We report on the observation of the two-dimensional weak antilocalization in (Cu0.1Bi0.9)2Te3.06 crystals relying on measurements of the magnetoresistance in a tilted field. The dephasing analysis and scanning tunneling spectroscopy corroborate the transport of the topological surface states (SS). The SSs contribute 3.3% conductance in 30{mu}m-thick material and become dominant in the 100nm-thick flakes. Such optimized topological SS transport is achieved by an intense aging process, when the bulk conductance is suppressed by four orders of magnitude in the long period. Scanning tunneling microscopy reveals that Cu atoms are initially inside the quintuple layers and migrate to the layer gaps to form Cu clusters during the aging. In combination with first-principles calculations, an atomic tunneling-clustering procedure across a diffusion barrier of 0.57eV is proposed.
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