Imaging anyons with scanning tunneling microscopy

Non-Abelian anyons have long been predicted to occur in the fractional quantum Hall (FQH) phases that form in two-dimensional electron gases in the presence of a large magnetic field. However, direct experimental evidence of anyons and tests that can distinguish between Abelian and non-Abelian quantum ground states with such excitations have remained ambiguous. Here we propose a new experimental approach to directly visualize the structure of interacting electronic states of FQH phases with the scanning tunneling microscope (STM). Our theoretical calculations show how spectroscopy mapping with the STM near individual impurity defects can be used to image fractional statistics in FQH states, identifying unique signatures that can distinguish different quantum Hall phases. In this talk, I'll talk about the theoretical signatures of Laughlin, Moore-Read and Hierarchy states.