Investigating the influence of surfactants on the stabilization of aqueous reduced graphene oxide dispersions and the characteristics of their composite films

The stabilization of reduced graphene oxide (RGO) sheets in aqueous dispersion using a wide range of surfactants of anionic, non-ionic and zwitterionic type has been investigated and compared under different conditions of pH, surfactant and RGO concentration, or sheet size. The observed differences in the performance of the surfactants were rationalized on the basis of their chemical structure (e.g., alkylic vs. aromatic hydrophobic tail or sulfonic vs. carboxylic polar head), thus providing a reference framework in the selection of appropriate surfactants for the processing of RGO suspensions towards particular purposes. RGO-surfactant composite paper-like films were also prepared through vacuum filtration of the corresponding mixed dispersions and their main characteristics were investigated. The composite paper-like films were also electrochemically characterized. Those prepared with two specific surfactants exhibited a high capacitance in relation to their surfactant-free counterpart.

Coherent transport in graphene nanoconstrictions

We study the effect of a structural nanoconstriction on the coherent transport properties of otherwise ideal zigzag-edged infinitely long graphene ribbons. The electronic structure is calculated with the standard one-orbital tight-binding model and the linear conductance is obtained using the Landauer formula. We find that, since the zero-bias current is carried in the bulk of the ribbon, this is very robust with respect to a variety of constriction geometries and edge defects. In contrast, the curve of zero-bias conductance versus gate voltage departs from the (2n+1)e2∕h staircase of the ideal case as soon as a single atom is removed from the sample. We also find that wedge-shaped constrictions can present nonconducting states fully localized in the constriction close to the Fermi energy. The interest of these localized states in regards to the formation of quantum dots in graphene is discussed.

Electronic structure of gated graphene and graphene ribbons

We study the electronic structure of gated graphene sheets. We consider both infinite graphene and finite width ribbons. The effect of Coulomb interactions between the electrically injected carriers and the coupling to the external gate are computed self-consistently in the Hartree approximation. We compute the average density of extra carriers n2D, the number of occupied subbands, and the density profiles as a function of the gate potential Vg. We discuss quantum corrections to the classical capacitance and we calculate the threshold Vg above which semiconducting armchair ribbons conduct. We find that the ideal conductance of perfectly transmitting wide ribbons is proportional to the square root of the gate voltage.

Performance limits of graphene-ribbon field-effect transistors

The performance of field effect transistors based on an single graphene ribbon with a constriction and a single back gate are studied with the help of atomistic models. It is shown how this scheme, unlike that of traditional carbon-nanotube-based transistors, reduces the importance of the specifics of the chemical bonding to the metallic electrodes in favor of the carbon-based part of device. The ultimate performance limits are here studied for various constriction and metal-ribbon contact models. In particular, we show that, even for poorly contacting metals, properly tailored constrictions can give promising values for both the on conductance and the subthreshold swing.

Prediction of hidden multiferroic order in graphene zigzag ribbons

An electronic phase with coexisting magnetic and ferroelectric order is predicted for graphene ribbons with zigzag edges. The electronic structure of the system is described with a mean-field Hubbard model that yields results very similar to those of density functional calculations. Without further approximations, the mean-field theory is recasted in terms of a BCS wave function for electron-hole pairs in the edge bands. The BCS coherence present in each spin channel is related to spin-resolved electric polarization. Although the total electric polarization vanishes, due to an internal phase locking of the BCS state, strong magnetoelectric effects are expected in this system. The formulation naturally accounts for the two gaps in the quasiparticle spectrun, Δ0 and Δ1, and relates them to the intraband and interband self-energies.

Vacancy-induced magnetism in graphene and graphene ribbons

We address the electronic structure and magnetic properties of vacancies and voids both in graphene and graphene ribbons. By using a mean-field Hubbard model, we study the appearance of magnetic textures associated with removing a single atom (vacancy) and multiple adjacent atoms (voids) as well as the magnetic interactions between them. A simple set of rules, based on the Lieb theorem, link the atomic structure and the spatial arrangement of the defects to the emerging magnetic order. The total spin S of a given defect depends on its sublattice imbalance, but some defects with S=0 can still have local magnetic moments. The sublattice imbalance also determines whether the defects interact ferromagnetically or antiferromagnetically with one another and the range of these magnetic interactions is studied in some simple cases. We find that in semiconducting armchair ribbons and two-dimensional graphene without global sublattice imbalance, there is a maximum defect density above which local magnetization disappears. Interestingly, the electronic properties of semiconducting graphene ribbons with uncoupled local moments are very similar to those of diluted magnetic semiconductors, presenting giant Zeeman splitting.

Hydrogenated graphene nanoribbons for spintronics

We show how hydrogenation of graphene nanoribbons at small concentrations can open venues toward carbon-based spintronics applications regardless of any specific edge termination or passivation of the nanoribbons. Density-functional theory calculations show that an adsorbed H atom induces a spin density on the surrounding π orbitals whose symmetry and degree of localization depends on the distance to the edges of the nanoribbon. As expected for graphene-based systems, these induced magnetic moments interact ferromagnetically or antiferromagnetically depending on the relative adsorption graphene sublattice, but the magnitude of the interactions are found to strongly vary with the position of the H atoms relative to the edges. We also calculate, with the help of the Hubbard model, the transport properties of hydrogenated armchair semiconducting graphene nanoribbons in the diluted regime and show how the exchange coupling between H atoms can be exploited in the design of novel magnetoresistive devices.

