In certain materials an electron’s – its built-in magnetic direction – is tied to the it sits in: flip one and you flip the other. Each valley responds only to light whose waves corkscrew one way – clockwise or anticlockwise – so both can be addressed with light.
Going deeper
In a monolayer without an inversion centre, spin–orbit coupling splits the valence band by hundreds of millielectronvolts, with opposite spin ordering in the two valleys. Spin and valley are then not independent labels – fixing one fixes the other.
Why spin and valley stop being separate
A monolayer of a -stacked has no centre of inversion, unlike its bulk crystal. from the heavy metal atom is then free to split the bands, and it does so most strongly at the edges at the Brillouin zone corners, by a few hundred millielectronvolts, growing with the mass of the metal. The splitting is out of plane, so the spin states are up or down relative to the sheet rather than tilted.
then forces the rest. It maps the K valley onto K′ while flipping spin, so whichever spin is uppermost in the valence band at K must be lowermost at K′. Spin and valley become two names for one degree of freedom: a hole at the top of the valence band in the K valley has a definite spin, and the only way to change that spin is to move it to the other valley.
What follows from the locking
The first consequence is optical. Interband transitions at K and K′ couple to opposite circular polarisations, so a beam of σ+ light creates carriers in one valley only, and the polarisation of the light that comes back reports which valley they are in. That makes the valley index addressable with a lamp rather than a magnet, which is the whole appeal of valleytronics.
The second is protection. Flipping the spin alone is forbidden, because it would put the carrier at an energy that does not exist in that valley; flipping the valley alone is equally forbidden. Both have to change together, which requires a scattering event that supplies both a large momentum and a spin flip, so both spin and valley polarisation live longer than either would alone. The and spin then appear together, for alike. The same locking is what protects against in-plane magnetic fields.
Where it leaks
The protection is real but partial, and the distinction that matters is between and resident carriers. A bright exciton has an electron and a hole whose couples the two valleys directly, and that mechanism depolarises excitons within picoseconds – which is why measured valley polarisation in depends strongly on how far above the gap the sample is excited, and is much better in WSe2 than in MoS2. Resident carriers, and localised or , keep their valley much longer.
Intervalley provide the other leak, and they become more available as the sample warms, which is why room-temperature valley polarisation is modest in most monolayers. A quoted valley polarisation is therefore only meaningful together with the temperature, the excitation energy and whether it refers to excitons or carriers.
For specialists
In TMDC monolayers, spin–orbit coupling and symmetry tie the spin of band-edge states to their valley.