Magnetoconductance in epitaxial bismuth quantum films: Beyond weak (anti)localization

Abstract

The complex behavior of magnetoconductance of Bi films grown epitaxially on Si(111) with a thickness of 20--100 bilayers (BL) was measured at $T$= 9 K in magnetic fields up to $B=4\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, oriented in-plane parallel and perpendicular to the electric dc current $I$. Contributions to magnetoconductance (MC) by diffuse scattering, by weak localization (WL) as well as by weak antilocalization (WAL) were identified. All these components to MC turned out to be isotropic in two dimensions, i.e., no dependence on angle between $B$ and $I$ within the surface plane was found. Only for $B\phantom{\rule{0.16em}{0ex}}\ensuremath{\perp}\phantom{\rule{0.16em}{0ex}}I$ an increase of MC was detected that is, to first approximation, $\ensuremath{\propto}{B}^{2}$. It is ascribed to ballistic scattering between the Rashba-split interfaces that allow Umklapp scattering without spin flip. While MC within the surface states, dominant at small thicknesses, $d$, shows negligible diffuse scattering under the chosen geometry, their quantum corrections are characterized by WAL with $\ensuremath{\alpha}=\ensuremath{-}0.3$ and a coupling strength that decays $\ensuremath{\propto}1/d$ with layer thickness. The admixing of quantized bulk states, which dominates MC above 50 BL, not only increases diffuse scattering, it introduces WL in combination with WAL. Presumably due to hybridization with the surface states, it also modifies strongly the WAL component for $d>60$ BL. Thus our findings suggest an intriguing interplay in magnetotransport between 2D and quantized 3D states at the Fermi surface of ultrathin bismuth quantum films and provide further deep insight into the electronic transport in quantized and partly spin split bands.