38 research outputs found
Electronic states in a graphene flake strained by a Gaussian bump
The effect of strain in graphene is usually modeled by a pseudo-magnetic
vector potential which is, however, derived in the limit of small strain. In
realistic cases deviations are expected in view of graphene's very high strain
tolerance, which can be up to 25%. Here we investigate the pseudo-magnetic
field generated by a Gaussian bump and we show that it exhibits significant
differences with numerical tight-binding results. Furthermore, we calculate the
electronic states in the strained region for a hexagon shaped flake with
armchair edges. We find that the six-fold symmetry of the wave functions inside
the Gaussian bump is directly related to the different effect of strain along
the fundamental directions of graphene: zigzag and armchair. Low energy
electrons are strongly confined in the armchair directions and are localized on
the carbon atoms of a single sublattice
Graphene Hall bar with an asymmetric pn-junction
We investigated the magnetic field dependence of the Hall and the bend
resistances in the ballistic regime for a single layer graphene Hall bar
structure containing a pn-junction. When both regions are n-type the Hall
resistance dominates and Hall type of plateaus are formed. These plateaus occur
as a consequence of the restriction on the angle imposed by Snell's law
allowing only electrons with a certain initial angles to transmit though the
potential step. The size of the plateau and its position is determined by the
position of the potential interface as well as the value of the applied
potential. When the second region is p-type the bend resistance dominates which
is asymmetric in field due to the presence of snake states. Changing the
position of the pn-interface in the Hall bar strongly affects these states and
therefore the bend resistance is also changed. Changing the applied potential
we observe that the bend resistance exhibits a peak around the
charge-neutrality point (CNP) which is independent of the position of the
pn-interface, while the Hall resistance shows a sign reversal when the CNP is
crossed, which is in very good agreement with a recent experiment [J. R.
Williams et al., Phys. Rev. Lett. 107, 046602(2011)]
Bilayer graphene Hall bar with a pn-junction
We investigate the magnetic field dependence of the Hall and the bend
resistances for a ballistic Hall bar structure containing a pn-junction
sculptured from a bilayer of graphene. The electric response is obtained using
the billiard model and we investigate the cases of bilayer graphene with and
without a band gap. Two different conduction regimes are possible: ) both
sides of the junction have the same carrier type, and ) one side of the
junction is n-type while the other one is p-type. The first case shows Hall
plateau-like features in the Hall resistance that fade away as the band gap
opens. The second case exhibits a bend resistance that is asymmetric in
magnetic field as a consequence of snake states along the pn-interface, where
the maximum is shifted away from zero magnetic field
Magnetic field dependence of the atomic collapse state in graphene
Quantum electrodynamics predicts that heavy atoms ()
will undergo the process of atomic collapse where electrons sink into the
positron continuum and a new family of so-called collapsing states emerges. The
relativistic electrons in graphene exhibit the same physics but at a much lower
critical charge () which has made it possible to confirm this
phenomenon experimentally. However, there exist conflicting predictions on the
effect of a magnetic field on atomic collapse. These theoretical predictions
are based on the continuum Dirac-Weyl equation, which does not have an exact
analytical solution for the interplay of a supercritical Coulomb potential and
the magnetic field. Approximative solutions have been proposed, but because the
two effects compete on similar energy scales, the theoretical treatment varies
depending on the regime which is being considered. These limitations are
overcome here by starting from a tight-binding approach and computing exact
numerical results. By avoiding special limit cases, we found a smooth evolution
between the different regimes. We predict that the atomic collapse effect
persists even after the magnetic field is activated and that the critical
charge remains unchanged. We show that the atomic collapse regime is
characterized: 1) by a series of Landau level anticrossings and 2) by the
absence of scaling of the Landau levels with regard to magnetic
field strength
Spectroscopy of snake states using a graphene Hall bar
An approach to observe snake states in a graphene Hall bar containing a
pn-junction is proposed. The magnetic field dependence of the bend resistance
in a ballistic graphene Hall bar structure containing a tilted pn-junction
oscillates as a function of applied magnetic field. We show that each
oscillation is due to a specific snake state that moves along the pn-interface.
Furthermore depending on the value of the magnetic field and applied potential
we can control the lead in which the electrons will end up and hence control
the response of the system
Quasi-bound states of Schrodinger and Dirac electrons in magnetic quantum dot
The properties of a two-dimensional electron are investigated in the presence
of a circular step magnetic field profile. Both electrons with parabolic
dispersion as well as Dirac electrons with linear dispersion are studied. We
found that in such a magnetic quantum dot no electrons can be confined.
Nevertheless close to the Landau levels quasi-bound states can exist with a
rather long life time.Comment: 9 pages, 10 figure
Pseudo magnetic field in strained graphene: revisited
We revisit the theory of the pseudo magnetic field as induced by strain in
graphene using the tight-binding approach. A systematic expansion of the
hopping parameter and the deformation of the lattice vectors is presented from
which we obtain an expression for the pseudo magnetic field for low energy
electrons. We generalize and discuss previous results and propose a novel
effective Hamiltonian. The contributions of the different terms to the pseudo
magnetic field expression is investigated for a model triaxial strain profile
and are compared with the full solution. Our work suggests that the previous
proposed pseudo magnetic field expression is valid up to reasonably high strain
15 % and there is no K-dependent pseudo-magnetic field.Comment: 11 pages, 4 figure
Scattering of Dirac electrons by circular mass barriers: valley filter and resonant scattering
The scattering of two-dimensional (2D) massless Dirac electrons is
investigated in the presence of a random array of circular mass barriers. The
inverse momentum relaxation time and the Hall factor are calculated and used to
obtain parallel and perpendicular resistivity components within linear
transport theory. We found a non zero perpendicular resistivity component which
has opposite sign for electrons in the different K and K' valleys. This
property can be used for valley filter purposes. The total cross-section for
scattering on penetrable barriers exhibit resonances due to the presence of
quasi-bound states in the barriers that show up as sharp gaps in the
cross-section while for Schr\"{o}dinger electrons they appear as peaks.Comment: 10 pages, 11 figure
Resonant valley filtering of massive Dirac electrons
Electrons in graphene, in addition to their spin, have two pseudospin degrees
of freedom: sublattice and valley pseudospin. Valleytronics uses the valley
degree of freedom as a carrier of information similar to the way spintronics
uses electron spin. We show how a double barrier structure consisting of
electric and vector potentials can be used to filter massive Dirac electrons
based on their valley index. We study the resonant transmission through a
finite number of barriers and we obtain the energy spectrum of a superlattice
consisting of electric and vector potentials. When a mass term is included the
energy bands and energy gaps at the K and K' points are different and they can
be tuned by changing the potential.Comment: 20 figure
Magnetic Kronig-Penney model for Dirac electrons in single-layer graphene
The properties of Dirac electrons in a magnetic superlattice (SL) on graphene
consisting of very high and thin (delta-function) barriers are investigated. We
obtain the energy spectrum analytically and study the transmission through a
finite number of barriers. The results are contrasted with those for electrons
described by the Schrodinger equation. In addition, a collimation of an
incident beam of electrons is obtained along the direction perpendicular to
that of the SL. We also highlight the analogy with optical media in which the
refractive index varies in space.Comment: 21 pages, 13 figures, to appear in New Journal of Physic