**5. Conclusion**

In the summary, in our fabricated topological insulator Bi<sup>2</sup> Te3 thin film Hall Bar device, we report the observation of weak antilocalization (WAL) behavior and linear magnetoresistance (LMR). The WAL characteristics is found to be in the low temperature and in the low magnetic field region and the LMR is considered to be accompanied with gapless energy spectrum of surface Dirac fermions and is believed to be quantum origin. A dip near 0 T magnetic fields is observed in the magnetoresistance (MR) characteristics of Bi<sup>2</sup> Te3 thin film hall Bar device. The originated dip is from the WAL effect and is found to be at low temperatures. By fitting to the HLN model for 10 nm thin film, we also derive relatively large phase breaking length of 155.8 nm at 4 K. This dependence on the thickness of the thin film has a pronounced behavior, i.e., below a certain critical thickness there is no observable WAL behavior. In our study and analysis, we observe disappearance of WAL in <5 nm thickness film. The reason is the film of topological insulator is so thinned that it leads to an opening of the gap at the Dirac point and results in a degenerate, massive Dirac dispersion, which leads to the diminishment of surface transport, by the observing flatness in the magnetoresistance curve.
