7 research outputs found
Spectrum of -electrons in Graphene As a Macromolecule
We report the exact solution of spectral problem for a graphene sheet framed
by two armchair- and two zigzag-shaped boundaries. The solution is found for
the electron Hamiltonian and gives, in particular, a closed analytic
expression of edge-state energies in graphene. It is shown that the lower
symmetry of graphene, in comparison with of 2D graphite, has a
profound effect on the graphene band structure. This and other obtained results
have far going implications for the understanding of graphene electronics. Some
of them are briefly discussed.Comment: Revised in connection with publication in PRL, editin
Spectrum of Electrons in Graphene as an Alternant Macromolecule and Its Specific Features in Quantum Conductance
An exact description of electrons based on the tight-binding model of
graphene as an alternant, plane macromolecule is presented. The model molecule
can contain an arbitrary number of benzene rings and has armchair- and
zigzag-shaped edges. This suggests an instructive alternative to the most
commonly used approach, where the reference is made to the honeycomb lattice
periodic in its A and B sublattices. Several advantages of the macromolecule
model are demonstrated. The newly derived analytical relations detail our
understanding of electron nature in achiral graphene ribbons and carbon
tubes and classify these structures as quantum wires.Comment: 13 pages 8 figures, revised in line with referee's comment
The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations
We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal)
conductance of a two dimensional electron system placed in a strong
perpendicular magnetic field, and subjected to periodic modulations and/or
disorder potentials. The scattering problem is recast as a set of
inhomogeneous, coupled linear equations, allowing us to find the transmission
probabilities from a finite-size system computation; the results are exact for
non-interacting electrons. Our method fully accounts for the effects of the
disorder and the periodic modulation, irrespective of their relative strength,
as long as Landau level mixing is negligible. In particular, we focus on the
interplay between the effects of the periodic modulation and those of the
disorder. This appears to be the relevant regime to understand recent
experiments [S. Melinte {\em et al}, Phys. Rev. Lett. {\bf 92}, 036802 (2004)],
and our numerical results are in qualitative agreement with these experimental
results. The numerical techniques we develop can be generalized
straightforwardly to many-terminal geometries, as well as other multi-channel
scattering problems.Comment: 13 pages, 11 figure
Lattice Green's function approach to the solution of the spectrum of an array of quantum dots and its linear conductance
In this paper we derive general relations for the band-structure of an array
of quantum dots and compute its transport properties when connected to two
perfect leads. The exact lattice Green's functions for the perfect array and
with an attached adatom are derived. The expressions for the linear conductance
for the perfect array as well as for the array with a defect are presented. The
calculations are illustrated for a dot made of three atoms. The results derived
here are also the starting point to include the effect of electron-electron and
electron-phonon interactions on the transport properties of quantum dot arrays.
Different derivations of the exact lattice Green's functions are discussed