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Spin-orbit coupling and weak antilocalization in thermoelectric material $β$-K$_{2}$Bi$_{8}$Se$_{13}$

We have studied the effect of spin-orbital coupling (SOC) on electronic transport properties of the thermoelectric material $β$-K$_{2}$Bi$_{8}$Se$_{13}$ via magnetoresistance (MR) measurements. We found that the strong SOC in this material results in weak antilocalization (WAL) effect, which can be well described by the three-dimensional weak localization model. The phase coherence length extracted from theoretical fitting exhibits a power-law temperature dependence with an exponent around 2.1, indicating that the electron phase dephasing is governed by electron - transverse phonon interactions. Like in topological insulators, the WAL effect in $β$-K$_{2}$Bi$_{8}$Se$_{13}$ can be quenched by magnetic impurities (Mn) but is robust against non-magnetic impurities (Te). Although our magnetotransport studies do not provide any evidences for topological surface states, our analyses suggest that SOC plays an important role in determining thermoelectric properties of $β$-K$_{2}$Bi$_{8}$Se$_{13}$.