Sondheimer Oscillation as a Fingerprint of Surface Dirac Fermions

Topological states of matter challenge the paradigm of symmetry breaking, characterized by gapless boundary modes and protected by the topological property of the ground state. Recently, angle-resolved photoemission spectroscopy (ARPES) has revealed that semiconductors of Bi$_{2}$Se$_{3}$ and Bi$_{2}$Te$_{3}$ belong to such a class of materials. Here, we present undisputable evidence for the existence of gapless surface Dirac fermions from transport in Bi$_{2}$Te$_{3}$. We observe Sondheimer oscillation in magnetoresistance (MR). This oscillation originates from the quantization of motion due to the confinement of electrons within the surface layer. Based on Sondheimer's transport theory, we determine the thickness of the surface state from the oscillation data. In addition, we uncover the topological nature of the surface state, fitting consistently both the non-oscillatory part of MR and the Hall resistance. The side-jump contribution turns out to dominate around 1 T in Hall resistance while the Berry-curvature effect dominates in 3 T $\sim$ 4 T.