Enhanced Rashba spin-orbit splitting inBi∕Ag(111)andPb∕Ag(111)surface alloys from first principles

Abstract

We present first-principles calculations of a $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ $\mathrm{Bi}∕\mathrm{Ag}(111)$-ordered surface alloy, which has recently been investigated experimentally using angle-resolved photoemission spectroscopy. The surface states in the $L$-projected bulk band gap show a Rashba-type spin-orbit splitting which is three times larger than what has been observed on a clean Bi(111) surface. This large enhancement can be explained by the strong distortion of the surface-state wave function which is caused by the substantial outward buckling of the Bi atom. Also, in a similar surface alloy, $\mathrm{Pb}∕\mathrm{Ag}(111)$, a strong Rashba-type splitting was found by our calculations. The comparison to the experimental data is more difficult due to the presence of a second, close-by surface state. We discuss the dependence of the two-dimensional band structure on the surface corrugation and compare to the experimental findings.