Designing electronic properties of two-dimensional crystals through optimization of deformations

TL;DR

This paper introduces a versatile optimization framework for designing the electronic properties of two-dimensional materials, especially graphene, by controlling local strain to achieve desired pseudomagnetic field profiles, facilitating experimental realization.

Contribution

The authors develop a general optimization method that solves the inverse problem of determining deformation parameters to produce targeted electronic effects in 2D materials, with applications beyond graphene.

Findings

Efficiently computes deformation parameters matching target pseudomagnetic fields.

Ensures deformations comply with elastic constraints of graphene.

Applicable to various physical quantities dependent on strain.

Abstract

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.