We propose spin valves where a 2D nonmagnetic conductor is intercalated between two ferromagnetic insulating layers. In this setup, the relative orientation of the magnetizations of the insulating layers can have a strong impact on the in-plane conductivity of the 2D conductor. We first show this for a graphene bilayer, described with a tight-binding model, placed between two ferromagnetic insulators. In the antiparallel configuration, a band gap opens at the Dirac point, whereas in the parallel configuration, the graphene bilayer remains conducting. We then compute the electronic structure of graphene bilayer placed between two monolayers of the ferromagnetic insulator CrI_{3}, using density functional theory. Consistent with the model, we find that a gap opens at the Dirac point only in the antiparallel configuration.

A variety of planar π-conjugated hydrocarbons such as heptauthrene, Clar's goblet and, recently synthesized, triangulene have two electrons occupying two degenerate molecular orbitals. The resulting spin of the interacting ground state is often correctly anticipated as S = 1, extending the application of Hund's rules to these systems, but this is not correct in some instances. Here we provide a set of rules to correctly predict the existence of zero mode states, as well as the spin multiplicity of both the ground state and the low-lying excited states, together with their open-or closed-shell nature. This is accomplished using a combination of analytical arguments and configuration interaction calculations with a Hubbard model, both backed by quantum chemistry methods with a larger Gaussian basis set. Our results go beyond the well established Lieb's theorem and Ovchinnikov's rule, as we address the multiplicity and the open-/closed-shell nature of both ground and excited states.

We investigate the fate of interaction-driven phases in the half-filled honeycomb lattice for finite systems via exact diagonalization with nearest-and next-nearest-neighbor interactions. We find evidence for a charge density wave phase, a Kekulé bond order, and a sublattice charge-modulated phase in agreement with previously reported mean-field phase diagrams. No clear sign of an interaction-driven Chern insulator phase (Haldane phase) is found despite being predicted by the same mean-field analysis. We characterize these phases by their ground-state degeneracy and by calculating charge-order and bond-order correlation functions.

The edges of graphene and graphene like systems can host localized states with evanescent wave function with properties radically different from those of the Dirac electrons in bulk. This happens in a variety of situations, that are reviewed here. First, zigzag edges host a set of localized non dispersive state at the Dirac energy. At half filling, it is expected that these states are prone to ferromagnetic instability, causing a very interesting type of edge ferromagnetism. Second, graphene under the influence of external perturbations can host a variety of topological insulating phases, including the conventional Quantum Hall effect, the Quantum Anomalous Hall (QAH) and the Quantum Spin Hall phase, in all of which phases conduction can only take place through topologically protected edge states. Here we provide an unified vision of the properties of all these edge states, examined under the light of the same one orbital tight-binding model. We consider the combined action of interactions, spin orbit coupling and magnetic field, which produces a wealth of different physical phenomena. We briefly address what has been actually observed experimentally.

Charge, spin, and lattice degrees of freedom are strongly entangled in iron superconductors. A neat consequence of this entanglement is the behavior of the A 1g As-phonon resonance in the different polarization symmetries of Raman spectroscopy when undergoing the magnetostructural transition. In this work, we show that the observed behavior could be a direct consequence of the coupling of the phonons with the electronic excitations in the anisotropic magnetic state. We discuss this scenario within a five-orbital tight-binding model coupled to phonons via the dependence of the Slater-Koster parameters on the As position. We identify two qualitatively different channels of the electron-phonon interaction: a geometrical one related to the Fe-As-Fe angle α and another one associated with the modification upon As displacement of the Fe-As energy integrals pdσ and pdπ. While both mechanisms result in a finite B 1g response, the behavior of the phonon intensity in the A 1g and B 1g Raman polarization geometries is qualitatively different when the coupling is driven by the angle or by the energy integral dependence. We discuss our results in view of the experimental reports.

Topological invariants allow one to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wave functions under twisted boundary conditions. However, those procedures do not allow one to calculate a topological invariant by evaluating the system locally, and thus require information about the wave functions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a one-dimensional topological superconductor and a two-dimensional quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the kernel polynomial method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.

We propose a mechanism to drive singlet-triplet spin transitions electrically in a wide class of graphene nanostructures that present pairs of in-gap zero modes, localized at opposite sublattices. Examples are rectangular nanographenes with short zigzag edges, armchair ribbon heterojunctions with topological in-gap states, and graphene islands with sp 3 functionalization. The interplay between the hybridization of zero modes and the Coulomb repulsion leads to symmetric exchange interaction that favors a singlet ground state. Application of an off-plane electric field to the graphene nanostructure generates an additional Rashba spin-orbit coupling, which results in antisymmetric exchange interaction that mixes S = 0 and S = 1 manifolds. We show that modulation in time of either the off-plane electric field or the applied magnetic field permits performing electrically driven spin resonance in a system with very long spin-relaxation times.

We revisit the problem of local moment formation in graphene due to chemisorption of individual atomic hydrogen or other analogous sp 3 covalent functionalizations. We describe graphene with the single-orbital Hubbard model, so that the H chemisorption is equivalent to a vacancy in the honeycomb lattice. To circumvent artifacts related to periodic unit cells, we use either huge simulation cells of up to 8 × 10 5 sites, or an embedding scheme that allows the modeling of a single vacancy in an otherwise pristine infinite honeycomb lattice. We find three results that stress the anomalous nature of the magnetic moment (m) in this system. First, in the noninteracting (U = 0) zero-temperature (T = 0) case, the m(B) is a continuous smooth curve with divergent susceptibility, different from the stepwise constant function found for single unpaired spins in a gapped system. Second, for U = 0 and T > 0, the linear susceptibility follows a power law ∝ T −α with an exponent of α = 0.77 different from the conventional Curie law. For U > 0, in the mean-field approximation, the integrated moment is smaller than m = 1μ B , in contrast with results using periodic unit cells. These three results highlight the fact that the magnetic response of the local moment induced by sp 3 functionalizations in graphene is different from that of local moments in gapped systems, for which the magnetic moment is quantized and follows a Curie law, and from Pauli paramagnetism in conductors, for which linear susceptibility can be defined at T = 0.