16,870 research outputs found
Random gap model for graphene and graphene bilayers
The effect of a randomly fluctuating gap, created by a random staggered
potential, is studied in a monolayer and a bilayer of graphene. The density of
states, the one-particle scattering rate and transport properties (diffusion
coefficient and conductivity) are calculated at the neutrality point. All these
quantities vanish at a critical value of the average staggered potential,
signaling a continuous transition to an insulating behavior. The calculations
are based on the self-consistent Born approximation for the one-particle
scattering rate and a massless mode of the two-particle Green's function which
is created by spontaneous symmetry breaking. Transport quantities are directly
linked to the one-particle scattering rate. Moreover, the effect of disorder is
very weak in the case of a monolayer but much stronger in bilayer graphene.Comment: 5 pages, 1 figur
Circular edge states in photonic crystals with a Dirac node
Edge states are studied for the two-dimensional Dirac equation in a circular
geometry. The properties of the two-component electromagnetic field are
discussed in terms of the three-component polarization field, which can form a
vortex structure near the Dirac node with a vorticity changing with the sign of
the Dirac mass. The Berry curvature of the polarization field is related to the
Berry curvature of the Dirac spinor state. This quantity is sensitive to a
change of boundary conditions. In particular, it vanishes for a geometry with a
single boundary but not for a geometry with two boundaries. This effect is
robust against the creation of a step-like edge inside the sample.Comment: 8 pages, 5 figure
Zero mode protection at particle-hole symmetry: a geometric interpretation
The properties of zero modes in particle-hole symmetric systems are analyzed
in the presence of strong random scattering by a disordered environment. The
study is based on the calculation of the time-averaged density distribution on
a lattice. In particular, a flat distribution is found for strong random
scattering. This result is compared with a decaying distribution for weak
random scattering by an analysis of the scattering paths. In the calculation we
consider the invariant measure of the average two-particle Green's function,
which is related to lattice-covering self-avoiding (LCSA) strings. In
particular, strong scattering is associated with LCSA loops, whereas weaker
scattering is associated with open LCSA strings. Our results are a
generalization of the delocalized state observed at the band center of a
one-dimensional tight-binding model with random hopping by Dyson in 1953.Comment: 12 pages, 3 figure
Controlling dynamical entanglement in a Josephson tunneling junction
We analyze the evolution of an entangled many-body state in a Josephson
tunneling junction. A N00N state, which is a superposition of two complementary
Fock states, appears in the evolution with sufficient probability only for a
moderate many-body interaction on an intermediate time scale. This time scale
is inversely proportional to the tunneling rate. Interaction between particles
supports entanglement: The probability for creating an entangled state decays
exponentially with the number of non-interacting particles, whereas it decays
only like the inverse square root of the number of interacting particles.Comment: 9 pages, 5 figure
Quantum diffusion in two-dimensional random systems with particle-hole symmetry
We study the scattering dynamics of an -component spinor wavefunction in a
random environment on a two-dimensional lattice. In the presence of
particle-hole symmetry we find diffusion on large scales. The latter is
described by a non-interacting Grassmann field, indicating a special kind of
asymptotic freedom in .Comment: 9 pages, no figures, extended versio
Short note on the Rabi model
The spectral density of the Rabi model is calculated exactly within a
continued fraction approach. It is shown that the method yields a convergent
solution.Comment: 4 pages, 1 figur
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