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Register a new userThe local density of states in the presence of impurity scattering in graphene at high magnetic field
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Authors
Cristina Bena
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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.
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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 study two lattice models, the honeycomb lattice (HCL) and a special square lattice (SQL), both reducing to the Dirac equation in the continuum limit. In the presence of disorder (gaussian potential disorder and random vector potential), we investigate the behaviour of the density of states (DOS) numerically and analytically. While an upper bound can be derived for the DOS on the SQL at the Dirac point, which is also confirmed by numerical calculations, no such upper limit exists for the HCL in the presence of random vector potential. A careful investigation of the lowest eigenvalues indeed indicate, that the DOS can possibly be divergent at the Dirac point on the HCL. In spite of sharing a common continuum limit, these lattice models exhibit different behaviour.
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.
We investigate the electronic transport properties of unbiased and biased bilayer graphene nanoribbon in n-p and n-n junctions subject to a perpendicular magnetic field. Using the non-equilibrium Greens function method and the Landauer-B{u}ttiker formalism, the conductance is studied for the cases of clean, on-site, and edge disordered bilayer graphene. We show that the lowest Hall plateau remains unchanged in the presence of disorder, whereas asymmetry destroys both the plateaus and conductance quantization. In addition, we show that disorder induces an enhancement of the conductance in the n-p region in the presence of magnetic fields. Finally, we show that the equilibration of quantum Hall edge states between distinctively doped regions causes Hall plateaus to appear in the regime of complete mode mixing.
The electron-phonon matrix element for edge states of carbon nanotubes and graphene at zigzag edges is calculated for obtaining renormalized energy dispersion of the edge states. Self-energy correction by electron-phonon interaction contributes to the energy dispersion of edge states whose energy bandwidth is similar to phonon energy. Since the energy-uncertainty of the edge state is larger than temperature, we conclude that the single-particle picture of the edge state in not appropriate when the electron-phonon interaction is taken into account. The longitudinal acoustic phonon mode contributes to the matrix element through the on-site deformation potential because the wavefunction of the edge state has an amplitude only on one of the two sublattices. The on-site deformation potentials for the longitudinal and in-plane tangential optical phonon modes are enhanced at the boundary. The results of local density of states are compared with the recent experimental data of scanning tunneling spectroscopy.
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