Spin Texture Changes in Different Surfaces of Topological Insulator Bi 2 Se 3

Spin utilization and manipulation plays a key role in spintronics and magnetic devices. Systems with intrinsic spin property provide platforms of spin control. One prominent example is the topological insulator (TI) which has a nontrivial topological Z2 invariant inherited in the bulk system. Due to the bulk-edge correspondence, the TI with boundary surface has surface states whose spin has preferred direction that exhibits the great advantage to be utilized in the spintronics devices. It was experimentally confirmed that the famous three-dimensional TI Bi 2 Se 3 stacking in the (111) z direction has surface states whose spin is locked perpendicular to the momentum direction. However, this does not fully utilize the potential to manipulate the spin in TI. Actually, the bulk-edge correspondence allows different spin textures in surface states localized in different boundary surfaces. Using the ab initio calculation, we demonstrated that the spin indeed has only one allowed direction (either parallel or antiparallel) near the $\Gamma$ point in Bi2Se3 cut in surface perpendicular to (111) direction, different from the observed spin circulation around the $\Gamma$ point in (111) cut Bi2Se3. The different spin texture in different surface orientation was theoretically demonstrated in the first-order continuum model [1] and was confirmed in our full ab initio calculation. Constructing the tight binding model from finite differencing the continuum model up to third order, we also confirmed the changes in spin textures in different cut surfaces from the same bulk Hamiltonian. The localization of these surface states was also confirmed. The different spin textures resulting from different surfaces can be utilized in spin manipulation and controls in devices.