Spatial fluctuations of helical Dirac fermions on the surface of topological insulators

Surfaces of topological insulators host a new class of states with Dirac dispersion and helical spin texture. Potential quantum computing and spintronic applications using these states require manipulation of their electronic properties at the Dirac energy of their band structure by inducing magnetism or superconductivity through doping and the proximity effect. Yet, the response of these states near the Dirac energy in their band structure to various perturbations has remained unexplored. Here we use spectroscopic mapping with the scanning tunnelling microscope to study their response to magnetic and non-magnetic bulk dopants in Bi 2 Te 3 and Bi 2 Se 3. Far from the Dirac energy, helicity provides remarkable resilience to backscattering even in the presence of ferromagnetism. However, approaching the Dirac point, where the surface states' wavelength diverges, bulk doping results in pronounced nanoscale spatial fluctuations of energy, momentum and helicity. Our results and their connection with similar studies of Dirac electrons in graphene demonstrate that although backscattering and localization are absent for Dirac topological surface states, reducing charge defects is required for both tuning the chemical potential to the Dirac energy and achieving high electrical mobility for these novel states.