Exchange driven dimerization, band gap, and magnetism of diamond(111) surface from first principles

Strong electron-electron interaction in ultraflat edge states can be responsible for correlated phases of matter, such as magnetism, charge density wave or superconductivity. The diamond(111) surface, after Pandey reconstruction, presents zig-zag carbon chains, generating a very flat surface band. More than 100 years after Bragg determined the structure of bulk diamond, the structure of the (111) surface of diamond is still controversial. Full structural optimization using hybrid density functionals with exact exchange shows that a substantial dimerization occurs on the Pandey π-chains — that is the primary mechanism for the opening of an insulating gap. This effect is absent in standard functionals. The exchange interaction further stabilizes a ferrimagnetic order along the Pandey π-chains with magnetic moments of 0.27 μB, opening a direct band gap of ~1.4 eV, in agreement with experiments. Our work is relevant for systems with flat bands in general and wherever the interplay between structural and electronic degrees of freedom is crucial, as in twisted bilayer graphene, IVB atoms on IVB(111) surfaces such as Pb/Si(111) or molecular crystals.