Non-centrosymmetric topological phase probed by non-linear Hall effect.

Non-centrosymmetric topological material has attracted intense attention due to its superior characteristics as compared with the centrosymmetric one, although probing the local quantum geometry in non-centrosymmetric topological material remains challenging. The non-linear Hall (NLH) effect provides an ideal tool to investigate the local quantum geometry. Here, we report a non-centrosymmetric topological phase in ZrTe, probed by using the NLH effect. The angle-resolved and temperature-dependent NLH measurement reveals the inversion and ab-plane mirror symmetries breaking at <30 K, consistently with our theoretical calculation. Our findings identify a new non-centrosymmetric phase of ZrTe and provide a platform to probe and control local quantum geometry via crystal symmetries.