Spin-orbit interactions at surfaces

In non-magnetic solids spin degeneracy of the electronic bands is a consequence of time reversal symmetry and inversion symmetry. However when inversion symmetry is broken, the degeneracy can be lifted by spin-orbit interactions. This interaction introduces a momentum-dependent effective magnetic field which separates the spin density of states in the reciprocal space. At surfaces, where translation symmetry is broken, this phenomenon is known as Rashba effect. The Rashba splitting was first evidenced in an ARPES study of the Shockley surface states of gold. It is also known to be at the origin of the peculiar properties of topological insulator.

On some peculiar materials the spin splitting is more than 10 times larger than expected by the Rashba effect. The origin of the giant spin orbit interaction at surfaces is still under debate. One of us has shown that spin selection rules control the hybridization of Rashba split states and was the first to discover a new mechanism producing giant splitting taking place at the surface of semiconductor: the Bi trimer structure on Si(111). In this system, the giant spin orbit splitting is shown to be the consequence of the peculiar band topology coupled to a standard Rashba effect. It evidences the possibility to obtain giant Rashba effect in materials with rather small spin-orbit interactions and multiplies the amount of samples being likely exhibiting giant spin-orbit interactions. Indeed, Rahsba spin-orbit splitting of various intensities was later evidenced in numerous samples consisting of a single layer at the surface of a semiconductor.

If superconductivity develops in the film, it is important to notice that Rashba interactions are expected to yield peculiar phenomena. At this point one has to notice that there is almost no experimental work done in this field while it is very promising from the theoretical point of view. Indeed, in normal superconductors, the Cooper pairs are formed of two electrons of opposite spins. The resulting quantum state is a singlet. However in superconductors with strong Rashba interaction, the parity of the superconducting state is no longer a good quantum number and Cooper pairs may be composed of a mix of spin-singlet and spin-triplet states.

References:

On giant spin-orbit interactions

1. E. Frantzeskakis et al. Tunable spin gaps in a quantum-confined geometry. Phys. Rev. Let., 101, 196805 (2008).
2. I. Gierz et al. Silicon Surface with Giant Spin Splitting. Phys. Rev. Let. 103, 046803 (2009).
3. E. Frantzeskakis, S.Pons, and M. Grioni. Band structure scenario for the giant spin-orbit splitting observed at the Bi/Si(111) interface. Phys. Rev. B 82, 085440 (2010).

On superconductivity whith Rhasba interactions

1. L. P. Gor’kov and E. I. Rashba. Superconducting 2D system with lifted spin degeneracy: Mixed single-triplet state. Phys. Rev. Lett. 87, 037004 (2001).
2. C. Brun et al. Remarkable effects of disorder on superconductivity of single atomic layers of lead on silicon, Nature Physics 10, 444–450 (2014).