Inverse Design of Strained Graphene Surfaces for Electron Control (Communications in Computational Physics, 2023)
This paper is devoted to the inverse design of strained graphene surfaces forthe control of electrons in the semi-classical optical-like regime. Assuming that chargecarriers are described by the Dirac equation in curved-space and exploiting the factthat 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 desiredeffective refractive index profile. The latter is first determined by solving semi-classicaltrajectories and by optimizing a chosen objective functional using a genetic algorithm.Then, the graded refractive index corresponding to the strain field is obtained by usingits connection to the metric component in isothermal coordinates. These coordinatesare evaluated via numerical quasiconformal transformations by solving the Beltramiequation with a finite volume method. The graphene surface deformation is finallyoptimized, also using a genetic algorithm, to reproduce the desired index of refraction. Some analytical results and numerical experiments are performed to illustratethe methodology.
Keywords: Graphene; isothermal coordinates; Beltrami equation; gravitational lens; waveguide; finite volume method; genetic algorithm; Dirac equation.