Modelling spin correlations in graphene and chiral molecules

Abstract

We first develop an analytical model to explain the spin-selectivity in experiments that measure conductance through DNA molecules attached to a Ni substrate and a gold electrode. Our model involves an electron con- ned to a helix potential; the spin-orbit due to the carbon atomic cores is modeled by a Rashba term. We calculate the eigenstates of the electron in the SO-active helix and by calculating the expectation value of the currents for eigenstates of di erent spins, we nd that electrons of di erent spins propagate with di erent velocities, thus generating the spin- ltering seen in the experiments. Moving on to graphene, we begin by studying superlattices of periodically hydrogenated graphene in a dilute regime. We include in our model the adatom-induced magnetism and spin-orbit couplings, and we investigate the topological properties of the band structure via a Berry curvature analysis. A direct visualization of the edge states is also carried out by calculating the spatial distribution of midgap states in the hydrogenated nanoribbon structure, and by looking at the DOS at the edge of semi-in nite structure. We also investigate the magnetic anisotropy induced by the spin-orbit coupling within a Hubbard model at the mean- eld approximation. Next, we consider pairwise interactions between adatoms in graphene. For distances in which their orbitals do not overlap, the adatoms may yet have indirect interactions mediated by the electrons of graphene. We calculate the total interaction energy via a two-impurity Anderson model. In unstrained graphene the interactions oscillate according to cos2( K 2 :r) a type of periodicity that is referred to in the literature as Hidden Kekul e ordering. We investigate how elastic strains in graphene modulate the pair-wise interactions between adatoms. We include in our description the e ects of adatom magnetization and consider also the interactions between adatoms in the hollow position and benzene-like adsorbates. Lastly, the e ect of electron-electron interactions in twisted bilayer graphene are investigated. The Fermi velocity is reduced for small twisting angles, leading to nearly at bands (strongly localized in the regions of AA-stacking) around the Fermi level for some twisting angles. We calculate the magnetic order within one unit cell using a collinear mean- eld approximation for the Hubbard term and we obtain that the semimetal-Mott insulator transition is facilitated by the reduction of the Fermi velocity. Unlike the antiferromagnetic phase in the monolayer honeycomb, this antiferromagnetism is strongly localized in the AA regions. We also take into account the e ect of an applied interlayer bias, which in the non-interacting limit enhances the electron-con nement. This enhanced con nement turns the moir e pattern of TBLG into a triangular superlattice of electrons con ned in AA-regions, and we nd that under interlayer bias the ground state becomes a 120 N eel state