Symmetry-protected isolation of the quantum metric in chiral type-II semi-Dirac semimetals

Quantum geometry, comprising the Berry curvature (BC) and the quantum metric (QM), underpins a wide array of topological and transport phenomena. However, in most solid-state platforms, BC and QM signals are inherently entangled, making their experimental separation highly challenging. Here, we demonstrate that the chiral limit of type-II semi-Dirac semimetals provides a symmetry-protected mechanism to cleanly isolate the QM. At the chiral limit where the spin-orbit gap $m_z=0$, chiral and $\mathcal{PT}$ symmetries strictly suppress the BC, its dipole (BCD), and the shift current, leaving the QM and its dipole (QMD) as the sole sources of the optical and nonlinear Hall responses. This pure-QM regime exhibits distinct experimental fingerprints, including a divergent longitudinal optical conductivity and a QMD-induced nonlinear Hall conductivity that exhibits a pronounced singularity as the chemical potential approaches the nodal point. Turning on a finite $m_z$ reactivates the BC channels, transitioning the system from a pure-QM phase into a mixed geometric phase. By deriving a scaling law for the nonlinear Hall conductivity, we establish a direct experimental strategy to separate the mixed Drude, BCD, and QMD contributions based on their distinct relaxation-time dependencies. Our findings identify chiral type-II semi-Dirac semimetals as highly tunable platforms for isolating and probing intrinsic quantum geometric effects.