Article pubs.acs.org/JPCC
Peierls Instability and Spin Orderings of Ultranarrow Graphene Nanoribbons in Graphane Hyun-Jung Kim,† Sangchul Oh,‡ Chaggan Zeng,§,∥ and Jun-Hyung Cho*,† †
Department of Physics and Research Institute for Natural Sciences, Hanyang University, 17 Haengdang-Dong, Seongdong-Ku, Seoul 133-791, South Korea ‡ Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260-1500, United States § Hefei National Laboratory for Physical Science at Microscale and Department of Physics, University of Science and Technology of China, 96 JinZhai Road, Hefei, Anhui 230026, China ∥ ICQD, University of Science and Technology of China, Hefei, Anhui, 230026, China ABSTRACT: Narrow graphene nanoribbons are a promising channel material for field-effect transistors. Here, using firstprinciples density functional calculations, we investigate the competition between Peierls instability and spin orderings in zigzag graphene nanoribbons carved in a fully hydrogenated graphene (graphane) as a function of their width N (the number of zigzag C chains composing a nanoribbon). We find that such a nanoribbon with N = 1 undergoes a Peierls instability caused by a strong electron−lattice coupling, leading to a band-gap opening. For N ≥ 2, the Peierls instability is significantly weakened or disappears because of the interaction of zigzag C chains, whereas a ferromagnetic spin ordering on each side is stabilized by the formation of the localized edge states. We find that the spins on both sides are further stabilized with their antiparallel alignments, accompanying the band gap opening. Therefore, ultranarrow zigzag graphene nanoribbons carved in graphane are semiconducting as a consequence of a Peierls instability or an antiferromagnetic spin ordering between the two edges which is useful for the application of field-effect transistors.
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INTRODUCTION Graphene has attracted much attention because of its unique massless Dirac fermion-like electronic structure, which may be utilized for potential applications in electronic devices.1−4 However, the absence of a band gap in graphene indicates low on−off ratios in the performance of field-effect transistors.4 There have been several attempts to open a band gap in graphene not only by using substrates,5 impurities,6−8 and vacancies9,10 but also with the formation of nanoribbons11−13 and quantum dots.14 In particular, graphene nanoribbons carved in a fully hydrogenated graphene (viz. graphane; see Figure 1a) represent one of the most promising strategies for graphene nanoelectronics.15,16 Such graphene nanoribbons with widths of a few C chains (see Figure 1b−d) can be realized by the selective removal of hydrogen atoms using the scanning tunneling microscope nanolithography, laser heating, or electron-beam irradiation techniques.17−20 Because of their excellent switching speed and high carrier mobility, the ultranarrow graphene nanoribbons are anticipated to be applicable to the field-effect transistors.21 Unlike a pristine graphene with a zero band gap, graphene nanoribbons with zigzag edges carved in graphane (termed ZGNR′, where a “prime” distinguishes from a similar acronym of ZGNR synthesized by cutting the graphene sheets and passivating the edge carbon atoms by hydrogen) were predicted © 2012 American Chemical Society
to have a band gap opening due to magnetic effects or Peierls instability.22−25 Therefore, the ZGNR′ with a narrow width represents a quasi 1D structure that shows a complex interplay between charge, lattice, and spin degrees of freedom. As a matter of fact, owing to their confinement of electrons within only one direction, 1D systems are known to exhibit a variety of exotic physical phenomena such as Peierls instability,26 spin orderings,27 and the formation of non-Fermi-liquid ground states.28 There are several first-principles density functional theory (DFT) calculations for the structural and electronic properties of ZGNR′s.22−25 Using the generalized gradient approximation with the Perdew−Burke−Ernzerhof (PBE) exchange-correlation functional,29 Singh and Yakobson22 found that the ZGNR′s with N = 1 and 2 (N is the number of zigzag C chains comprising ZGNR′; see Figure 1) are nonmagnetic (NM) with a negligible gap opening, whereas the ZGNR′s with N ≥ 3 have an antiferromagnetic (AFM) ground state that slightly favors over the ferromagnetic (FM) state. Here the AFM (FM) state with an antiferromagnetic (ferromagnetic) coupling between the two ferromagnetic edges is semiconducting (metallic). Received: March 21, 2012 Revised: May 10, 2012 Published: June 6, 2012 13795
dx.doi.org/10.1021/jp302733p | J. Phys. Chem. C 2012, 116, 13795−13799
The Journal of Physical Chemistry C
Article
width of ZGNR′s, consistent with previous DFT calculations for ZGNR33,34 and ZGNR′.22−25
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CALCULATION METHOD We perform a first-principles DFT calculation using numerical atom-centered orbital (NAO) basis functions within the generalized-gradient approximation (GGA). We use the PBE exchange-correlation functional for the GGA. The present NAO-based all-electron full-potential calculations have been performed using the FHI-aims package.35 The simulations of ZGNR′s were employed using a periodic supercell with an inplane unitcell length of 26.4 Å, large enough to avoid the spurious interactions with the periodic images. For the Brillouin zone integration, we use 128 k points in the surface Brillouin zone. All of the atoms are allowed to relax along the calculated forces until all the residual force components are
