Fig. 2: Charge transport across charge neutrality point.

a Hall resistance R_xy vs. magnetic field H after hydrogenation and on annealing at different temperatures T_a. Initially, the pristine Bi₂Te₃ crystal is p-type. The conversion from p-to n-type and back is indicated by the sign change of the slope dR_xy/dH. b Evolution of magnetoresistance (normalized to the value at zero field) under annealing with time steps \({{\Delta }}t=30\,\min\) implemented to tune Bi₂Te₃ crystal to stable CNP; it evolves from a quadratic field dependence of a typical bulk metal to a weak antilocalization (WAL) regime with a characteristic low-field cusp near CNP. The cusp fit parameter α = 2 × 0.5 signifies contributions from top and bottom surfaces (0.5 from each), see text and Supplementary Fig. 1. c Band structure cartoon for Bi₂Te₃ illustrates the upshift of the Fermi level E_F on hydrogenation (cyan arrow) and the reversal by de-hydrogenation (red arrow). Bulk conduction and bulk valence bands are labeled BCB and BVB correspondingly. The 2D electron gas (2DEG) bands at the bottom of BCB are shown in gray, see details in the Supplementary Fig. 5. In Bi₂Te₃, the \({E}_{{{{{\rm{F}}}}}}^{0}\) at the CNP is slightly above the Dirac point (DP) and the Dirac electrons dominate the transport when E_F is within the bulk gap^1,2. d Within the bulk gap, longitudinal sheet resistance R_xx vs. magnetic field scales with the out-of-plane field component \({H}_{\perp }=H\cos \theta\). e The change in WAL magnetoconductance ΔG_xx vs. magnetic field at different temperatures. With increasing temperature the WAL cusp in ΔG_xx smoothly vanishes and above ∼30 K transforms into a classical parabolic magnetoconductance. f The quantum dephasing length \({l}_{\phi }\propto 1/\sqrt{T}\), obtained from the fits to 2D localization theory (HLN²⁸, see text), is characteristic of the 2D transport. Inset: Hydrogenation preserves the topological π-Berry phase estimated from SdH quantum oscillations (see Supplementary Fig. 6).