Sparse Big Data Spectroscopy: Advanced techniques for maximally resolving microARPES data on topological insulators

Topological insulators are bulk semiconductors that manifest in-gap surface states with massless Dirac-like dispersion due to the topological bulk-boundary correspondence principle. These surface states can be manipulated by the interface environment to display various emergent phenomena. Here, we use angle-resolved photoemission spectroscopy (ARPES) and scanning tunnelling microscopy (STM) to investigate the interplay of crystallographic inhomogeneity with the topologically ordered band structure in a model topological insulator. We develop quantitative analysis methods to obtain spectroscopic information in spite of a limited dwell time on each measured point. We find that the band energies vary on the scale of 50 meV across the sample surface, and this enables single-sample measurements that are analogous to a multi-sample doping series. By focusing separately on the bulk and surface electrons we reveal a hybridisation-like interplay between fluctuations in the surface and bulk state energetics.