Electronic origin of the surface reconstruction of the (001) surface of Cr,Mo and W

The d-band effects on the reconstruction of the (001) surface of Cr, Mo and W are discussed with a tight-binding model. Response functions corresponding to some models for the reconstruction and their q-dependence are calculated by using Haydrock et al.'s recursion method. The present calculation shows that an energy gain by broadening the surface state peak near the Fermi energy is most remarkable for the model proposed by Debe and King, and therefore gives a theoretical support to it. The energy gain is attributed to an enhancement in the bonding property by pairing of surface atoms in the Debe and King model. Response functions without an electron-phonon matrix element (EPME) are also calculated, which show only a very weak q-dependence. Detailed discussions are given on the mode dependence, that is, on the effect of EPME.