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

TL;DR

This paper theoretically investigates the direct Rashba spin-orbit interaction in Si and Ge nanowires, revealing strong, electrically controllable SOI influenced by growth direction and electric fields, with implications for spintronic applications.

Contribution

It introduces the concept of direct Rashba spin-orbit interaction in Si and Ge nanowires and analyzes its dependence on orientation, electric field, and cross section, providing new insights into spin control.

Findings

Strong Rashba SOI observed in Ge/Si nanowires

Dependence of SOI on nanowire orientation and electric field

Potential for millielectronvolt spin-orbit energies in Si nanowires

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-light-hole 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.