Investigation of magnetoresistance mechanisms of Bi$_{1.1-x}$Sn$_x$Sb$_{0.9}$Te$_2$S topological insulator

The magnetoresistance mechanisms of Bi$_{1.1-x}$Sn$_x$Sb$_{0.9}$Te$_2$S (x = 0.02 and 0.04) topological insulators were investigated. The studied crystals have suppressed bulk conductivity, which al-lows us to study the low temperature effects that occur in the surface conducting states. In the measurements by four-probe DC resistance measurements the quantum correction improving conductivity in low fields (H > 1 kOe) was detected. This quantum correction corresponds to the case of weak antilocalization. The parameter of the phase coherence length 𝑙ϕ was extracted and its temperature dependence was determined. It was found that an external magnetic field (H > 1 kOe) activation gap appears in the energy spectrum of surface current carriers in Bi$_{1.1-x}$Sn$_x$Sb$_{0.9}$Te$_2$S (x = 0.02 and 0.04) TI. The energy of the activation gap was estimated and its dependence on the stannum concentration and the applied magnetic field was determined: 𝛥 of the order of 2 meV for Bi$_{1.06}$Sn$_{0.04}$Sb$_{0.9}$Te$_2$S and 60 μeV for Bi$_{1.08}$Sn$_{0.02}$Sb$_{0.9}$Te$_2$S at H = 5 kOe.