Probing the quantum metric of 3D topological insulators

Abstract

The surface states of 3D topological insulators possess geometric structures that imprint distinctive signatures on electronic transport. A prime example is the Berry curvature, which controls, for instance, electric frequency doubling via its higher order moments. In addition to the Berry curvature, topological surface states are expected to exhibit a nontrivial quantum metric, which plays a key role in governing nonlinear magnetotransport. However, its manifestation has yet to be experimentally observed and controlled in 3D topological insulators. Here, we provide evidence for a nonlinear response activated by the quantum metric of the topological surface states of Sb$_2$Te$_3$. We measure a time-reversal odd, nonlinear magnetoresistance that is independent from the temperature and the scattering time below 30 K, and is thus of intrinsic geometrical origin. This quantum metric magnetoresistance can be controlled by tuning the contributions of the top and bottom topological surface states by voltage gating. Our measurements thus demonstrate the existence and tunability of quantum geometry-induced transport in topological phases of matter and provide strategies for designing novel functionalities in topological devices.