Spin-orbit coupling and optical detection of spin polarisation in triangular graphene quantum dots

We present a theory of the effect of spin-orbit coupling on optical properties of triangular graphene quantum dots (TGQD). TGQDs with zigzag edges exhibit a degenerate band of states at the Fermi level. For the charge neutral TGQD, the shell is expected to be half-filled by spin polarised electrons leading to finite magnetisation. Using four-band tight-binding and effective Kane-Mele models, we show that, if the TGQD is spin polarised, the low energy optical absorption spectrum reveals two distinct peaks corresponding to left and right circularly polarised light while the unpolarised TGQD shows only one peak. This allows optical detection of spin polarisation, its direction and the strength of spin-orbit coupling in TGQDs.