Third‐Order Nonlinear Hall Effect for Probing Berry‐Connection Polarizability and Quantum Metric

Quantum geometric tensor has two components: the real part corresponds to quantum metric and the imaginary part contains Berry curvature. Physics associated with Berry curvature has been extensively studied in the past, while quantum metric also started to attract significant attention very recently. Third‐order nonlinear Hall effect (TNHE) is induced by the Berry connection polarizability (BCP) tensor, which is intimately connected to quantum metric. In this work, we study the temperature dependence of third‐order Hall susceptibility in a semimetal TaIrTe 4 . At low temperatures, we find the effective carrier density is approximately invariant, and the scaling analysis renders a good description of TNHE. At higher temperatures, we observe large deviations from low‐temperature behavior and even a sign change of the signal around 134 K. We show this anomalous feature is consistent with the temperature‐dependent variation of effective carrier density and is qualitatively explained by first‐principles simulations, which captures the BCP contribution. Our findings provide insights into the controllability of BCP and quantum metric and suggest possible applications of TNHE.