Green's function modeling of response of two-dimensional materials to point probes for scanning probe microscopy

•Green's function for Laplace/Poisson equation for two-dimensional materials with defects.•Sensitive to shape and nature of defects especially antidots.•Useful for thermal and electrostatic characterization of two-dimensional materials.•Suggested that Green's function is a physical characteristic of materials.•Green's function for two-dimensional materials can be measured by scanning probe microscopy.

A Green's function (GF) method is developed for interpreting scanning probe microscopy (SPM) measurements on new two-dimensional (2D) materials. GFs for the Laplace/Poisson equations are calculated by using a virtual source method for two separate cases of a finite material containing a rectangular defect and a hexagonal defect. The prescribed boundary values are reproduced almost exactly by the calculated GFs. It is suggested that the GF is not just a mathematical artefact but a basic physical characteristic of material systems, which can be measured directly by SPM for 2D solids. This should make SPM an even more powerful technique for characterization of 2D materials.