News and Events

Abstract

We show the charge Hall and spin Hall conductivity are generally non-vanishing in presence of magnetic impurities and spin orbit interaction in graphene. For single magnetic impurity on bi-layer and tri-layer graphene, the anomalous region where local magnetic moment exists for a bare impurity level higher than the Fermi energy shrinks due to non-relativistic contribution from the interlayer coupling. Employing a partial-wave representation we further study the nature of the coupling between the impurity and the conducting electrons for two configurations: the adatom is above one carbon atom (ADA) and above the center of the honeycomb (ADC). For ADA the impurity is coupled with one flavor for both A and B sublattice and both Dirac cones. For ADC the impurity couples with multi-flavor states for a spinor state of the impurity. We show, explicitly for a 3d magnetic atom, d_z²，（d_xz, d_yz） and (d_z²-_y²，d_xy) couple respectively with the Γ₁, Γ₅ (E₁) and Γ₆ (E₂) representations of C_6v group in ADC case. We further study the ADA case in terms of slave-boson method and introduce a topological picture to analyze the phase shift and the occupation on the impurity. In order to investigate Kondo effect in this material in this case, we calculate the higher-order correction to the Green’s function. It is found that the Kondo resonance occurs in a narrow energy range of the impurity level around the Fermi energy, which can be tuned by a gate voltage. We show that this range is linear in the Fermi energy |μ| and is significantly narrower than in the case of a normal metal. The singularity in the full Green’s function is also analyzed with the help of a transparent geometrical method. The relations between the various self-energies and the implications for the experimental observations are discussed.

Coffee and tea will be served 20 minutes prior to the seminar.