Quantum geometric signatures of Link-Unlink transitions and nonlinear Hall response in Hopf-link semimetals

Abstract

Quantum geometry, comprising of quantum metric and Berry curvature, plays a significant role in the electronic transport properties of solids. In this work, we theoretically investigate the quantum geometric properties of a Hopf-link semimetal, a distinct topological class that is charecterized by a nodal link-unlink transition. We compute the interband optical conductivity of the Hopf link, which effectively distinguishes between linked and trivial phases. While recent studies establish quantum metric dipole-mediated scattering-free nonlinear Hall effect, this effect becomes even more fascinating in systems where the Berry-curvature-dipole contribution to nonlinear Hall conductivity vanishes. Owing to the underlying $PT$ symmetry of the Hopf-link semimetal, the Berry curvature and its corresponding contribution to the nonlinear Hall effect are entirely suppressed. Consequently, by introducing an appropriate perturbation, a finite nonlinear Hall conductivity emerges solely due to the quantum metric in the Hopf semimetal. Notably, this purely intrinsic, symmetry-driven nonlinear response remains entirely unmixed with extrinsic components.