AbstractEnhancing the transport contribution of surface states in topological insulators is vital if they are to be incorporated into practical devices. Such efforts have been limited by the defect behaviour of Bi₂Te₃ (Se₃) topological materials, where the subtle bulk carrier from intrinsic defects is dominant over the surface electrons. Compensating such defect carriers is unexpectedly achieved in (Cu_0.1Bi_0.9)₂Te_3.06 crystals. Here we report the suppression of the bulk conductance of the material by four orders of magnitude by intense ageing. The weak antilocalization analysis, Shubnikov–de Haas oscillations and scanning tunnelling spectroscopy corroborate the transport of the topological surface states. Scanning tunnelling microscopy reveals that Cu atoms are initially inside the quintuple layers and migrate to the layer gaps to form Cu clusters during the ageing. In combination with first-principles calculations, an atomic tunnelling–clustering picture across a diffusion barrier of 0.57 eV is proposed.