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

Aging the Cu-doped Bi2Te3 crystals for the topological transport and its atomic tunneling-clustering dynamics