Spin-orbit interaction in curved graphene ribbons

We study the electronic properties of electrons in flat and curved zigzag graphene nanoribbons using a tight-binding model within the Slater Koster approximation, including spin-orbit interaction. We find that a constant curvature across the ribbon dramatically enhances the action of the spin-orbit term, strongly influencing the spin orientation of the edge states: Whereas spins are normal to the surface in the case of flat ribbons, this is no longer the case for curved ribbons. This effect is very pronounced, the spins deviating from the normal to the ribbon, even for very small curvature and a realistic spin orbit coupling of carbon. We find that curvature results also in an effective second neighbor hopping that modifies the electronic properties of zigzag graphene ribbons. We discuss the implications of our findings in the spin Hall phase of curved graphene ribbons.

Interplay between sublattice and spin symmetry breaking in graphene

We study the effect of sublattice symmetry breaking on the electronic, magnetic, and transport properties of two-dimensional graphene as well as zigzag terminated one- and zero-dimensional graphene nanostructures. The systems are described with the Hubbard model within the collinear mean field approximation. We prove that for the noninteracting bipartite lattice with an unequal number of atoms in each sublattice, in-gap states still exist in the presence of a staggered on-site potential ±Δ/2. We compute the phase diagram of both 2D and 1D graphene with zigzag edges, at half filling, defined by the normalized interaction strength U/t and Δ/t, where t is the first neighbor hopping. In the case of 2D we find that the system is always insulating, and we find the Uc(Δ) curve above which the system goes antiferromagnetic. In 1D we find that the system undergoes a phase transition from nonmagnetic insulator for Ugraphene ribbon electrodes connected to a finite length armchair ribbon and we find a strong spin filter effect.

Impurity states in the quantum spin Hall phase in graphene

Two-dimensional insulators with time-reversal symmetry can have two topologically different phases, the quantum spin Hall and the normal phase. The former is revealed by the existence of conducting edge states that are topologically protected. Here we show that the reaction to impurity, in bulk, is radically different in the two phases and can be used as a marker for the topological phase. Within the context of the Kane-Mele model for graphene, we find that strictly normalizable in-gap impurity states only occur in the quantum spin Hall phase and carry a dissipationless current whose chirality is determined by the spin and pseudospin of the residing electron.

Magnetism in graphene nanoislands

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.

Giant magnetoresistance in ultrasmall graphene based devices

By computing spin-polarized electronic transport across a finite zigzag graphene ribbon bridging two metallic graphene electrodes, we demonstrate, as a proof of principle, that devices featuring 100% magnetoresistance can be built entirely out of carbon. In the ground state a short zigzag ribbon is an antiferromagnetic insulator which, when connecting two metallic electrodes, acts as a tunnel barrier that suppresses the conductance. The application of a magnetic field makes the ribbon ferromagnetic and conductive, increasing dramatically the current between electrodes. We predict large magnetoresistance in this system at liquid nitrogen temperature and 10 T or at liquid helium temperature and 300 G.

Spin-filtered edge states in graphene

Spin–orbit coupling changes graphene, in principle, into a two-dimensional topological insulator, also known as quantum spin Hall insulator. One of the expected consequences is the existence of spin-filtered edge states that carry dissipationless spin currents and undergo no backscattering in the presence of non-magnetic disorder, leading to quantization of conductance. Whereas, due to the small size of spin–orbit coupling in graphene, the experimental observation of these remarkable predictions is unlikely, the theoretical understanding of these spin-filtered states is shedding light on the electronic properties of edge states in other two-dimensional quantum spin Hall insulators. Here we review the effect of a variety of perturbations, like curvature, disorder, edge reconstruction, edge crystallographic orientation, and Coulomb interactions on the electronic properties of these spin filtered states.

Efficient intrinsic spin relaxation in graphene due to flexural distortions

We propose an intrinsic spin scattering mechanism in graphene originated by the interplay of atomic spin-orbit interaction and the local curvature induced by flexural distortions of the atomic lattice. Starting from a multiorbital tight-binding Hamiltonian with spin-orbit coupling considered non-perturbatively, we derive an effective Hamiltonian for the spin scattering of the Dirac electrons due to flexural distortions. We compute the spin lifetime due to both flexural phonons and ripples and we find values in the 1-10 ns range at room temperature. The proposed mechanism dominates the spin relaxation in high mobility graphene samples and should also apply to other planar aromatic compounds.

Graphene single-electron transistor as a spin sensor for magnetic adsorbates

We study single-electron transport through a graphene quantum dot with magnetic adsorbates. We focus on the relation between the spin order of the adsorbates and the linear conductance of the device. The electronic structure of the graphene dot with magnetic adsorbates is modeled through numerical diagonalization of a tight-binding model with an exchange potential. We consider several mechanisms by which the adsorbate magnetic state can influence transport in a single-electron transistor: tuning the addition energy, changing the tunneling rate, and in the case of spin-polarized electrodes, through magnetoresistive effects. Whereas the first mechanism is always present, the others require that the electrode has to have either an energy- or spin-dependent density of states. We find that graphene dots are optimal systems to detect the spin state of a few magnetic centers.