spectroscopy (ARPES) scans using a double Mott detector setup [21], which systematically measures all three components of the spin of a photoelectron as a function of its energy and momentum throughout the Brillouin zone (Supplementary Information). Although the surface electrons of both Bi$_{2}$Se$_{3}$ and Bi$_{2}$Te$_{3}$ exhibit a finite density of states near E$_{F}$ (Figs 1(a)-(d)), there is an additional contribution to the density of states around momentum ¯ Γ from the spin-degenerate bulk conduction band in Bi$_{2}$Se$_{3}$ [15]. Therefore, the helical nature of the surface electrons is most clearly resolved in Bi$_{2}$Te$_{3}$. We analyzed the spin-polarization of photoelectrons emitted at a binding energy E$_{B}$ = -20 meV along the k$_{x}$ ( ‖ ¯ Γ- ¯ M) cut in Bi$_{2}$Te$_{3}$ (inset Fig. 1(e)). Because the surface state dispersion of Bi$_{2}$X$_{3}$ exhibits a pronounced time dependence after cleavage (SI) related to semiconductor band bending effects [17], data collection times were only long enough to ensure a level of statistics sufficient to measure the spin-polarized character of the surface states. Figures 1(e) and (f) show the measured spin polarization spectra P$_{i}$ of the i = x , y and z (out-of-plane) components along the ¯ Γ- ¯ M direction. In the x and z directions, no clear signal can be discerned within the margins of statistical error. In the y direction on the other hand, clear polarization signals of equal magnitude and opposite sign are observed for surface electrons of opposite momentum, evidence that the spin and momentum directions are one-to-one locked. This is most clearly seen in the spin-resolved spectra ( I ↑ , ↓ y ; Fig. 1(g)), which are calculated from P$_{y}$ according to I$_{y}$ = I$_{tot}$ (1+ P$_{y}$ )/2 and I$_{y}$ = I$_{tot}$ (1- P$_{y}$ )/2, where I$_{tot}$ is the spin-averaged intensity. To extract the spin polarization vectors of the forward (+ k$_{x}$ ) and backward (- k$_{x}$ ) moving electrons, we performed a standard numerical fit (SI) [21]. The fit results yield 100( ± 15)% polarized (see Fig. 1(h)) spins that point along the ( k × z ) direction, which is consistent with its spin-orbit coupling origin [14, 21]. Our combined observations of a linear dispersion relation and a one-to-one locking of momentum and spin directions allow us to conclude that the surface electrons of Bi$_{2}$X$_{3}$ (X = Se, Te) are helical Dirac fermions of Z$_{2}$ topological order origin (Fig. 1). To experimentally access these helical Dirac fermions for research device applications, the electronic structure must be in the topological transport regime where there is zero charge fermion density [7–9]. This regime occurs when E$_{F}$ lies in between the bulk valence band maximum (VBM) and the bulk conduction band minimum (CBM), and exactly at the surface Dirac point, which should in turn lie at a Kramers’ time-reversal invariant momentum [3, 4]. This is clearly not the case in either Bi$_{2}$Te$_{3}$, Bi$_{2}$(Sn)Te$_{3}$, Bi$_{2}$Se$_{3}$ or 4