The Rashba effect, or Rashba-Dresselhaus effect, is a momentum-dependent splitting of spin bands in two-dimensional condensed matter systems (heterostructures and surface states) similar to the splitting of particles and anti-particles in the Dirac Hamiltonian. The splitting is a combined effect of atomic spin-orbit coupling and asymmetry of the potential in the direction perpendicular to the two-dimensional plane. This effect is named in honour of Emmanuel Rashba who discovered it.
Contents
- The Rashba Hamiltonian
- Naive derivation of the Rashba Hamiltonian
- Estimation of the Rashba coupling in a realistic system the tight binding approach
- Application
- The Dresselhaus spin orbit coupling
- References
Remarkably, this effect can drive a wide variety of novel physical phenomena even when it is a small correction to the band structure of the two-dimensional metallic state.
Additionally, superconductors with large Rashba splitting are suggested as possible realizations of the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state and the longed for topological p-wave superconductor.
Lately, a momentum dependent pseudospin-orbit coupling has been realized in cold atom systems.
The Rashba Hamiltonian
The Rashba effect is most easily seen in the simple model Hamiltonian known as the Rashba Hamiltonian
where
The Rashba model in solids can be derived in the framework of the
Naive derivation of the Rashba Hamiltonian
The Rashba effect is a direct result of inversion symmetry breaking in the direction perpendicular to the two-dimensional plane. Therefore, let us add to the Hamiltonian a term that breaks this symmetry in the form of an electric field
Due to relativistic corrections an electron moving with velocity v in the electric field will experience an effective magnetic field B
where
where
Within this toy model, the Rashba Hamiltonian is given by
where
Estimation of the Rashba coupling in a realistic system - the tight binding approach
In this section we will sketch a method to estimate the coupling constant
The necessary ingredients to get Rashba splitting are atomic spin-orbit coupling
and an asymmetric potential in the direction perpendicular to the 2D surface
The main effect of the symmetry breaking potential is to open a band gap
where
where
The Rashba effect can be understood as a second order perturbation theory in which a spin-up hole, for example, jumps from a
where
Application
Spintronics - Electronic devices are based on the ability to manipulate the electrons position by means of electric fields. Similarly, devices can be based on the manipulation of the spin degree of freedom. The Rashba effect allows to manipulate the spin by the same means, that is, without the aid of a magnetic field. Such devices have many advantages over their electronic counterparts.
Topological quantum computation - Lately it has been suggested that the Rashba effect can be used to realize a p-wave superconductor. Such a superconductor has very special edge-states which are known as Majorana bound states. The non-locality immunizes them to local scattering and henceforth they are predicted to have long coherence times. Decoherence is one of the largest barriers on the way to realize a full scale quantum computer and these immune states are therefore considered good candidates for a quantum bit.
Discovery of giant Rashba effect in bulk crystals such as BiTeI and ferroelectric GeTe and in a number of low-dimensional systems bears a promise of creating devices operating electrons spins at nanoscale and possessing short operational times.
The Dresselhaus spin orbit coupling
The Rashba spin-orbit coupling is typical for systems with uniaxial symmetry, e.g., for hexagonal crystals of CdS and CdSe for which it was originally found, and for heterostructures where it develops as a result of a symmetry breaking field in the direction perpendicular to the 2D surface. All these systems lack inversion symmetry. A similar effect, known as the Dresselhaus spin orbit coupling arises in cubic crystals of A