36 research outputs found
Conductance quantization in mesoscopic graphene
Using a generalized Landauer approach we study the non-linear transport in
mesoscopic graphene with zig-zag and armchair edges. We find that for clean
systems, the low-bias low-temperature conductance, G, of an armchair edge
system in quantized as G/t=4 n e^2/h, whereas for a zig-zag edge the
quantization changes to G/t t=4(n+1/2)e^2/h, where t is the transmission
probability and n is an integer. We also study the effects of a non-zero bias,
temperature, and magnetic field on the conductance. The magnetic field
dependence of the quantization plateaus in these systems is somewhat different
from the one found in the two-dimensional electron gas due to a different
Landau level quantization.Comment: 6 pages, 9 figures. Final version published in Physical Review
Electronic properties of disordered two-dimensional carbon
Two-dimensional carbon, or graphene, is a semimetal that presents unusual low-energy electronic excitations described in terms of Dirac fermions. We analyze in a self-consistent way the effects of localized (impurities or vacancies) and extended (edges or grain boundaries) defects on the electronic and transport properties of graphene. On the one hand, point defects induce a finite elastic lifetime at low energies with the enhancement of the electronic density of states close to the Fermi level. Localized disorder leads to a universal, disorder independent, electrical conductivity at low temperatures, of the order of the quantum of conductance. The static conductivity increases with temperature and shows oscillations in the presence of a magnetic field. The graphene magnetic susceptibility is temperature dependent (unlike an ordinary metal) and also increases with the amount of defects. Optical transport properties are also calculated in detail. On the other hand, extended defects induce localized states near the Fermi level. In the absence of electron-hole symmetry, these states lead to a transfer of charge between the defects and the bulk, the phenomenon we call self-doping. The role of electron-electron interactions in controlling self-doping is also analyzed. We also discuss the integer and fractional quantum Hall effect in graphene, the role played by the edge states induced by a magnetic field, and their relation to the almost field independent surface states induced at boundaries. The possibility of magnetism in graphene, in the presence of short-range electron-electron interactions and disorder is also analyzed
Coulomb Interactions and Ferromagnetism in Pure and Doped Graphene
We study the presence of ferromagnetism in the phase diagram of the
two-dimensional honeycomb lattice close to half-filling (graphene) as a
function of the strength of the Coulomb interaction and doping. We show that
exchange interactions between Dirac fermions can stabilize a ferromagnetic
phase at low doping when the coupling is sufficiently large. In clean systems,
the zero temperature phase diagram shows both first order and second order
transition lines and two distinct ferromagnetic phases: one phase with only one
type of carriers (either electrons or holes) and another with two types of
carriers (electrons and holes). Using the coherent phase approximation (CPA) we
argue that disorder further stabilizes the ferromagnetic phase.Comment: 10 pages; published versio
Dirac Fermion Confinement in Graphene
We study the problem of Dirac fermion confinement in graphene in the presence
of a perpendicular magnetic field B. We show, analytically and numerically,
that confinement leads to anomalies in the electronic spectrum and to a
magnetic field dependent crossover from \sqrt{B}, characteristic of
Dirac-Landau level behavior, to linear in B behavior, characteristic of
confinement. This crossover occurs when the radius of the Landau level becomes
of the order of the width of the system. As a result, we show that the
Shubnikov-de Haas oscillations also change as a function of field, and lead to
a singular Landau plot. We show that our theory is in excellent agreement with
the experimental data.Comment: 4 pages, 6 figure
Localized states at zigzag edges of bilayer graphene
We report the existence of zero energy surface states localized at zigzag
edges of bilayer graphene. Working within the tight-binding approximation we
derive the analytic solution for the wavefunctions of these peculiar surface
states. It is shown that zero energy edge states in bilayer graphene can be
divided into two families: (i) states living only on a single plane, equivalent
to surface states in monolayer graphene; (ii) states with finite amplitude over
the two layers, with an enhanced penetration into the bulk. The bulk and
surface (edge) electronic structure of bilayer graphene nanoribbons is also
studied, both in the absence and in the presence of a bias voltage between
planes.Comment: 4 pages, 5 figure
Electronic properties of graphene multilayers
We study the effects of disorder in the electronic properties of graphene
multilayers, with special focus on the bilayer and the infinite stack. At low
energies and long wavelengths, the electronic self-energies and density of
states exhibit behavior with divergences near half-filling. As a consequence,
the spectral functions and conductivities do not follow Landau's Fermi liquid
theory. In particular, we show that the quasiparticle decay rate has a minimum
as a function of energy, there is a universal minimum value for the in-plane
conductivity of order e^2/h per plane and, unexpectedly, the c-axis
conductivity is enhanced by disorder at low doping, leading to an enormous
conductivity anisotropy at low temperatures.Comment: 4 pages, 4 figure. Reference to exciting new ARPES results on
graphite added (we thank A. Lanzara for sharing the paper prior to its
publication
Disorder Induced Localized States in Graphene
We consider the electronic structure near vacancies in the half-filled
honeycomb lattice. It is shown that vacancies induce the formation of localized
states. When particle-hole symmetry is broken, localized states become
resonances close to the Fermi level. We also study the problem of a finite
density of vacancies, obtaining the electronic density of states, and
discussing the issue of electronic localization in these systems. Our results
also have relevance for the problem of disorder in d-wave superconductors.Comment: Replaced with published version. 4 pages, 4 figures. Fig. 1 was
revise
Bilayer graphene: gap tunability and edge properties
Bilayer graphene -- two coupled single graphene layers stacked as in graphite
-- provides the only known semiconductor with a gap that can be tuned
externally through electric field effect. Here we use a tight binding approach
to study how the gap changes with the applied electric field. Within a parallel
plate capacitor model and taking into account screening of the external field,
we describe real back gated and/or chemically doped bilayer devices. We show
that a gap between zero and midinfrared energies can be induced and externally
tuned in these devices, making bilayer graphene very appealing from the point
of view of applications. However, applications to nanotechnology require
careful treatment of the effect of sample boundaries. This being particularly
true in graphene, where the presence of edge states at zero energy -- the Fermi
level of the undoped system -- has been extensively reported. Here we show that
also bilayer graphene supports surface states localized at zigzag edges. The
presence of two layers, however, allows for a new type of edge state which
shows an enhanced penetration into the bulk and gives rise to band crossing
phenomenon inside the gap of the biased bilayer system.Comment: 8 pages, 3 fugures, Proceedings of the International Conference on
Theoretical Physics: Dubna-Nano200
Electronic transport in graphene: A semi-classical approach including midgap states
Using the semi-classical Boltzmann theory, we calculate the conductivity as
function of the carrier density. As usually, we include the scattering from
charged impurities, but conclude that the estimated impurity density is too low
in order to explain the experimentally observed mobilities. We thus propose an
additional scattering mechanism involving midgap states which leads to a
similar k-dependence of the relaxation time as charged impurities. The new
scattering mechanism can account for the experimental findings such as the
sublinear behavior of the conductivity versus gate voltage and the increase of
the minimal conductivity for clean samples. We also discuss temperature
dependent scattering due to acoustic phonons.Comment: 10 pages, 4 figure