Quantum Monte Carlo studies of edge magnetism in chiral graphene nanoribbons

Abstract

We investigate chiral graphene nanoribbons using projective quantum Monte Carlo simulations within the local Hubbard model description and study the effects of electron-electron interactions on the electronic and magnetic properties at the ribbons' edges. Static and dynamical properties are analyzed for nanoribbons of varying width and edge chirality, and compared to a self-consistent Hartee-Fock mean-field approximation. Our results show that for chiral ribbons of sufficient width, the spin correlations exhibit exceedingly long correlation lengths, even between zigzag segments that are well separated by periodic armchair regions. Characteristic enhancements in the magnetic correlations for distinct ribbon widths and chiralities are associated with energy gaps in the tightbinding limit of such ribbons. We identify specific signatures in the local density of states and lowenergy modes in the local spectral function which directly relate to enhanced electronic correlations along graphene nanoribbons. These signatures in the local density of states might be accessed by scanning tunneling spectroscopy on graphene nanoribbons.

Room-temperature magnetic order on zigzag edges of narrow graphene nanoribbons

“…For z-GNRS narrower than 7 nm a fairly large bandgap of about 200 -300 meV has been observed. As discussed above, the broadly predicted origin of bandgap opening in zigzag ribbons are electronelectron interactions and so far the only predicted many-body ground state implies the magnetization of the edges 16,18,19 .However, in contrast to first principles theoretical predictions 16 the measured gap suddenly vanishes for zigzag ribbons wider than 8 nm. We attribute this discrepancy to the fact that these calculations have been performed at zero temperature and without doping, while the experimental data has been acquired at room temperature and finite doping (E F  +50 -+100 meV, see Extended data: Fig.…”

“…This enables us to detect the signature of edge magnetism on individual graphene nanostructures by investigating their electronic structure, as directly measuring magnetic signals would require a macroscopic amount of such ribbons. The edge-state magnetism and the associated bandgap opening in zigzag ribbons is consistently predicted by various theoretical models, including first principles DFT 16 , mean-field theory based Hubbard 18 and Quantum Monte Carlo calculations 19 , indicating that the edge-magnetism is a robust property of z-GNRs, not sensitive to the specific details of the models. However, the stability of the magnetic order on real graphene edges and experimental conditions is strongly debated.…”

“…For z-GNRS narrower than 7 nm a fairly large bandgap of about 200 -300 meV has been observed. As discussed above, the broadly predicted origin of bandgap opening in zigzag ribbons are electronelectron interactions and so far the only predicted many-body ground state implies the magnetization of the edges 16,18,19 .…”

“…Though the 4 magnetic order is expected to persist to some extent on zigzag segments of randomly oriented graphene edges, the mixing of different edge types are expected to substantially weaken the effect 19,22 . Therefore, the lack of experimental control over the edge orientation seems one of the main reasons that the magnetic graphene edge states consistently predicted by various theoretical models remained experimentally so elusive.…”

Electronic Transport and Optical Properties of Graphene

“…[1,2] This particular material offers an excellent system for studying two-dimensional (2D) physical properties, such as the quantum Hall effects, [3][4][5][6][7][8][9][10][11][12][13][14][15] and these properties could be preliminarily comprehended by the energy dispersion (or called energy band structure), which can directly reflect the main features of electronic properties. In the low-energy region of bands.…”