259 research outputs found
Negative static permittivity and violation of Kramers-Kronig relations in quasi-two-dimensional crystals
We investigate the wave-vector and frequency-dependent screening of the
electric field in atomically thin (quasi-two-dimensional) crystals. For
graphene and hexagonal boron nitride we find that, above a critical wave-vector
, the static permittivity
becomes negative and the Kramers-Kronig relations do not hold for
. Thus, in quasi-two-dimensional crystals,
we reveal the physical confirmation of a proposition put forward decades ago
(Kirzhnits, 1976), allowing for the breakdown of Kramers-Kronig relations and
for the negative static permittivity. In the vicinity of the critical
wave-vector, we find a giant growth of the permittivity. Our results, obtained
in the {\it ab initio} calculations using both the random-phase approximation
and the adiabatic time-dependent local-density approximation, and further
confirmed with a simple slab model, allow us to argue that the above
properties, being exceptional in the three-dimensional case, are common to
quasi-two-dimensional systems.Comment: 9 pages, 13 figure
Electronic excitations in quasi-2D crystals: What theoretical quantities are relevant to experiment?
The ab initio theory of electronic excitations in atomically thin
[quasi-two-dimensional (Q2D)] crystals presents extra challenges in comparison
to both the bulk and purely 2D cases. We argue that the conventionally used
energy-loss function Im (where ,
, and are the dielectric function, the momentum, and the
energy transfer, respectively) is not, generally speaking, the suitable
quantity for the interpretation of the electron-energy loss spectroscopy (EELS)
in the Q2D case, and we construct different functions pertinent to the EELS
experiments on Q2D crystals. Secondly, we emphasize the importance and develop
a convenient procedure of the elimination of the spurious inter-layer
interaction inherent to the use of the 3D super-cell method for the calculation
of excitations in Q2D crystals. Thirdly, we resolve the existing controversy in
the interpretation of the so-called and excitations in
monolayer graphene by demonstrating that both dispersive collective excitations
(plasmons) and non-dispersive single-particle (inter-band) transitions fall in
the same energy ranges, where they strongly influence each other.Comment: 19 pages, 6 figure
A comparison theorem for nonsmooth nonlinear operators
We prove a comparison theorem for super- and sub-solutions with non-vanishing
gradients to semilinear PDEs provided a nonlinearity is function with
. The proof is based on a strong maximum principle for solutions of
divergence type elliptic equations with VMO leading coefficients and with lower
order coefficients from a Kato class. An application to estimation of periodic
water waves profiles is given.Comment: 12 page
Oblique derivative problem for non-divergence parabolic equations with discontinuous in time coefficients in a wedge
We consider an oblique derivative problem in a wedge for nondivergence
parabolic equations with discontinuous in coefficients. We obtain weighted
coercive estimates of solutions in anisotropic Sobolev spaces.Comment: 26 page
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