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Low-dimensional electron systems often show a delicate interplay betweenelectron-phonon and electron-electron interactions, giving rise to interestingquantum phases such as the charge density wave (CDW) and magnetism. Using thedensity-functional theory (DFT) calculations with the semilocal and hybridexchange-correlation functionals as well as the exact-exchange plus correlationin the random-phase approximation (EX + cRPA), we systematically investigatethe ground state of the metallic atom wires containing dangling-bond (DB)electrons, fabricated by partially hydrogenating the GaN(10${\overline{1}}$0)and ZnO(10${\overline{1}}$0) surfaces. We find that the CDW orantiferromagnetic (AFM) order has an electronic energy gain due to a band-gapopening, thereby being more stabilized compared to the metallic state. Oursemilocal DFT calculation predicts that both DB wires inGaN(10${\overline{1}}$0) and ZnO(10${\overline{1}}$0) have the same CDW groundstate, whereas the hybrid DFT and EX+cRPA calculations predict the AFM groundstate for the former DB wire and the CDW ground state for the latter one. It isrevealed that more localized Ga DB electrons in GaN(10${\overline{1}}$0) preferthe AFM order, while less localized Zn DB electrons in ZnO(10${\overline{1}}$0)the CDW formation. Our findings demonstrate that the drastically differentground states are competing in the DB wires created on the two representativecompound semiconductor surfaces.

Competing charge density wave and antiferromagnetism of metallic atom wires in GaN(10${\overline{1}}$0) and ZnO(10${\overline{1}}$0)