The quantum metric of electrons with spin-momentum locking.

Quantum materials are characterized by electromagnetic responses intrinsically linked to the geometry and topology of electronic wavefunctions that are encoded in the quantum metric and Berry curvature. Whereas Berry curvature-mediated transport effects have been identified in several magnetic and nonmagnetic systems, quantum metric-induced transport phenomena remain limited to topological antiferromagnets. Here, we show that spin-momentum locking, a general characteristic of the electronic states at surfaces and interfaces of spin-orbit-coupled materials, leads to a finite quantum metric. This metric activates a nonlinear in-plane magnetoresistance that we measured and electrically controlled in 111-oriented LaAlO3/SrTiO3 interfaces. These findings demonstrate the existence of quantum metric effects in a vast class of materials and enable previously unexplored strategies to design functionalities based on quantum geometry.