Screening of long-range Coulomb interaction in graphene nanoribbons: Armchair versus zigzag edges

Abstract

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.

Magnetic, charge, and transport properties of graphene nanoflakes

“…However, it is well-known that the long-range part of the electron-electron Coulomb interaction is not screened in single-layer graphene. This suggests that the interactions beyond nearest neighbor distance can also have a crucial impact on physics of graphene nanosystems, which is confirmed by ab initio calculations [40]. Although there are several papers focused on investigating the effects of long-range interaction in graphene nanoflakes beyond the nearest-neighbor interactions [9,34,[41][42][43], most of them are limited to the 1/r [41,42] or 1/ √ r 2 + a 2 [34] dependence of non-local potential on distance r, the parameter a accounts for finite radius of graphene π orbitals.…”

Ground-state properties of the narrowest zigzag graphene nanoribbon from quantum Monte Carlo and comparison with density functional theory

“…We can conclude that the PBE+U functional with U=5.0 eV is the best among all the DFT functionals reported in this work, in terms of geometry, electron localization, magnetic moment, and AFM stabilization energy. The optimal U repulsion strength in PBE+U is in a very good agreement with its cRPA-PBE determination 35 , and with a previous estimate based on the measured magnitude of ZGNR gaps and on the semiconductor-metal transition ZGNR width, found experimentally 12 . Hence, it would be rather safe to extend the use of PBE+U from 2-ZGNR to computing materials properties of analogous C-based systems, with a graphene pattern: nanotubes, nanoribbons, graphene impurities with doping and magnetism.…”

“…Thus, we relaxed the geometry within DFT+U at a given U value and we then computed the final corresponding M. In this way, we found U=5.0 eV (U=7.6 eV) as optimal value in PBE+U (LDA+U). Interestingly enough, these values are fully in range with those predicted by restricted random phase approximation (cRPA) calculations 35 of ZGNRs, further strengthening our procedure. Indeed, sitespecific cRPA estimates of the local U repulsion, based on the same PBE functional, show a reduction from the "bulk" value of graphene (U=9.3 eV) 32,34 to the edge value of ≈ 5 eV, in nice agreement with our findings.…”

“…Various other attempts have been made to model strong correlations in graphene and graphene derivatives using Hubbard Hamiltonians 29,30 on a honeycomb lattice. However, a relevant question still debated in this framework is about the correct value of Hubbard U repulsion one has to use to reproduce the physics taking place in a more realistic setting [31][32][33][34][35] . At variance with model Hamiltonian approaches 36 , which suffer from this issue, our QMC framework includes electron correlations entirely from first principles.…”

Strength of effective Coulomb interaction in two-dimensional transition-metal Halides MX$_2$ and MX$_3$ (M=Ti, V, Cr, Mn, Fe, Co, Ni; X=Cl, Br, I)

“…From a theoretical point of view, according to the Mermin-Wagner theorem [7], long-range magnetic order is not possible in 2D systems at finite temperatures, but this restriction is removed by magnetic anisotropy, which enables the formation of long-range magnetic order even in monolayers. Several standard approaches such as adsorption of atoms [8][9][10][11][12], point defects [13][14][15][16][17], and edge engineering [18][19][20][21][22] were developed to induce ferromagnetism in graphene and other graphene-like 2D materials. But these systematic ways are not well controlled for realistic applications.…”