76 research outputs found
Quantum transport across van der Waals domain walls in bilayer graphene
Bilayer graphene can exhibit deformations such that the two graphene sheets
are locally detached from each other resulting in a structure consisting of
domains with different inter-layer coupling. Here we investigate how the
presence of these domains affect the transport properties of bilayer graphene.
We derive analytical expressions for the transmission probability, and the
corresponding conductance, across walls separating different inter-layer
coupling domain. We find that the transmission can exhibit a valley-dependent
layer asymmetry and that the domain walls have a considerable effect on the
chiral tunnelling properties of the charge carriers. We show that transport
measurements allow one to obtain the strength with which the two layers are
coupled. We performed numerical calculations for systems with two domain walls
and find that the availability of multiple transport channels in bilayer
graphene modifies significantly the conductance dependence on inter-layer
potential asymmetry.Comment: 20 pages, 24 Figure
The Dirac-Coulomb Problem: a mathematical revisit
We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb
operator in a suitable complete square integrable basis. Orthogonal polynomials
techniques along with Darboux method are used to obtain the bound states energy
spectrum, the relativistic scattering amplitudes and phase shifts from the
asymptotic behavior of the polynomial solutions associated with the resulting
three-term recursion relation.Comment: 8 page
Confined states in graphene quantum blisters
Bilayer graphene samples may exhibit regions where the two layers are locally
delaminated forming a so-called quantum blister in the graphene sheet. Electron
and hole states can be confined in this graphene quantum blisters (GQB) by
applying a global electrostatic bias. We scrutinize the electronic properties
of these confined states under the variation of interlayer bias, coupling, and
blister's size. The spectra display strong anti-crossings due to the coupling
of the confined states on upper and lower layers inside the blister. These
spectra are layer localized where the respective confined states reside on
either layer or equally distributed. For finite angular momentum, this layer
localization can be at the edge of the blister and corresponds to degenerate
modes of opposite momenta. Furthermore, the energy levels in GQB exhibit
electron-hole symmetry that is sensitive to the electrostatic bias. Finally, we
demonstrate that confinement in GQB persists even in the presence of a
variation in the inter-layer coupling.Comment: 12 pages, 13 figure
Taming the Yukawa potential singularity: improved evaluation of bound states and resonance energies
Using the tools of the J-matrix method, we absorb the 1/r singularity of the
Yukawa potential in the reference Hamiltonian, which is handled analytically.
The remaining part, which is bound and regular everywhere, is treated by an
efficient numerical scheme in a suitable basis using Gauss quadrature
approximation. Analysis of resonance energies and bound states spectrum is
performed using the complex scaling method, where we show their trajectories in
the complex energy plane and demonstrate the remarkable fact that bound states
cross over into resonance states by varying the potential parameters.Comment: 8 pages, 2 tables, 1 figure. 2 mpg videos and 1 pdf table file are
available upon request from the corresponding Autho
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