PHYSICAL REVIEW B 98, 205123 (2018) Screening of long-range Coulomb interaction in graphene nanoribbons: Armchair versus zigzag edges H. Hadipour, 1 , * E. ¸ Sa¸ sıo˘ glu, 2 , † F. Bagherpour, 1 C. Friedrich, 3 S. Blügel, 3 and I. Mertig 2 1 Department of Physics, University of Guilan, 41335-1914 Rasht, Iran 2 Institute of Physics, Martin Luther University Halle-Wittenberg, 06120 Halle (Saale), Germany 3 Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany (Received 21 June 2018; revised manuscript received 1 October 2018; published 14 November 2018) We study the electronic screening of the long-range Coulomb interaction in graphene nanoribbons (GNRs) with armchair and zigzag edges as a function of the ribbon width by employing ab initio calculations in conjunction with the random-phase approximation. We find that in GNRs with armchair edges quantum confinement effects lead to oscillatory behavior of the on-site screened Coulomb interaction with the ribbon width. Furthermore, the reduced dimensionality and the existence of a band gap result in a nonconventional screening of the Coulomb interaction; that is, it is screened at short distances and antiscreened at intermediate distances, and finally, it approaches the bare (unscreened) interaction at large distances. In the case of GNRs with zigzag edges the presence of edge states strongly affects the screening, which leads to a strong reduction of the effective on-site Coulomb interaction (Hubbard U ) parameters at the edge. We find that the interactions turn out to be local; the nonlocal part is strongly screened due to edge states, making GNRs with zigzag edges correlated materials. On the basis of the calculated effective Coulomb interaction parameter U , we discuss the appearance of ferromagnetism at zigzag edges of GNRs within the Stoner model. DOI: 10.1103/PhysRevB.98.205123 I. INTRODUCTION The experimental synthesis of graphene has led to a huge growth in interest in the application of carbon-based ma- terials for nanoelectronics [1–3]. Despite its extraordinary electronic and mechanical properties, graphene is not mag- netic and has no band gap, which makes it difficult to use in practical digital circuits as well as for spintronic appli- cations. Cutting graphene along particular directions, which produces graphene nanoribbons (GNRs) with armchair and zigzag edges, can change dramatically the electronic and magnetic properties of graphene [4–14]. GNRs with arm- chair edges are considered to be promising materials for low-power, high-frequency field-effect transistors due to their finite band gaps [15]. A number of spintronic devices based on spin-polarized edge states of GNRs with zigzag edges have been proposed [16–20]. Various fabrication techniques such as lithographic methods [14,21,22], unzipping of carbon nanotubes [23–26], and chemical synthesis [27–29] have been developed to produce high-quality GNRs with widths smaller than 10 nm. GNRs with armchair edges are classified into different categories depending on their electronic band structures [6,7]. The band gaps of 1–10-nm-wide armchair GNRs were found to be in the range 0.15 to 1 eV in experiment [5,6], and they decrease with increasing ribbon width [5–7]. The reduced dimensionality in GNRs with armchair edges is expected to give rise to a significant enhancement of the Coulomb * hanifhadipour@gmail.com † ersoy.sasioglu@physik.uni-halle.de interaction. The incorporation of electron-electron correlation effects within the GW approximation results in large band- gap values of about 2.5 eV in armchair GNRs of 1.5 nm width [30]. On the other hand, the interplay of reduced dimensionality and finite band gap results in nonconventional screening of the long-range part of the Coulomb interaction in low-dimensional semiconductors and insulators [31–35]. One of the consequences of such a nonconventional screening is the large exciton binding energy (as large as 1.5 eV) [36–41]. The latter was determined experimentally in armchair GNRs of 0.7–1-nm width. This value is in good agreement with ab initio calculations [31,36,39]. Nonconventional screening of the Coulomb interactions occurs also in semiconducting carbon nanotubes [33]. In spite of several theoretical studies of Coulomb interactions in two-dimensional graphene [42–49] and the experimental indication of nonconventional screening in GNRs with armchair edges, up to now there has not been a study addressing Coulomb interactions from an ab initio perspective. The existence of spin-polarized edge states in GNRs with zigzag edges makes these systems extremely important not only for technological applications but also for testing theories of magnetism for one-dimensional (quasi-one-dimensional) materials. According to the Mermin-Wagner theorem, a long- range magnetic order in one- and two-dimensional systems at finite temperatures is not possible [50]. However, theoretical studies have shown that due to the very high value of the spin- wave stiffness (D = 2100 meV Å 2 ) the spin correlation length was found to be around 1 nm at room temperature [51,52]. Recent experiments provided evidence for ferromagnetism in GNRs with zigzag edges at room temperature [5]. The presence of edge states results in a relatively large contribution 2469-9950/2018/98(20)/205123(9) 205123-1 ©2018 American Physical Society