Figure 5: Correlating potential fluctuations with point defects.

(a) Two dI/dV curves taken from different regions on Bi₂Se₃ show how the Dirac point shift can be correlated, to first order, with the intensity shift in dI/dV intensity—this allows single-pass dI/dV scans to map the Dirac point fluctuations. (b) A scatter plot determined from line spectroscopy data across 300 nm of Bi₂Se₃ shows the first-order relation between the Dirac point and the lock-in signal at −540 meV; R²=0.72. (c) Seven-point moving average from the line spectroscopy visually shows the correlation from b. A 350 × 50 nm region of Bi₂Se₃ is then investigated with this technique: topography (d) at −200 meV shows Se vacancies, and the dI/dV image of the same region taken at −540 meV shows fluctuations in the Dirac point (e). In e, the red circles represent bright triangular defects, determined from d. (f) dI/dV image at −270 meV showing that the dI/dV map gives an inverse image of e above the Dirac point. The cross-correlation coefficient is −0.5, quantitatively confirming the contrast reversal despite the higher noise level in f. A visualization of the deviations from the distribution mean for dim-type Bi_Se defects is shown in g, where red points indicate a Bi_Se defect with an energy state that is more positive than the distribution mean, and blue points indicate a Bi_Se defect below the distribution mean (see inset). The dI/dV image at −350 meV (h) shows both dim and bright type defects. The fluctuations in the Bi_Se defect energy scale correlates directly with the fluctuations in the Dirac point; a few extreme examples are highlighted in boxes in e–h. Colour scales: d, 40 pm; e, 30 meV; h, 10 pA/V.