57 research outputs found
Curvatronics with bilayer graphene in an effective spacetime
We show that in AB stacked bilayer graphene low energy excitations around the
semimetallic points are described by massless, four dimensional Dirac fermions.
There is an effective reconstruction of the 4 dimensional spacetime, including
in particular the dimension perpendicular to the sheet, that arises dynamically
from the physical graphene sheet and the interactions experienced by the
carriers. The effective spacetime is the Eisenhart-Duval lift of the dynamics
experienced by Galilei invariant L\'evy-Leblond spin particles
near the Dirac points. We find that changing the intrinsic curvature of the
bilayer sheet induces a change in the energy level of the electronic bands,
switching from a conducting regime for negative curvature to an insulating one
when curvature is positive. In particular, curving graphene bilayers allows
opening or closing the energy gap between conduction and valence bands, a key
effect for electronic devices. Thus using curvature as a tunable parameter
opens the way for the beginning of curvatronics in bilayer graphene.Comment: 8 pages, 3 figures. Revised version with additional materia
Morse Theory for geodesics in singular conformal metrics
Motivated by the use of degenerate Jacobi metrics for the study of brake
orbits and homoclinics, we develop a Morse theory for geodesics in conformal
metrics having conformal factors vanishing on a regular hypersurface of a
Riemannian manifold.Comment: 22 pages. To appear in Communications in Analysis and Geometr
Gravitational collapse of homogeneous scalar fields
Conditions under which gravity coupled to self interacting scalar field
determines singularity formation are found and discussed. It is shown that,
under a suitable matching with an external space, the boundary, if collapses
completely, may give rise to a naked singularity. Issues related to the
strength of the singularity are discussed.Comment: LaTeX2e; revised versio
On the normal exponential map in singular conformal metrics
Brake orbits and homoclinics of autonomous dynamical systems correspond, via
Maupertuis principle, to geodesics in Riemannian manifolds endowed with a
metric which is singular on the boundary (Jacobi metric). Motivated by the
classical, yet still intriguing in many aspects, problem of establishing
multiplicity results for brake orbits and homoclinics, as done in [6, 7, 10],
and by the development of a Morse theory in [8] for geodesics in such kind of
metric, in this paper we study the related normal exponential map from a global
perspective.Comment: 10 page
Functions on the sphere with critical points in pairs and orthogonal geodesic chords
Using an estimate on the number of critical points for a Morse-even function
on the sphere , , we prove a multiplicity result for
orthogonal geodesic chords in Riemannian manifolds with boundary that are
diffeomorphic to Euclidean balls. This yields also a multiplicity result for
brake orbits in a potential well.Comment: 12 pages, 3 figure
Electronic properties of curved few-layers graphene: a geometrical approach
We show the presence of non-relativistic L\'evy-Leblond fermions in flat
three- and four-layers graphene with AB stacking, extending the results
obtained in [Curvatronics2017] for bilayer graphene. When the layer is curved
we obtain a set of equations for Galilean fermions that are a variation of
those of L\'evy-Leblond with a well defined combination of pseudospin, and that
admit L\'evy-Leblond spinors as solutions in an approriate limit. The local
energy of such Galilean fermions is sensitive to the intrinsic curvature of the
surface. We discuss the relationship between two-dimensional pseudospin,
labelling layer degrees of freedom, and the different energy bands. For
L\'evy-Leblond fermions an interpretation is given in terms of massless
fermions in an effective 4D spacetime, and in this case the pseudospin is
related to four dimensional chirality. A non-zero energy band gap between
conduction and valence electronic bands is obtained for surfaces with positive
curvature.Comment: 16 pages, 4 figures. Matches the published version. Refined theory
that describes the unique combination of isospin states ocurring in curved
bilayer graphene sheet
New mathematical framework for spherical gravitational collapse
A theorem, giving necessary and sufficient condition for naked singularity
formation in spherically symmetric non static spacetimes under hypotheses of
physical acceptability, is formulated and proved. The theorem relates existence
of singular null geodesics to existence of regular curves which are
super-solutions of the radial null geodesic equation, and allows us to treat
all the known examples of naked singularities from a unified viewpoint. New
examples are also found using this approach, and perspectives are discussed.Comment: 8 pages, LaTeX2
Spherically symmetric perfect fluid in area-radial coordinates
We study the spherically symmetric collapse of a perfect fluid using
area-radial coordinates. We show that analytic mass functions describe a static
regular centre in these coordinates. In this case, a central singularity can
not be realized without an infinite discontinuity in the central density. We
construct mass functions involving fluid dynamics at the centre and investigate
the relationship between those and the nature of the singularities.Comment: Accepted by CQG. LaTex file, 14 pages, no figure
Collapse of spherical charged anisotropic fluid spacetimes
A class of spherical collapsing exact solutions with electromagnetic charge
is derived. This class of solutions -- in general anisotropic -- contains
however as a particular case the charged dust model already known in
literature. Under some regularity assumptions that in the uncharged case give
rise to naked singularities, it is shown that the process of shell focusing
singularities avoidance -- already known for the dust collapse -- also takes
place here, determing shell crossing effects or a completely regular solution.Comment: 13 pages, 2 figures. Version to appear on Class Quantum Gra
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