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 the 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 re-visit the experiments on Pb$_{1-x}$Sn$_x$Se, ZrTe$_5$, Ag$_2$Te families, and will be particularly useful for controversial small-gap materials at the boundary between topological insulator and normal insulator.