We have investigated the weak antilocalization (WAL) effect in the p-type Bi$_2$Se$_{2.1}$Te$_{0.9}$ topological system. The magnetoconductance shows a cusp-like feature at low magnetic fields, indicating the presence of the WAL effect. The WAL curves measured at different tilt angles merge together when they are plotted as a function of the normal field components, showing that surface states dominate the magnetoconductance in the Bi$_2$Se$_{2.1}$Te$_{0.9}$ crystal. We have calculated magnetoconductance per conduction channel and applied the Hikami-Larkin-Nagaoka formula to determine the physical parameters that characterize the WAL effect. The number of conduction channels and the phase coherence length do not change with temperature up to T=5 K. In addition, the sample shows a large positive magnetoresistance that reaches 1900% under a magnetic field of 35 T at T=0.33K with no sign of saturation. The magnetoresistance value decreases with both increasing temperature and tilt angle of the sample surface with respect to the magnetic field. The large magnetoresistance of topological insulators can be utilized in future technology such as sensors and memory devices.
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