64 research outputs found
Computation of electron quantum transport in graphene nanoribbons using GPU
The performance potential for simulating quantum electron transport on
graphical processing units (GPUs) is studied. Using graphene ribbons of
realistic sizes as an example it is shown that GPUs provide significant
speed-ups in comparison to central processing units as the transverse dimension
of the ribbon grows. The recursive Green's function algorithm is employed and
implementation details on GPUs are discussed. Calculated conductances were
found to accumulate significant numerical error due to single-precision
floating-point arithmetic at energies close to the charge neutrality point of
the graphene.Comment: published version with correction
Edge channels in a graphene Fabry-Perot interferometer
Quantum-mechanical calculations of electron magnetotransport in graphene
Fabry-P\'{e}rot interferometers are presented. The role of edge channels and
their spatial structure on Aharonov-Bohm interference is elucidated. For an
interferometer that is made by removing carbon atoms, which is typically
realized in nanolithography experiments, the constrictions are shown to cause
strong inter-channel scattering that establishes local equilibrium over a short
distance and makes the electron transport non-adiabatic. Nevertheless,
two-terminal conductance is found to reveal a common Aharonov-Bohm oscillation
pattern, independent of crystallographic orientation, which is accompanied by
single-particle states that sweep through the Fermi energy for the edge
channels circulating along the physical boundary of the device. It is also
found that the interferometer constrictions host the localized states that
might shorten the device or disrupt the oscillation pattern. For an
interferometer that is created by electrostatic confinement, which is typically
done in the split-gate experiments, electron transport is shown to be
adiabatic, similar to the well-studied regime in traditional GaAs-based
interferometers.Comment: Recalculated transmissions, acknowledgements, minor update
Fabry-Perot and Aharonov-Bohm interference in ideal graphene nanoribbons
Quantum-mechanical calculations of electron magneto-transport in ideal
graphene nanoribbons are presented. In noninteracting theory, it is predicted
that an ideal ribbon that is attached to wide leads should reveal Fabry-Perot
conductance oscillations in magnetic field. In the theory with Coulomb
interaction taken into account, the oscillation pattern should rather be
determined by the Aharonov-Bohm interference effect. Both of these theories
predict the formation of quasi-bound states, albeit of different structures,
inside the ribbon because of strong electron scattering on the interfaces
between the connecting ribbon and the leads. Conductance oscillations are a
result of resonant backscattering via these quasi-bound states.Comment: Recalculated Hartree DOS, minor update
Spin polarization and g-factor enhancement in graphene nanoribbons in magnetic field
We provide a systematic quantitative description of spin polarization in
armchair and zigzag graphene nanoribbons in a perpendicular magnetic field. We
first address spinless electrons within the Hartree approximation studying the
evolution of the magnetoband structure and formation of the compressible
strips. We discuss the potential profile and the density distribution near the
edges and the difference and similarities between armchair and zigzag edges.
Accounting for the Zeeman interaction and describing the spin effects via the
Hubbard term we study the spin-resolved subband structure and relate the spin
polarization of the system at hand to the formation of the compressible strips
for the case of spinless electrons. At high magnetic field the calculated
effective g-factor varies around a value of ~2.25 for armchair nanoribbons
and ~3 for zigzag nanoribbons. An important finding is that in zigzag
nanoribbons the zero-energy mode remains pinned to the Fermi-energy and becomes
fully spin-polarized for all magnetic fields, which, in turn, leads to a strong
spin polarization of the electron density near the zigzag edge.Comment: 9 pages, 4 figure
Nonlinear conductance quantization in graphene ribbons
We present numerical studies of non-linear conduction in graphene nanoribbons
when a bias potential is applied between the source and drain electrodes. We
find that the conductance quantization plateaus show asymmetry between the
electron and hole branches if the potential in the ribbon equals the source or
drain electrode potential and strong electron (hole) scattering occurs. The
scattering may be at the ends of a uniform ballistic ribbon connecting wider
regions of graphene or may be due to defects in the ribbon. We argue that, in
ribbons with strong defect scattering, the ribbon potential is pinned to that
of the drain (source) for electron (hole) transport. In this case symmetry
between electron and hole transport is restored and our calculations explain
the upward shift of the conductance plateaus with increasing bias that was
observed experimentally by Lin et al. [Phys. Rev. B 78, 161409 (2008)].Comment: 6 pages, 3 figure
Suppression of compressible edge channels and spatial spin polarization in the integer quantum Hall regime
We perform systematic numerical studies of the structure of spin-resolved
compressible strips in split-gate quantum wires taking into account the
exchange and correlation interactions within the density functional theory in
the local spin-density approximation. We find that for realistic parameters of
the wire the exchange interaction can completely suppress the formation of the
compressible strips. As the depletion length or magnetic field are increased,
the compressible strips starts to form first for the spin-down and then for
spin-up edge channels. We demonstrate that the widths of these strips plus the
spatial separation between them caused by the exchange interaction are equal to
the width of the compressible strip calculated in the Hartree approximation for
spinless electrons. We also discuss the effect of electron density on the
suppression of the compressible strips in quantum wires.Comment: 5 pages, 4 figures, submitted to Phys. Rev.
Origin of the 0.25-anomaly in the nonlinear conductance of a quantum point contact
We calculate the non-linear conductance of a quantum point contact using the
non-equilibrium Greens function technique within the Hartree approximation of
spinless electrons. We quantitative reproduce the 0.25-anomaly in the
differential conductance (i.e. the lowest plateau at 0.25-0.3*2e^2/h) as well
as an upward bending of higher conductance half-integer plateaus seen in the
experiments, and relate these features to the non-linear screening and pinning
effects.Comment: 6 pages, 4 figure
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