38 research outputs found
Obtaining localization properties efficiently using the Kubo-Greenwood formalism
We establish, through numerical calculations and comparisons with a recursive
Green's function based implementation of the Landauer-B\"uttiker formalism, an
efficient method for studying Anderson localization in quasi-one-dimensional
and two-dimensional systems using the Kubo-Greenwood formalism. Although the
recursive Green's function method can be used to obtain the localization length
of a mesoscopic conductor, it is numerically very expensive for systems that
contain a large number of atoms transverse to the transport direction. On the
other hand, linear-scaling has been achieved with the Kubo-Greenwood method,
enabling the study of effectively two-dimensional systems. While the
propagating length of the charge carriers will eventually saturate to a finite
value in the localized regime, the conductances given by the Kubo-Greenwood
method and the recursive Green's function method agree before the saturation.
The converged value of the propagating length is found to be directly
proportional to the localization length obtained from the exponential decay of
the conductance.Comment: 7 pages, 6 figure
Electronic and transport properties in geometrically disordered graphene antidot lattices
A graphene antidot lattice, created by a regular perforation of a graphene
sheet, can exhibit a considerable band gap required by many electronics
devices. However, deviations from perfect periodicity are always present in
real experimental setups and can destroy the band gap. Our numerical
simulations, using an efficient linear-scaling quantum transport simulation
method implemented on graphics processing units, show that disorder that
destroys the band gap can give rise to a transport gap caused by Anderson
localization. The size of the defect induced transport gap is found to be
proportional to the radius of the antidots and inversely proportional to the
square of the lattice periodicity. Furthermore, randomness in the positions of
the antidots is found to be more detrimental than randomness in the antidot
radius. The charge carrier mobilities are found to be very small compared to
values found in pristine graphene, in accordance with recent experiments.Comment: 8 pages, 8 figures, An unused figure from the previous version is
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Ab initio transport fingerprints for resonant scattering in graphene
We have recently shown that by using a scaling approach for randomly distributed topological defects in graphene, reliable estimates for transmission properties of macroscopic samples can be calculated based even on single-defect calculations [A. Uppstu et al., Phys. Rev. B 85, 041401 (2012)]. We now extend this approach of energy-dependent scattering cross sections to the case of adsorbates on graphene by studying hydrogen and carbon adatoms as well as epoxide and hydroxyl groups. We show that a qualitative understanding of resonant scattering can be gained through density functional theory results for a single-defect system, providing a transmission “fingerprint” characterizing each adsorbate type. This information can be used to reliably predict the elastic mean free path for moderate defect densities directly using ab initio methods. We present tight-binding parameters for carbon and epoxide adsorbates, obtained to match the density-functional theory based scattering cross sections.Peer reviewe
Quantum confined electronic states in atomically well-defined graphene nanostructures
Despite the enormous interest in the properties of graphene and the potential
of graphene nanostructures in electronic applications, the study of quantum
confined states in atomically well-defined graphene nanostructures remains an
experimental challenge. Here, we study graphene quantum dots (GQDs) with
well-defined edges in the zigzag direction, grown by chemical vapor deposition
(CVD) on an iridium(111) substrate, by low-temperature scanning tunneling
microscopy (STM) and spectroscopy (STS). We measure the atomic structure and
local density of states (LDOS) of individual GQDs as a function of their size
and shape in the range from a couple of nanometers up to ca. 20 nm. The results
can be quantitatively modeled by a relativistic wave equation and atomistic
tight-binding calculations. The observed states are analogous to the solutions
of the text book "particle-in-a-box" problem applied to relativistic massless
fermions.Comment: accepted for publication in Phys. Rev. Let
Electronic transport in graphene-based structures: an effective cross section approach
We show that transport in low-dimensional carbon structures with finite
concentrations of scatterers can be modeled by utilising scaling theory and
effective cross sections. Our reults are based on large scale numerical
simulations of carbon nanotubes and graphene nanoribbons, using a tightbinding
model with parameters obtained from first principles electronic structure
calculations. As shown by a comprehensive statistical analysis, the scattering
cross sections can be used to estimate the conductance of a quasi-1D system
both in the Ohmic and localized regimes. They can be computed with good
accuracy from the transmission functions of single defects, greatly reducing
the computational cost and paving the way towards using first principles
methods to evaluate the conductance of mesoscopic systems, consisting of
millions of atoms.Comment: Submitted to Physical Review Letter
Single-mode and multimode Fabry-Perot interference in suspended graphene
We have achieved high-quality Fabry-PĂ©rot interference in a suspended graphene device both in conductance and in shot noise. A Fourier analysis of these reveals two sets of overlapping, coexisting interference patterns, with the ratios of the resonance intervals being equal to the width to length ratio of the device. We show that these sets originate from the unique coexistence of longitudinal and transverse resonances, with the longitudinal resonances occurring due to bunching of modes with low transverse momentum. Finally, the high quality of our samples allows us to probe the interaction renormalization of the Fermi velocity as well as the coexistence of Fabry-PĂ©rot oscillations with universal conductance fluctuations.Peer reviewe