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

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.

arXiv comment37 pages, 9 figures. This submission contains low-resolution bitmap images; high-resolution images can be found in version 1, which is ~13.5 MB

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• Band flattening in buckled monolayer graphene
• Gauge fields in graphene with nonuniform elastic deformations: A quantum field theory approach
• Patched Green's function techniques for two dimensional systems: Electronic behaviour of bubbles and perforations in graphene
• Quantized transport, strain-induced perfectly conducting modes and valley filtering on shape-optimized graphene Corbino devices
• Preparing local strain patterns in graphene by atomic force microscope based indentation
• Optimal control of plate shape with incompatible strain fields
• Straintronics beyond homogeneous deformation
• Sound waves induce Volkov-like states, band structure and collimation effect in graphene
• Bubbles in graphene - a computational study