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
