Direct Observation of Chirality-Dependent Berry Curvature Dipole via Cross-Axial Nonlinear Hall Effect in Trigonal Te
Quantum geometric quantities, such as Berry curvature (BC) and quantum metric, are known to govern the physical and topological properties of materials, making access to these quantities critically important for the comprehensive understanding of the materials. Chiral crystals offer a natural platform in which structural handedness can control quantum geometry and nonlinear transport, but direct experimental access to the quantum geometric quantities has remained elusive. Here, we show that trigonal tellurium (Te) hosts an enantiomer-dependent Berry curvature dipole (BCD) that can be accessed through the measurement of cross-axial nonlinear Hall effect (NHE), unlike previously studied in-plane configurations where the BCD contribution vanishes. Angle-resolved measurements on left- and right-handed Te devices reveal a second-order transverse response whose sign reverses with crystal chirality. The extracted cross-axial nonlinear susceptibility, $χ_{yxz}$, exceeds the in-plane susceptibility, $χ_{xxx}$, by more than two-folds, indicating a strong BCD-driven contribution. First-principles calculations attribute this behavior to a topologically nontrivial hedgehog-like BC texture near the H points and predict a BCD that reverses sign between opposite enantiomers, consistent with experiment. These results establish cross-axial nonlinear Hall transport as a symmetry-selective probe of chirality-controlled quantum geometry in tellurium and related chiral materials.