The spin-orbit interaction (SOI) of a two-dimensional hole gas in the inversion symmetric semiconductor Ge is studied in a strained-Ge=SiGe quantum well structure. We observe weak antilocalization (WAL) in the magnetoconductivity measurement, revealing that the WAL feature can be fully described by the k-cubic Rashba SOI theory. Furthermore, we demonstrate electric field control of the Rashba SOI. Our findings reveal that the heavy hole (HH) in strained Ge is a purely cubic Rashba system, which is consistent with the spin angular momentum m j ¼ AE3=2 nature of the HH wave function. DOI: 10.1103/PhysRevLett.113.086601 PACS numbers: 72.25.Dc, 73.20.Fz, 73.21.-b The spin-orbit interaction (SOI) in a two-dimensional system is a subject of considerable interest because the SOI induces spin splitting at a zero magnetic field, which is important in both fundamental research and electronic device applications [1]. Recent developments of SOI-induced phenomena in the solid state demonstrate many possibilities utilizing spin current and the emergence of new physics such as the spin interferometer [2,3], persistent spin helix [4,5], spin Hall effect [6][7][8], and quantum spin Hall effect [9,10]. Up to now, there have been two well-known SOIs existing in solids: the Dresselhaus SOI [11] due to bulk inversion asymmetry (BIA) in the crystal structure and the Rashba SOI [12,13] due to spatial inversion asymmetry (SIA).In low-dimensional systems, the Rashba SOI becomes more important because it is stronger at the heterointerface and can be controlled by an external electric field. Many of the pioneering studies on the SOI-induced phenomena mentioned above were performed in two-dimensional electron systems, where the Rashba SOI is described by the k-linear Rashba term. In the Hamiltonian, the k-linear Rashba term can be written aswhere σ AE ¼ 1=2ðσ x AE iσ y Þ denote combinations of Pauli spin matrices, k AE ¼ k x AE ik y , and k x , k y are the components of the in-plane wave vector k ∥ . The effective magnetic field Ω 1 ðk ∥ Þ acting on the transport carrier due to the k-linear Rashba term is illustrated in Fig. 1(a).Recently, a higher-order contribution of the Rashba SOI, the so-called k 3 (k-cubic) Rashba SOI, has received more attention [14,15]. The Hamiltonian for the k-cubic Rashba SOI is expressed asand the effective magnetic field Ω 3 ðk ∥ Þ in k space is illustrated in Fig. 1(b) [15]. There is a significant difference in the effective field symmetry between the k-linear and the k-cubic Rashba SOI with one and three rotations in k space, respectively. The k 3 symmetry of the SOI is an interesting subject because it influences all of the SOI-induced phenomena as opposed to the k-linear Rashba term. For example, in case of the spin Hall effect, the k-cubic Rashba term is predicted to give rise to a larger spin Hall conductivity [17][18][19].

Direct-contact HfO2∕Si interfaces, which have virtually no interfacial SiO2 layer, exhibit characteristic interface-charge distribution. The authors report that direct-contact interfaces demonstrate a negative flatband-voltage shift that is reduced by the insertion of a ∼0.5-nm-thick Si-oxide layer. The authors propose that the observed flatband-voltage shift is mainly caused by an electrostatic dipole (∼0.5V) formed at the HfO2∕Si interface rather than fixed charges. The effects of the dipole on leakage current are also discussed.

Electron paramagnetic resonance of ensembles of phosphorus donors in silicon has been detected electrically with externally applied magnetic fields lower than 200 G. Because the spin Hamiltonian was dominated by the contact hyperfine term rather than by the Zeeman terms at such low magnetic fields, superposition states α |↑↓ + β |↓↑ and −β |↑↓ + α |↓↑ were formed between phosphorus electron and nuclear spins, and electron paramagnetic resonance transitions between these superposition states and |↑↑ or |↓↓ states are observed clearly. A continuous change of α and β with the magnetic field was observed with a behavior fully consistent with theory of phosphorus donors in silicon.

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We report on a magnetophotoluminescence study of isotopically pure 70 Ge / Si self-assembled type-II quantum dots. Oscillatory behaviors attributed to the Aharonov-Bohm effect are simultaneously observed for the emission energy and intensity of excitons subject to an increasing magnetic field. When the magnetic flux penetrates through the ringlike trajectory of an electron moving around each quantum dot, the ground state of an exciton experiences a change in its angular momentum. Our results provide the experimental evidence for the phase coherence of localized electron wave functions in group-IV Ge/Si self-assembled quantum structures.