arXiv:1709.10251v2 [cond-mat.mtrl-sci] 2 Dec 2017 Competing charge density wave and antiferromagnetism of metallic atom wires in GaN(10 10) and ZnO(10 10) Yoon-Gu Kang, Sun-Woo Kim, and Jun-Hyung Cho * Department of Physics and Research Institute for Natural Sciences, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul, 133-791, Korea (Dated: July 29, 2018) Low-dimensional electron systems often show a delicate interplay between electron-phonon and electron- electron interactions, giving rise to interesting quantum phases such as the charge density wave (CDW) and magnetism. Using the density-functional theory (DFT) calculations with the semilocal and hybrid exchange- correlation functionals as well as the exact-exchange plus correlation in the random-phase approximation (EX + cRPA), we systematically investigate the ground state of the metallic atom wires containing dangling-bond (DB) electrons, fabricated by partially hydrogenating the GaN(10 10) and ZnO(10 10) surfaces. We find that the CDW or antiferromagnetic (AFM) order has an electronic energy gain due to a band-gap opening, thereby being more stabilized compared to the metallic state. Our semilocal DFT calculation predicts that both DB wires in GaN(10 10) and ZnO(10 10) have the same CDW ground state, whereas the hybrid DFT and EX+cRPA calculations predict the AFM ground state for the former DB wire and the CDW ground state for the latter one. It is revealed that more localized Ga DB electrons in GaN(10 10) prefer the AFM order, while less localized Zn DB electrons in ZnO(10 10) the CDW formation. Our findings demonstrate that the drastically different ground states are competing in the DB wires created on the two representative compound semiconductor surfaces. I. INTRODUCTION Due to the confinement of electrons in low-dimensional structures, there have been many interesting quantum phases such as charge density wave (CDW) 1–4 , magnetism 5,6 , and non-Fermi-liquid ground states 7,8 . Specifically, the CDW is usually driven by the Fermi surface nesting or the strong coupling between an electron charge modulation and a peri- odic lattice distortion 1,2 . Meanwhile, magnetism is associ- ated with the strong electron-electron magnetic interactions 9 . These two macroscopic quantum condensates indeed repre- sent the competing interplay between electron-phonon and electron-electron interactions, which can occur frequently in one-dimensional (1D) electron systems 10 . To realize 1D electron systems, the adsorption of metal atoms on semiconductor surfaces has been widely em- ployed 4,5 . For example, the In wires on Si(111) 4 and Au wires on Si(553) 5 have offered unique playgrounds to search for the CDW and antiferromagnetic (AFM) orders, respectively. In contrast with such quasi-1D systems that feature atomic wires of several-atom width, a variant of hydrogen resist STM nano- lithography technique, termed feedback controlled lithogra- phy 11–13 , has been used to generate a quasi-1D wire composed of dangling-bond (DB) electrons by selectively removing H atoms from an H-passivated Si(001) surface along one side of an Si dimer row 14–19 . For this one-atom-wide Si DB wire, first-principles density-functional theory (DFT) calculations showed that the the Peierls-instability-driven CDW formation and the AFM spin ordering can be competing with respect to the wire length 19 . Meanwhile, similarly fabricated DB wires on the H-passivated C(001) and Ge(001) surfaces were the- oretically predicted to have different ground states with the AFM and CDW orders, respectively 20 . It is thus most likely that the AFM or CDW ground state can be determined de- pending on the different degrees of localization of the 2 p,3 p, and 4 p DB electrons in these C, Si, and Ge wires, respec- tively 20 . Recently, Zhao et al . 21 proposed a way to fabricate one- atom-wide metal wires on the H-passivated (10 10) surface of wurtzite semiconductors. They found that, as tempera- ture increases, H atoms bonding to the surface Ga and Zn atoms can be selectively desorbed from the fully H-passivated GaN(10 10) and ZnO(10 10) surfaces, respectively. The result- ing Ga and Zn DB wires are hereafter denoted as GaN(10 10)- 1H and ZnO(10 10)-1H, respectively. Using the DFT calcu- lations with the generalized-gradient approximation (GGA) functional of Perdew and Wang (PW) 22 , Zhao et al . 21 pre- dicted that the metallic 1×1 structure of these DB wires is unstable against Peierls distortion, leading to an insulating CDW ground state. Subsequently, more accurate schemes with the hybrid DFT and the exact-exchange plus correlation in the random-phase approximation (EX + cRPA) were em- ployed to show that GaN(10 10)-1H has the AFM ground state rather than the CDW formation 23 . Thus, it has been discussed that GaN(10 10)-1H and ZnO(10 10)-1H exhibit the competi- tion between the AFM and CDW orders depending on the dif- ferent localizations of Ga and Zn DB electrons 23,24 . In this paper, we systematically investigate the ground states of GaN(10 10)-1H and ZnO(10 10)-1H by using the semilocal (or GGA) and hybrid DFT calculations as well as the EX + cRPA. We find that GGA predicts the CDW ground state for GaN(10 10)-1H and ZnO(10 10)-1H, in good agree- ment with a previous GGA calculation 21 . However, both the hybrid DFT and EX + cRPA schemes predict the AFM and CDW ground states for GaN(10 10)-1H and ZnO(10 10)-1H, respectively. Our electronic-structure analysis shows that the DB electronic state in GaN(10 10)-1H is relatively more local- ized than that in ZnO(10 10)-1H. These different degrees of localization of the DB electrons between GaN(10 10)-1H and ZnO(10 10)-1H invoke the interplay of electron-electron and electron-phonon interactions, thereby leading to the AFM or- der and the CDW formation, respectively. These contrasting ground states of GaN(10 10)-1H and ZnO(10 10)-1H are antic- ipated to be a promising perspective in designing nanoelec- Typeset by REVT E X