Using first-principles calculations, we identify a robust R30° reconstruction of a Si3 trimer bilayer on the Si(111) surface with a La coverage of 2/3 monolayer. Each surface unit cell contains two Si3 trimers and two La atoms, where the upper Si3 trimer is located just above the lower one with a rotation of about 60°, while two La atoms with different heights are distributed between the Si3 trimers and located on the T4 top site of the Si(111) surface, forming a honeycomb-like network structure. We find that the two La atoms have different valence states, La2+ and La3+, respectively. The high structural stability is attributed to the lower La atom saturating all the three dangling bonds of the upper Si3 trimer, while the higher La atom compensates two electrons to the lower Si3 trimer. The electronic band structure and band-decomposed charge density distribution show a semiconducting characteristic with a small surface band gap of 42 meV. Moreover, simulated STM images show a good structural match with the recent experimental observations.
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