High-order reconstructions of the Ge(100) surface

We have performed ab initio density-functional calculations of total energies of the Ge(100) surface to compare the ground states of (2×{}1), c(4×{}2), p(2×{}2), and p(4×{}1) symmetry dimer reconstructions. We find that p(2×{}2) and c(4×{}2) are the lowest-energy reconstructions and are nearly degenerate in energy. From these ab initio total energies, we compute the coupling constants for a model Hamiltonian for the surface and predict the phase-transition temperature from either an ordered c(4×{}2) or p(2×{}2) state to a disordered buckled b(2×{}1) state.