Spin-Orbit Interaction in Symmetry-Broken Environments

Spintronics devices are based on the ability to manipulate the electron spin by electric (instead of magnetic) fields. One example for such a device is the spin field effect transistor proposed by Datta and Das that is based on the Rashba effect. According to the Rashba model the spin-orbit interaction will lift the spin degeneracy of the electronic band structure in a system where space inversion symmetry is broken. Typical examples are the two-dimensional electron gases that form at the interface of semiconductor heterojunctions or at the (111) surface of, e.g., a gold single crystal. The resulting characteristic Rashba dispersion consists of two spin-polarized parabolas with effective mass m^* and an offset ±k_R= (α_R m^*)/ℏ² away from k_∥= 0, where α_R is the Rashba constant.

Rashba effect: in the symmetry-broken environment at a crystal surface or at the interface between two semiconductors a strong spin-orbit interaction will lift the spin degeneracy of the two-dimensional states localized at the surface or interface. The resulting dispersion consists of two spin-polarized parabolas with a momentum offset kR away from k∥ = 0 and a corresponding offset in energy ER. The size of the spin splitting is given by the Rashba constant αR. — Rashba effect: in the symmetry-broken environment at a crystal surface or at the interface between two semiconductors a strong spin-orbit interaction will lift the spin degeneracy of the two-dimensional states localized at the surface or interface. The resulting dispersion consists of two spin-polarized parabolas with a momentum offset k_R away from k_∥= 0 and a corresponding offset in energy E_R. The size of the spin splitting is given by the Rashba constant α_R.

Rashba effect: in the symmetry-broken environment at a crystal surface or at the interface between two semiconductors a strong spin-orbit interaction will lift the spin degeneracy of the two-dimensional states localized at the surface or interface. The resulting dispersion consists of two spin-polarized parabolas with a momentum offset k_R away from k_∥= 0 and a corresponding offset in energy E_R. The size of the spin splitting is given by the Rashba constant α_R.

In real systems the size of the Rashba constant (and hence the size of the spin splitting) depends on the asymmetry of the electronic wave function in the vicinity of heavy nuclei. Hence, the size of the spin splitting is highly sensitive to the detailed atomic structure at the interface or surface. This offers the potential to control the electron spin with light, e.g. by coherently driving the atoms with strong light fields.