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Defects in graphene are of crucial importance for its electronic and magnetic properties. Here impurity effects on the electronic structure of surrounding carbon atoms are considered and the distribution of the local densities of states (LDOS) is calculated. As the full range from near field to the asymptotic regime is covered, our results are directly accessible by scanning tunnelling microscopy (STM). We also include exchange scattering at magnetic impurities and eludicate how strongly spin polarized impurity states arise.
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We study the problem of non-magnetic impurities adsorbed on bilayer graphene in the diluted regime. We analyze the impurity spectral densities for various concentrations and gate fields. We also analyze the effect of the adsorbate on the local density of states (LDOS) of the different C atoms in the structure and present some evidence of strong localization for the electronic states with energies close to the Dirac point.
We study graphene which has both spin-orbit coupling (SOC), taken to be of the Kane-Mele form, and a Zeeman field induced due to proximity to a ferromagnetic material. We show that a zigzag interface of graphene having SOC with its pristine counterpart hosts robust chiral edge modes in spite of the gapless nature of the pristine graphene; such modes do not occur for armchair interfaces. Next we study the change in the local density of states (LDOS) due to the presence of an impurity in graphene with SOC and Zeeman field, and demonstrate that the Fourier transform of the LDOS close to the Dirac points can act as a measure of the strength of the spin-orbit coupling; in addition, for a specific distribution of impurity atoms, the LDOS is controlled by a destructive interference effect of graphene electrons which is a direct consequence of their Dirac nature. Finally, we study transport across junctions which separates spin-orbit coupled graphene with Kane-Mele and Rashba terms from pristine graphene both in the presence and absence of a Zeeman field. We demonstrate that such junctions are generally spin active, namely, they can rotate the spin so that an incident electron which is spin polarized along some direction has a finite probability of being transmitted with the opposite spin. This leads to a finite, electrically controllable, spin current in such graphene junctions. We discuss possible experiments which can probe our theoretical predictions.
We have examined the impact of charged impurity scattering on charge carrier transport in bilayer graphene (BLG) by deposition of potassium in ultra-high vacuum at low temperature. Charged impurity scattering gives a conductivity which is supra-linear in carrier density, with a magnitude similar to single-layer graphene for the measured range of carrier densities of 2-4 x 10^12 cm^-2. Upon addition of charged impurities of concentration n_imp, the minimum conductivity Sigma_min decreases proportional to n_imp^-1/2, while the electron and hole puddle carrier density increases proportional to n_imp^1/2. These results for the intentional deposition of potassium on BLG are in good agreement with theoretical predictions for charged impurity scattering. However, our results also suggest that charged impurity scattering alone cannot explain the observed transport properties of pristine BLG on SiO2 before potassium doping.
We study the Fourier transform of the local density of states (LDOS) in graphene in the presence of a single impurity at high magnetic field. We find that the most pronounced features occur for energies of the STM tip matching the Landau level energies. The Fourier transform of the LDOS shows regions of high intensity centered around the center and the corners of the Brillouin zone (BZ). The radial intensity dependence of these features is determined by the form of the wavefunctions of the electrons in the quantum Hall regime. Moreover, some of these regions break rotational symmetry, and their angular dependence is determined by the chirality of the graphene electrons. For the zeroth Landau level, the ratio between the features at the corners and center of the BZ depends on the nature of the disorder: it goes to zero for potential disorder, and is finite for hopping disorder. We believe that a comparison between our analysis and experiments will help understand the form of the quasiparticle wavefunction, as well as the nature of disorder in graphene.
The advent of topological phases of matter revealed a variety of observed boundary phenomena, such as chiral and helical modes found at the edges of two-dimensional (2D) topological insulators. Antichiral states in 2D semimetals, i.e., copropagating edge modes on opposite edges compensated by a counterpropagating bulk current, are also predicted, but, to date, no realization of such states in a solid-state system has been found. Here, we put forward a procedure to realize antichiral states in twisted van der Waals multilayers, by combining the electronic Dirac-cone spectra of each layer through the combination of the orbital moire superstructure, an in-plane magnetic field, and inter-layer bias voltage. In particular, we demonstrate that a twisted van der Waals heterostructure consisting of graphene/two layers of hexagonal boron nitride [(hBN)$_2$]/graphene will show antichiral states at in-plane magnetic fields of 8 T, for a rotation angle of 0.2$^{circ}$ between the graphene layers. Our findings engender a controllable procedure to engineer antichiral states in solid-state systems, as well as in quantum engineered metamaterials.
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