Direct Rashba spin-orbit interaction in Si and Ge nanowires with different growth directions

Abstract

We study theoretically the low-energy hole states in Si, Ge, and Ge/Si core/shell nanowires (NWs). The NW core in our model has a rectangular cross section, the results for a square cross section are presented in detail. In the case of Ge and Ge/Si core/shell NWs, we obtain very good agreement with previous theoretical results for cylindrically symmetric NWs. In particular, the NWs allow for an unusually strong and electrically controllable spin-orbit interaction (SOI) of Rashba type. We find that the dominant contribution to the SOI is the "direct Rashba spin-orbit interaction" (DRSOI), which is an important mechanism for systems with heavy-hole-lighthole mixing. Our results for Si NWs depend significantly on the orientation of the crystallographic axes. The numerically observed dependence on the growth direction is consistent with analytical results from a simple model, and we identify a setup where the DRSOI enables spin-orbit energies of the order of millielectronvolts in Si NWs. Furthermore, we analyze the dependence of the SOI on the electric field and the cross section of the Ge or Si core. A helical gap in the spectrum can be opened with a magnetic field. We obtain the largest g factors with magnetic fields applied perpendicularly to the NWs. arXiv:1712.03476v1 [cond-mat.mes-hall]

Simple model for electrical hole spin manipulation in semiconductor quantum dots: Impact of dot material and orientation

“…When there is a significant b z component, |⇑ ≈ |⇑ and |⇓ ≈ |⇓ as |g z | |g x |, |g y | for mostly heavy-hole states [Eqs. (33)]. This large g z 6κ is the fingerprint of the strong, ∝ b z splitting between the majority |±3/2 components of |1− .…”

Spin–Orbit Interaction and Induced Superconductivity in a One-Dimensional Hole Gas

“…We use the Luttinger-Kohn Hamiltonian for holes that has been established for modelling Ge-Si core shell nanowires. 4,5 Below we give this Hamiltonian in detail, the description was adapted from Ref. 5.…”

“…4,5 Below we give this Hamiltonian in detail, the description was adapted from Ref. 5. The bulk Hamiltonian of the Ge core is…”

“…We observe that the impact of the cross section shape on the qualitative result is small, in agreement with what was reported for the comparison between a circular and square cross section. 5 Hence we use a square cross section with 6 nm side length in further calculations. square (a = 0.5 nm) Figure S4: Dispersion of an infinite wire with hexagon (left) and square (middle, right) cross sections for different discretization grid spacings a = 0.1 nm (left, middle) and a = 0.5 nm (right).…”

“…The predicted strong SOI is interesting for controlling the spin in a quantum dot electrically. 5,6 Combining this strong SOI with superconductivity is a promising route towards a topological superconductor. 7,8 Signatures of Majorana bound states (MBSs) have been found in multiple NW experiments.…”