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.