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We provide a detailed microscopic characterization of the influence ofdefects-induced disorder onto the Dirac spectrum of three dimensionaltopological insulators. By spatially resolved Landau-levels spectroscopymeasurements, we reveal the existence of nanoscale fluctuations of both theDirac point energy as well as of the Dirac-fermions velocity which is found tospatially change in opposite direction for electrons and holes, respectively.These results evidence a scenario which goes beyond the existing picture basedon chemical potential fluctuations. The findings are consistently explained byconsidering the microscopic effects of local stain introduced by defects, whichour model calculations show to effectively couple to topological states,reshaping their Dirac-like dispersion over a large energy range. In particular,our results indicate that the presence of microscopic spatially varying stain,inevitably present in crystals because of the random distribution of defects,effectively couple to topological states and should be carefully considered forcorrectly describing the effects of disorder.

Mapping the effect of defect-induced strain disorder on the Dirac states of topological insulators