The Rashba effect can arise in a crystal lacking inversion symmetry—inversion symmetry is invariance of an object after reflection around a point—as spin up and spin down electrons separate into different conduction bands—”lifting the spin degeneracy of conduction band electrons at finite momentum,” they write.
Now a spin-orbit coupling that had previously been neglected is found to possibly be strong enough to give rise to an unconventional type of superconductivity in certain materials. The study by Yasha Gindikin and Alex Kamenev of the University of Minnesota is published in Physical Review B.
An inversion asymmetry is no longer necessary. “This key insight—that the electric field… can arise from the Coulomb forces—opens up an entirely new research avenue,” the co-authors write. The Coulomb fields can reach magnitudes as high as 100 million volts per centimeter.
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The Rashba spin-orbit coupling allows a way to control spin states using electrical rather than magnetic means. It has been crucial to the development of “spintronics,” electronics based on the spin of the electron, and was the basis for the proposal of the spin transistor.
It’s small at a low atomic number, due to the square of the fine structure constant (≈ 1/137) but becomes significant when the atomic number is large. It’s especially strong when the spin and the angular momentum (regular angular momentum, not spin angular momentum) point in the same direction, and zero when they are perpendicular.
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In particular, they propose that in certain materials, this pair spin-orbit interaction can be strong enough to give rise to an unconventional form of superconductivity. The spin-orbit coupling can cause electrons to pair up, much like Cooper pairs, and produce a superconducting state with odd parity.
The neglected coupling is from the Rashba effect, due to the combined effect of a spin–orbit interaction and asymmetry of the crystal’s potential, resulting in a force perpendicular to a two-dimensional plane. (The effect was first discovered in three dimensions in 1959.)
So, when an electron moves in the electric field of another electron, this special relativistic effect results in the moving electron interacting with a magnetic field, and hence with the electron’s spin angular momentum.
The “Rashba spin-orbit coupling of conduction band electrons, a result of the band mixing with spin-orbit-split valence bands, manifests itself in electron-electron interaction effects.”
