Rashba effect — splitting by spin

Spin

-In mathematics, science and technology:* Electron magnetic dipole moment* Rotation or spin, a movement of an object in a circular motion* Social Phobia Inventory, abbreviated as SPIN, a psychological test of social anxiety disorder....

 in solid

Solid

Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...

s (particularly in heterostructures) by strong spin-orbit interaction

Spin-orbit interaction

In quantum physics, the spin-orbit interaction is any interaction of a particle's spin with its motion. The first and best known example of this is that spin-orbit interaction causes shifts in an electron's atomic energy levels due to electromagnetic interaction between the electron's spin and...

. Named in honour of Emmanuel Rashba

Emmanuel Rashba

Emmanuel Rashba is a Ukrainian theoretical physicist known for his contributions to semiconductor physics and spintronics including the Rashba effect....

, co-worker of National Academy of Sciences of USSR who discovered it.

If a potential gradient is applied perpendicular the semiconductor hetero junction plane, a spin-orbit interaction in proportion to the potential gradient as well as two-dimensional wavevector k is exerted to the electrons. As a result the electron spin is quantized in the direction perpendicular to both the plane normal and k, thus splitting the energy band.

In free space Hamiltonian

Hamiltonian

Hamiltonian may refer toIn mathematics :* Hamiltonian system* Hamiltonian path, in graph theory** Hamiltonian cycle, a special case of a Hamiltonian path* Hamiltonian group, in group theory* Hamiltonian...

 of spin-orbit coupling is on inverce proportion to double Einstein energy . But for semiconductor

Semiconductor

A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...

s, in nearly-free electron model

Nearly-free electron model

In solid-state physics, the nearly-free electron model is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model is closely related to the more conceptual Empty Lattice Approximation...

 it is on inverse proportion to band gap

Band gap

In solid state physics, a band gap, also called an energy gap or bandgap, is an energy range in a solid where no electron states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference between the top of the valence band and the...

 energy . Typically and , so spin-orbit coupling in solids is considerably stronger in comparison with free space. Heterostructures have asymmetric spatial zone and internal electric field distribution. It results in splitting of electron states

Density of states

In solid-state and condensed matter physics, the density of states of a system describes the number of states per interval of energy at each energy level that are available to be occupied by electrons. Unlike isolated systems, like atoms or molecules in gas phase, the density distributions are not...

 for electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s with opposite spins along axis of wave vector

Wave vector

In physics, a wave vector is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave , and its direction is ordinarily the direction of wave propagation In...

s. It is called Rashba effect. In contrast to Rashba effect splitting in external magnetic field

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

s change energies of electrons with opposite spins.

Spin-orbit coupling of Rashba type plays important role in the internal spin Hall effect.

Application

Unlike regular electronic circuitry, spintronic devices foster current based on the electron's spin, leading to much higher efficiencies as a consequence of reduced heat loss. However, spintronics is not yet ready to manufacture, mainly because manipulating spin is difficult and often requires very low temperatures. A crucial ingredient is the electric control of spin, achievable through spin-orbit interaction (SOI), which couples the electron's motion to its spin. This was demonstrated in a semiconductor (Bismuth selenide) that is far larger than has ever been seen before and could lead the way towards room-temperature spintronic devices.