Forbidden Backscattering and Resistance Dip in the Quantum Limit as a Signature for Topological Insulators

Identifying topological insulators and semimetals often focuses on their surface states, using spectroscopic methods such as angle-resolved photoemission spectroscopy or scanning tunneling microscopy. In contrast, studying the topological properties of topological insulators from their bulk-state transport is more accessible in most labs but seldom addressed. We show that, in the quantum limit of a topological insulator, the backscattering between the only two states on the Fermi surface of the lowest Landau band can be forbidden, at a critical magnetic field. The conductivity is determined solely by the backscattering between the two states, leading to a resistance dip that may serve as a signature for topological insulator phases. More importantly, this forbidden backscattering mechanism for the resistance dip is irrelevant to details of disorder scattering. Our theory can be applied to revisit the experiments on Pb$_{1-x}$Sn$_x$Se, ZrTe$_5$, and Ag$_2$Te families, and will be particularly useful for controversial small-gap materials at the boundary between topological and normal insulators.