Inverse design of strained graphene surfaces for electron control

TL;DR

This paper introduces a computational method for designing strained graphene surfaces to control electron trajectories by tailoring their effective refractive index profiles using inverse design and genetic algorithms.

Contribution

It presents a novel inverse design approach combining semi-classical trajectories, quasiconformal mappings, and genetic algorithms for strain engineering in graphene.

Findings

Successfully designed strain fields for targeted electron control.

Demonstrated the effectiveness of the inverse design methodology.

Validated the approach with analytical and numerical experiments.

Abstract

This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime. Assuming that charge carriers are described by the Dirac equation in curved-space and exploiting the fact that wave propagation can be described by ray-optics in this regime, a general computational strategy is proposed in order to find strain fields associated with a desired effective refractive index profile. The latter is first determined by solving semi-classical trajectories and by optimizing a chosen objective functional using a genetic algorithm. Then, the graded refractive index corresponding to the strain field is obtained by using its connection to the metric component in isothermal coordinates. These coordinates are evaluated via numerical quasiconformal transformations by solving the Beltrami equation with a finite volume method. The graphene surface deformation is finally optimized, also using a genetic algorithm, to reproduce the desired index of refraction. Some analytical results and numerical experiments are performed to illustrate the methodology.