Direct measurements of the spin and valley splittings in the magnetization of aSi∕SiGequantum well in tilted magnetic fields

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.

Valley splitting ofSi∕Si1−xGexheterostructures in tilted magnetic fields

“…However, as pointed out by Wilde et al in Ref. [13], results reported by different groups are ambiguous and inconsistent with previous band calculations. The nature of this valley splitting, especially its behavior under strong B-fields, stays as an unsettled problem.…”

“…More than a decade ago, the introduction of the graded buffer scheme significantly improved the sample quality of the Si/SiGe heterostructures [7]. To date, the valley splitting has been studied by various experimental techniques, including thermal activation [8], tilted field magnetotransport [9,10], magnetocapacitance [11], microwave photoconductivity [12] and magnetization [13]. However, as pointed out by Wilde et al in Ref.…”

Theory of single electron spin relaxation in Si/SiGe lateral coupled quantum dots

“…Measurements in silicon heterostructures reveal a valley splitting of the order of µeV. 30,[34][35][36][37][38][39] On the other hand, theoretical estimates of perfectly flat structures propose a splitting about three orders of magnitude larger. 40 Taking into account detailed properties of the interface (e.g.…”

De Haas-van Alphen effect and energy gaps of a correlated two-dimensional electron system in an AlAs two-valley pseudospin system

“…This was realized recently using a micromechanical torque magnetometer. 13 References 14 and 15 provide a review on the status in this field.…”