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, 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 measure and electrically control in 111-oriented LaAlO${}_3$/SrTiO${}_3$ 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.