Phase diagram and magnetic collective excitations of the Hubbard model for graphene sheets and layers

Peres, N. M. R.; Araújo, M. A. N.; Bozi, D.

doi:10.1103/physrevb.70.195122

Cited by 123 publications

(96 citation statements)

References 26 publications

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“…Using the same procedure as above to fix U, we find that its value decreases as the size of the islands increase. The values of U so obtained are always below the critical value U ' 2:2t ' 5:5 eV above which infinite graphene would become antiferromagnetic [12,24].…”

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confidence: 99%

Magnetism in Graphene Nanoislands

2007

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We study the magnetic properties of nanometer-sized graphene structures with triangular and hexagonal shapes terminated by zigzag edges. We discuss how the shape of the island, the imbalance in the number of atoms belonging to the two graphene sublattices, the existence of zero-energy states, and the total and local magnetic moment are intimately related. We consider electronic interactions both in a mean-field approximation of the one-orbital Hubbard model and with density functional calculations. Both descriptions yield values for the ground state total spin S consistent with Lieb's theorem for bipartite lattices. Triangles have a finite S for all sizes whereas hexagons have S 0 and develop local moments above a critical size of 1:5 nm. DOI: 10.1103/PhysRevLett.99.177204 PACS numbers: 75.75.+a, 73.20.ÿr, 75.50.Xx, 75.70.Cn The study of graphene-based field effect devices has opened a new research venue in nanoelectronics [1][2][3][4][5]. Graphene is a truly two-dimensional zero-gap semiconductor with peculiar transport and magnetotransport propreties, including the room temperatrue quantum Hall effect [6], that makes it very different from conventional semiconductors and metals [7]. Progress in the fabrication of graphene-based lower dimensional structures has been reported both in the form of one-dimensional ribbons [8,9] and zero-dimensional dots [2,7,10]. Interestingly, the electronic properties of graphene change in a nontrivial manner when going to lower dimensions. Ribbons, for instance, can be either semiconducting with a size dependent gap or metallic [8,9].The electronic structure of graphene-based nanostructures is expected to be different from bulk graphene because of surface, or, more properly, edge effects [11]. This is particularly true in the case of structures with zizzag edges which present magnetic properties [12 -14]. Whereas bulk graphene is a diamagnetic semimetal, simple tight-binding models predict that one-dimensional ribbons with zigzag edges have two flat bands at the Fermi energy [11,12,[15][16][17], i.e., are paramagnetic metals. Spin polarized density functional theory (DFT) [13] and mean-field [12] calculations confirm that these bands are prone to magnetic instabilities.The fabrication of graphene nanostructures using topbottom techniques does not permit creating atomically defined edges to date [10]. In contrast, bottom-up processing of graphene nanoislands is very promising [18]. Hexagonal shape nanoislands with well-defined zigzag edges atop the 0001 surface of Ru have already been achieved [19]. This experimental progress motivates our study of the electronic structure of graphene nanostructures with various shapes. Graphene quantum dots also hold the promise of extremely long spin relaxation and decoherence time because of the very small spin-orbit and hyperfine coupling in carbon [20].We have found that, remarkably, both the DFT calculations and the mean-field approximation of the single-band Hubbard model with first-neighbors hopping yield very similar results in all c...

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Magnetism in Graphene Nanoislands

2007

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“…Recent theoretical studies showed that intrinsic fer-romagnetism of graphene may exist [29,30,31], but it has not been observed so far. Room-temperature ferromagnetism was observed [32], but it was attribued to the presence of the defects on graphene.…”

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confidence: 99%

Tunneling conductance of graphene ferromagnet-insulator-superconductor junctions

Hsu

Guo

2010

Phys. Rev. B

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We study the transport properties of a graphene ferromagnet-insulator-superconductor (FIS) junction within the Blonder-Tinkham-Klapwijk formalism by solving spin-polarized Dirac-Bogoliubovde-Gennes equation. In particular, we calculate the spin-polarization of tunneling current at the I-S interface and invesigate how the exchange splitting of the Dirac fermion bands influences the characteristic conductance oscillation of the graphene junctions. We find that the retro and specular Andreev reflections in the graphene FIS junction are drastically modified in the presence of exchange interaction and that the spin-polarization (PT ) of tunneling current can be tuned from the positive to negative value by bias voltage (V ). In the thin-barrier limit, the conductance G of a graphene FIS junction oscillates as a function of barrier strength χ. Both the amplitude and phase of the conductance oscillation varies with the exchange energy Eex. For Eex < EF (Fermi energy), the amplitude of oscillation decreases with Eex. For E c ex > Eex > EF , the amplitude of oscillation increases with Eex, where E c ex = 2EF + U0 (U0 is the applied electrostatic potential on the superconducting segment of the junction). For Eex > E c ex , the amplitude of oscillation decreases with Eex again. Interestingly, a universal phase difference of π/2 in χ exists between the G − χ curves for Eex > EF and Eex < EF . Finally, we find that the transitions between retro and specular Andreev reflections occur at eV = |EF − Eex| and eV = Eex + EF , and hence the singular behavior of the conductance near these bias voltages results from the difference in transport properties between specular and retro Andreev reflections.

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“…However, since the DOS is very low, these peaks are small, and a very high (Hubbard) interaction is required to enter the DW regime. 10 The situation changes if we strongly dope graphene around the value μ ≈ |t|, where μ is the chemical potential and t ≈ 2.8 eV is the hopping parameter. The Fermi surface then acquires a hexagonal shape and nesting occurs in three directions (see Fig.…”

Section: Introductionmentioning

confidence: 99%

Spin-density-wave instability in graphene doped near the van Hove singularity

et al. 2011

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We study the instability of the metallic state toward the formation of a different ground state in graphene doped near the van Hove singularity. The system is described by the Hubbard model and a field theoretical approach is used to calculate the charge and spin susceptibility. We find that for repulsive interactions, within the random phase approximation, there is a competition between ferromagnetism and the spin-density wave (SDW). It turns out that a SDW with a triangular geometry is more favorable when the Hubbard parameter is above the critical value U c (T ), which depends on the temperature T , even if there are small variations in the doping. Our results can be verified by angle-resolved photoemission spectroscopy or neutron scattering experiments in highly doped graphene.

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Phase diagram and magnetic collective excitations of the Hubbard model for graphene sheets and layers

Cited by 123 publications

References 26 publications

Magnetism in Graphene Nanoislands

Magnetism in Graphene Nanoislands

Tunneling conductance of graphene ferromagnet-insulator-superconductor junctions

Spin-density-wave instability in graphene doped near the van Hove singularity

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