1,782 research outputs found
Designing electronic properties of two-dimensional crystals through optimization of deformations
One of the enticing features common to most of the two-dimensional electronic
systems that are currently at the forefront of materials science research is
the ability to easily introduce a combination of planar deformations and
bending in the system. Since the electronic properties are ultimately
determined by the details of atomic orbital overlap, such mechanical
manipulations translate into modified electronic properties. Here, we present a
general-purpose optimization framework for tailoring physical properties of
two-dimensional electronic systems by manipulating the state of local strain,
allowing a one-step route from their design to experimental implementation. A
definite example, chosen for its relevance in light of current experiments in
graphene nanostructures, is the optimization of the experimental parameters
that generate a prescribed spatial profile of pseudomagnetic fields in
graphene. But the method is general enough to accommodate a multitude of
possible experimental parameters and conditions whereby deformations can be
imparted to the graphene lattice, and complies, by design, with graphene's
elastic equilibrium and elastic compatibility constraints. As a result, it
efficiently answers the inverse problem of determining the optimal values of a
set of external or control parameters that result in a graphene deformation
whose associated pseudomagnetic field profile best matches a prescribed target.
The ability to address this inverse problem in an expedited way is one key step
for practical implementations of the concept of two-dimensional systems with
electronic properties strain-engineered to order. The general-purpose nature of
this calculation strategy means that it can be easily applied to the
optimization of other relevant physical quantities which directly depend on the
local strain field, not just in graphene but in other two-dimensional
electronic membranes.Comment: 37 pages, 9 figures. This submission contains low-resolution bitmap
images; high-resolution images can be found in version 1, which is ~13.5 M
Inverse Scattering and the Geroch Group
We study the integrability of gravity-matter systems in D=2 spatial
dimensions with matter related to a symmetric space G/K using the well-known
linear systems of Belinski-Zakharov (BZ) and Breitenlohner-Maison (BM). The
linear system of BM makes the group structure of the Geroch group manifest and
we analyse the relation of this group structure to the inverse scattering
method of the BZ approach in general. Concrete solution generating methods are
exhibited in the BM approach in the so-called soliton transformation sector
where the analysis becomes purely algebraic. As a novel example we construct
the Kerr-NUT solution by solving the appropriate purely algebraic
Riemann-Hilbert problem in the BM approach.Comment: 30 pages. v2: Typos correcte
Multisymplectic geometry, variational integrators, and nonlinear PDEs
This paper presents a geometric-variational approach to continuous and
discrete mechanics and field theories. Using multisymplectic geometry, we show
that the existence of the fundamental geometric structures as well as their
preservation along solutions can be obtained directly from the variational
principle. In particular, we prove that a unique multisymplectic structure is
obtained by taking the derivative of an action function, and use this structure
to prove covariant generalizations of conservation of symplecticity and
Noether's theorem. Natural discretization schemes for PDEs, which have these
important preservation properties, then follow by choosing a discrete action
functional. In the case of mechanics, we recover the variational symplectic
integrators of Veselov type, while for PDEs we obtain covariant spacetime
integrators which conserve the corresponding discrete multisymplectic form as
well as the discrete momentum mappings corresponding to symmetries. We show
that the usual notion of symplecticity along an infinite-dimensional space of
fields can be naturally obtained by making a spacetime split. All of the
aspects of our method are demonstrated with a nonlinear sine-Gordon equation,
including computational results and a comparison with other discretization
schemes.Comment: LaTeX2E, 52 pages, 11 figures, to appear in Comm. Math. Phy
Conformally parametrized surfaces associated with CP^(N-1) sigma models
Two-dimensional conformally parametrized surfaces immersed in the su(N)
algebra are investigated. The focus is on surfaces parametrized by solutions of
the equations for the CP^(N-1) sigma model. The Lie-point symmetries of the
CP^(N-1) model are computed for arbitrary N. The Weierstrass formula for
immersion is determined and an explicit formula for a moving frame on a surface
is constructed. This allows us to determine the structural equations and
geometrical properties of surfaces in R^(N^2-1). The fundamental forms,
Gaussian and mean curvatures, Willmore functional and topological charge of
surfaces are given explicitly in terms of any holomorphic solution of the CP^2
model. The approach is illustrated through several examples, including surfaces
immersed in low-dimensional su(N) algebras.Comment: 32 page
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