Focus on the Rashba effect

Abstract

The Rashba effect, discovered in 1959, continues to supply fertile ground for fundamental research and applications.It provided the basis for the proposal of the spin transistor by Datta and Das in 1990, which has largely inspired the broad and dynamic field of spintronics.More recent developments include new materials for the Rashba effect such as metal surfaces, interfaces and bulk materials.It has also given rise to new phenomena such as spin currents and the spin Hall effect, including its quantized version, which has led to the very active field of topological insulators.The Rashba effect plays a crucial role in yet more exotic fields of physics such as the search for Majorana fermions at semiconductorsuperconductor interfaces and the interaction of ultracold atomic Bose and Fermi gases.Advances in our understanding of Rashba-type spin-orbit couplings, both qualitatively and quantitatively, can be obtained in many different ways.This focus issue brings together the wide range of research activities on Rashba physics to further promote the development of our physical pictures and concepts in this field.The present Editorial gives a brief account on the history of the Rashba effect including material that was previously not easily accessible before summarizing the key results of the present focus issue as a guidance to the reader.The importance of spin-orbit (SO) coupling for the band structure of Bloch electrons was first noted by Elliott [1,2] and Dresselhaus et al [3].Elliott [2] pointed out that we obtain (at least) a two-fold spin degeneracy of the energy bands k E ( ) n for each wave vector k throughout the Brillouin zone if space inversion is a good symmetry of the crystal structure.Dresselhaus et al [3] (see also [4]) demonstrated that the SO splitting of the atomic p orbitals may qualitatively alter cyclotron resonance spectra in silicon and germanium.Using group theory, Dresselhaus [5] studied the effect of SO coupling on semiconductors with the inversion asymmetric zincblende structure, which is the crystal structure of many III-V and II-VI semiconductors such as GaAs, InSb, and CdTe (see also [6]).He predicted an anisotropic spin splitting of the dispersion k E ( ), cubic in the wave vector k for bands with symmetry Γ 6 , which became known as 'Dresselhaus SO splitting'.The second important crystal structure besides zincblende, realized by many III-V and II-VI semiconductors is the likewise inversion asymmetric wurtzite structure (e.g., GaN, CdS, and ZnO).In 1959 Rashba published two papers on the 'Symmetry of Energy Bands in Crystals of Wurtzite Type'.Part I discussed the 'Symmetry of Bands Disregarding Spin-Orbit Interaction' [7].In the second part with the subtitle 'Symmetry of Bands with Spin-Orbit Interaction Included' [8] published with Sheka, the authors demonstrated that the spin splitting of the dispersion k E ( ) of s electrons near the Γ point = k 0 is linear in k and isotropic for k perpendicular to the wurtzite c axis so that we get a ring of extrema in the dispersion k E ( ).It is this feature which we associate nowadays with Rashba SO coupling.However, Rashba's second paper appeared in a special issue of Fizika Tverdogo Tela that was not translated into English and that was hardly available even in the Soviet Union.Thus it became rather difficult to trace back the Rashba effect to its origin.Indeed, this paper contains a much more comprehensive study than just the proper derivation of what we call today the Rashba effect, a fact which makes this work highly interesting for current research on materials