Topological insulators are a class of solids in which the non-trivial inverted bulk band structure gives rise to metallic surface states that are robust against impurity scattering. In three-dimensional (3D) topological insulators, however, the surface Dirac fermions intermix with the conducting bulk, thereby complicating access to the low-energy (Dirac point) charge transport or magnetic response. Here we use differential magnetometry to probe spin rotation in the 3D topological material family (Bi2Se3, Bi2Te3 and Sb2Te3). We report a paramagnetic singularity in the magnetic susceptibility at low magnetic fields that persists up to room temperature, and which we demonstrate to arise from the surfaces of the samples. The singularity is universal to the entire family, largely independent of the bulk carrier density, and consistent with the existence of electronic states near the spin-degenerate Dirac point of the 2D helical metal. The exceptional thermal stability of the signal points to an intrinsic surface cooling process, probably of thermoelectric origin, and establishes a sustainable platform for the singular field-tunable Dirac spin response.

Surfaces of three-dimensional topological insulators have emerged as one of the most remarkable states of condensed quantum matter 1-5 where exotic electronic phases of Dirac particles should arise 1,6-8 . Here we report a discovery of surface superconduc-

Topological insulators are potentially transformative quantum solids with metallic surface states which have Dirac band structure and are immune to disorder. Ubiquitous charged bulk defects, however, pull the Fermi energy into the bulk bands, denying access to surface charge transport. Here we demonstrate that irradiation with swift (∼2.5 MeV energy) electron beams allows to compensate these defects, bring the Fermi level back into the bulk gap and reach the charge neutrality point (CNP). Controlling the beam fluence, we tune bulk conductivity from p- (hole-like) to n-type (electron-like), crossing the Dirac point and back, while preserving the Dirac energy dispersion. The CNP conductance has a two-dimensional character on the order of ten conductance quanta and reveals, both in Bi2Te3 and Bi2Se3, the presence of only two quantum channels corresponding to two topological surfaces. The intrinsic quantum transport of the topological states is accessible disregarding the bulk size.

Robustness to disorder is the defining property of any topological state. The ultimate disorder limits to topological protection are still unknown, although a number of theories predict that even in the amorphous state a quantized conductance might yet reemerge. Here we report that in strongly disordered thin films of the topological material Sb 2 Te 3 disorder-induced spin correlations dominate transport of charge-they engender a spin memory phenomenon, generated by the nonequilibrium charge currents controlled by localized spins. We directly detect a glassy yet robust disorder-induced magnetic signal in films free of extrinsic magnetic dopants, which becomes null in a lower-disorder crystalline state. This is where large isotropic negative magnetoresistance (MR)-a hallmark of spin memory-crosses over to positive MR, first with only one e 2 /h quantum conduction channel, in a weakly antilocalized diffusive transport regime with a 2D scaling characteristic of the topological state. A fresh perspective revealed by our findings is that spin memory effect sets a disorder threshold to the protected topological state. It also points to new possibilities of tuning spin-dependent charge transport by disorder engineering of topological materials.