Relativistic electronic structure of the Pb (001) surface

Abstract

The surface electronic band structure of the Pb (001) was calculated using the self-consistent, first-principles linear-augmented-plane-wave method and the norm-conserving pseudopotentiai method. In the nonrelativistic case, forbidden gaps appear above and below the Fermi levelin the bulk projected band structure of lead. An occupied surface state at the$\overline M$ point and two surface states in a wide forbidden gap above E_F are found. A characteristic feature of the electronic structure of the Pb (001) surface is the absence of a surface state within the forbidden S-P gap in the vicinity of the$\overline \Gamma$ point. The inclusion of scalar-relativistic effects leads to the merger of several S-P gaps into one wide gap extending throughout the entire Brillouin zone. At the same time, the occupied state at point$\overline M$ extends to point$\overline X$ and its energy decreases by 2 eV. New, relatively weak surface states in the$\overline {XM}$ direction and unoccupied states in the vicinity of the$\overline \Gamma$ point appear. An unoccupied surface state is found at the bottom of the forbidden gap at point$\overline M$. Including the contribution of the spinorbit pseudopotentiai leads to the appearance of two-spin orbit gas; however, the surface level structure is practically unchanged (except for the disappearance of the unoccupied surface state of P_z-symmetry at point$\overline M$).