1,529 research outputs found
Scattering by flexural phonons in suspended graphene under back gate induced strain
We have studied electron scattering by out-of-plane (flexural) phonon modes
in doped suspended graphene and its effect on charge transport. In the
free-standing case (absence of strain) the flexural branch shows a quadratic
dispersion relation, which becomes linear at long wavelength when the sample is
under tension due to the rotation symmetry breaking. In the non-strained case,
scattering by flexural phonons is the main limitation to electron mobility.
This picture changes drastically when strains above are considered. Here we study in particular the
case of back gate induced strain, and apply our theoretical findings to recent
experiments in suspended graphene.Comment: 4 pages, 3 figures, published versio
Measurement of Scattering Rate and Minimum Conductivity in Graphene
The conductivity of graphene samples with various levels of disorder is
investigated for a set of specimens with mobility in the range of
cm/V sec. Comparing the experimental data with the
theoretical transport calculations based on charged impurity scattering, we
estimate that the impurity concentration in the samples varies from cm. In the low carrier density limit, the conductivity exhibits
values in the range of , which can be related to the residual
density induced by the inhomogeneous charge distribution in the samples. The
shape of the conductivity curves indicates that high mobility samples contain
some short range disorder whereas low mobility samples are dominated by long
range scatterers.Comment: 4 pages 4 figure
Symbolic dynamics for the -centre problem at negative energies
We consider the planar -centre problem, with homogeneous potentials of
degree -\a<0, \a \in [1,2). We prove the existence of infinitely many
collisions-free periodic solutions with negative and small energy, for any
distribution of the centres inside a compact set. The proof is based upon
topological, variational and geometric arguments. The existence result allows
to characterize the associated dynamical system with a symbolic dynamics, where
the symbols are the partitions of the centres in two non-empty sets
The Non-Trapping Degree of Scattering
We consider classical potential scattering. If no orbit is trapped at energy
E, the Hamiltonian dynamics defines an integer-valued topological degree. This
can be calculated explicitly and be used for symbolic dynamics of
multi-obstacle scattering.
If the potential is bounded, then in the non-trapping case the boundary of
Hill's Region is empty or homeomorphic to a sphere.
We consider classical potential scattering. If at energy E no orbit is
trapped, the Hamiltonian dynamics defines an integer-valued topological degree
deg(E) < 2. This is calculated explicitly for all potentials, and exactly the
integers < 2 are shown to occur for suitable potentials.
The non-trapping condition is restrictive in the sense that for a bounded
potential it is shown to imply that the boundary of Hill's Region in
configuration space is either empty or homeomorphic to a sphere.
However, in many situations one can decompose a potential into a sum of
non-trapping potentials with non-trivial degree and embed symbolic dynamics of
multi-obstacle scattering. This comprises a large number of earlier results,
obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more
detailed proofs and remark
Bailout Embeddings, Targeting of KAM Orbits, and the Control of Hamiltonian Chaos
We present a novel technique, which we term bailout embedding, that can be
used to target orbits having particular properties out of all orbits in a flow
or map. We explicitly construct a bailout embedding for Hamiltonian systems so
as to target KAM orbits. We show how the bailout dynamics is able to lock onto
extremely small KAM islands in an ergodic sea.Comment: 3 figures, 9 subpanel
Temperature dependent transport in suspended graphene
The resistivity of ultra-clean suspended graphene is strongly temperature
dependent for 5K<T<240K. At T~5K transport is near-ballistic in a device of
~2um dimension and a mobility ~170,000 cm^2/Vs. At large carrier density,
n>0.5*10^11 cm^-2, the resistivity increases with increasing T and is linear
above 50K, suggesting carrier scattering from acoustic phonons. At T=240K the
mobility is ~120,000 cm^2/Vs, higher than in any known semiconductor. At the
charge neutral point we observe a non-universal conductivity that decreases
with decreasing T, consistent with a density inhomogeneity <10^8 cm^-2
Canonical Melnikov theory for diffeomorphisms
We study perturbations of diffeomorphisms that have a saddle connection
between a pair of normally hyperbolic invariant manifolds. We develop a
first-order deformation calculus for invariant manifolds and show that a
generalized Melnikov function or Melnikov displacement can be written in a
canonical way. This function is defined to be a section of the normal bundle of
the saddle connection.
We show how our definition reproduces the classical methods of Poincar\'{e}
and Melnikov and specializes to methods previously used for exact symplectic
and volume-preserving maps. We use the method to detect the transverse
intersection of stable and unstable manifolds and relate this intersection to
the set of zeros of the Melnikov displacement.Comment: laTeX, 31 pages, 3 figure
Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene
Bilayer graphene (BLG) at the charge neutrality point (CNP) is strongly
susceptible to electronic interactions, and expected to undergo a phase
transition into a state with spontaneous broken symmetries. By systematically
investigating a large number of singly- and doubly-gated bilayer graphene (BLG)
devices, we show that an insulating state appears only in devices with high
mobility and low extrinsic doping. This insulating state has an associated
transition temperature Tc~5K and an energy gap of ~3 meV, thus strongly
suggesting a gapped broken symmetry state that is destroyed by very weak
disorder. The transition to the intrinsic broken symmetry state can be tuned by
disorder, out-of-plane electric field, or carrier density
- …