Validity of the constant relaxation time approximation in topological insulator: Sn-BSTS a case study

Gate-voltage dependent quantum oscillations in topological insulator Sn0.02Bi1.08Sb0.9Te2S (Sn-BSTS) are analyzed on the basis of the Lifshitz−Kosevich theory. The angular dependence of the quantum oscillations and Landau-level fan diagram analysis show that the quantum oscillations originate from topological surface states with the Berry phase of π. Gate-voltage control allows precise control of the Fermi energy, and a very weak energy dependence of the relaxation time τ of the topological surface states is revealed. By a simple algebraic argument using the linear response theory, it is shown that the weak energy dependence of τ validates the constant relaxation time approximation [τE,T=τ0] in the calculation of the Seebeck coefficient S and zTel=σS2T/κel.