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 U

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.

Local probe of fractional edge states of S=1 Heisenberg spin chains

Spin chains are among the simplest physical systems in which electron-electron interactions induce novel states of matter. Here we propose to combine atomic scale engineering and spectroscopic capabilities of state of the art scanning tunnel microscopy to probe the fractionalized edge states of individual atomic scale S=1 spin chains. These edge states arise from the topological order of the ground state in the Haldane phase. We also show that the Haldane gap and the spin-spin correlation length can be measured with the same technique.

On the forbidden gap of finite graphene nanoribbons

The electronic structure of isolated finite graphene nanoribbons is investigated by solving, at the Hartree-Fock (HF) level, the Pariser, Parr and Pople (PPP) many-body Hamiltonian. The study is mainly focused on 7-AGNR and 13-AGNR (Armchair Graphene Nano-Ribbons), whose electronic structures have been recently experimentally investigated. Only paramagnetic solutions are considered. The characteristics of the forbidden gap are studied as a function of the ribbon length. For a 7-AGNR, the gap monotonically decreases from a maximum value of ~6.5 eV for short nanoribbons to a very small value of ~0.12 eV for the longer calculated systems. Gap edges are defined by molecular orbitals that are spatially localized near the nanoribbon extremes, that is, near both zig-zag edges. On the other hand, two delocalized orbitals define a much larger gap of about 5 eV. Conductance measurements report a somewhat smaller gap of ~3 eV. The small real gap lies in the middle of the one given by extended states and has been observed by STM and reproduced by DFT calculations. On the other hand, the length dependence of the gap is not monotonous for a 13-AGNR. It decreases initially but sharply increases for lengths beyond 30 Å remaining almost constant thereafter at a value of ~2.1 eV. Two additional states localized at the nanoribbon extremes show up at energies 0.31 eV below the HOMO (Highest Occupied Molecular Orbital) and above the LUMO (Lowest Unoccupied Molecular Orbital). These numbers compare favorably with those recently obtained by means of STS for a 13-AGNR sustained by a gold surface, namely 1.4 eV for the energy gap and 0.4 eV for the position of localized band edges. We show that the important differences between 7- and 13-AGNR should be ascribed to the charge rearrangement near the zig-zag edges obtained in our calculations for ribbons longer than 30 Å, a feature that does not show up for a 7-AGNR no matter its length.

Noncollinear magnetic phases and edge states in graphene quantum Hall bars

Application of a perpendicular magnetic field to charge neutral graphene is expected to result in a variety of broken symmetry phases, including antiferromagnetic, canted, and ferromagnetic. All these phases open a gap in bulk but have very different edge states and noncollinear spin order, recently confirmed experimentally. Here we provide an integrated description of both edge and bulk for the various magnetic phases of graphene Hall bars making use of a noncollinear mean field Hubbard model. Our calculations show that, at the edges, the three types of magnetic order are either enhanced (zigzag) or suppressed (armchair). Interestingly, we find that preformed local moments in zigzag edges interact with the quantum spin Hall like edge states of the ferromagnetic phase and can induce backscattering.

Theoretical Rationalization of the Singlet–Triplet Gap in OLEDs Materials: Impact of Charge-Transfer Character

New materials for OLED applications with low singlet–triplet energy splitting have been recently synthesized in order to allow for the conversion of triplet into singlet excitons (emitting light) via a Thermally Activated Delayed Fluorescence (TADF) process, which involves excited-states with a non-negligible amount of Charge-Transfer (CT). The accurate modeling of these states with Time-Dependent Density Functional Theory (TD-DFT), the most used method so far because of the favorable trade-off between accuracy and computational cost, is however particularly challenging. We carefully address this issue here by considering materials with small (high) singlet–triplet gap acting as emitter (host) in OLEDs and by comparing the accuracy of TD-DFT and the corresponding Tamm-Dancoff Approximation (TDA), which is found to greatly reduce error bars with respect to experiments thanks to better estimates for the lowest singlet–triplet transition. Finally, we quantitatively correlate the singlet–triplet splitting values with the extent of CT, using for it a simple metric extracted from calculations with double-hybrid functionals, that might be applied in further molecular engineering studies.