Upstanding Rashba spin in honeycomb lattices: Electrically reversible surface spin polarization

The spin-split states subject to Rashba spin-orbit coupling in two-dimensional systems have long been accepted as pointing inplane and perpendicular to the corresponding wave vectors. This is in general true for free-electron model, but exceptions do exist elsewhere. Within the tight-binding model, we unveil the unusual upstanding behavior of those Rashba spins around K and K-' points in honeycomb lattices. Our calculation (i) explains the recent experiment of the Tl/Si(111)-(1x1) surface alloy [K. Sakamoto , Phys. Rev. Lett. 102, 096805 (2009)], where abrupt upstanding spin states near K are observed and (ii) predicts an electrically reversible out-of-plane surface spin polarization.