Quantitative analysis of the weak anti-localization effect in ultrathin bismuth films

Magnetic-field dependence of conductivity in ultrathin Bi films is measured in applied magnetic fields up to 9 T, in both directions, perpendicular and parallel to the film plane, at temperatures down to 0.4 K, and analyzed in terms of the weak anti-localization theory in two-dimensional systems. With the reduction of film thickness, the classical magnetoresistance effect is completely suppressed, and only the weak anti-localization effect is observed. The parameters extracted from the analysis allow the study of the contribution of the different scattering mechanisms to the electronic transport properties in ultrathin Bi films. In particular, the thickness-independent spin-orbit scattering length indicates that the spin-orbit split surface states dominate the transport in the ultrathin-film limit.