Detection of current induced spin polarization in epitaxial Bi₂Te₃ thin film

For Rashba 2DEG formed on the surface of a Bi₂Se₃ film with band bending of 0.13 eV over 20 nm distance,²⁴ the splitting $Δk$ was calculated to be $0.004 Å−1$ which corresponds to $λ=(ℏΔk/2m*)=1.7×104$ m/s, assuming $m*$ in Bi₂Se₃ is 0.13 times the free electron mass.²⁵ To compare, the value of $vF=5×105$ m/s in Bi₂Se₃ and $vF=4×105$ m/s in Bi₂Te₃.^1–3 

The spin relaxation time of the TI SS is typically in the order of 0.01–0.1 ps,²⁹ same as the momentum scattering timescale.³³ 

Assuming two 2D surface states and at least two degenerate quasi-2D (because of our thin film) bulk states being populated, i.e., at least 4 states being filled, an upper limit of k_F is estimated from the carrier concentration n_c using $kF=πnc$⁠.