine the g factor. It yields a constant value g * Х 3.2 for filling factors ജ 10. A detailed analysis of the magnetization traces enabled us also to determine quantitatively the residual level broadening ⌫ in this highmobility Si/ SiGe system. We obtain a small value of ⌫ = 0.15 meVϫ B Ќ ͓T͔ 1/2 for the Si/ SiGe heterostructure of 200 000 cm 2 / ͑V s͒ mobility at 0.3 K.

We 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)

No abstract