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Quantum geometry - the geometry of electron Bloch wavefunctions - is centralto modern condensed matter physics. Due to the quantum nature, quantum geometryhas two parts, the real part quantum metric and the imaginary part Berrycurvature. The studies of Berry curvature have led to countless breakthroughs,ranging from the quantum Hall effect in 2DEGs to the anomalous Hall effect(AHE) in ferromagnets. However, in contrast to Berry curvature, the quantummetric has rarely been explored. Here, we report a new nonlinear Hall effectinduced by quantum metric by interfacing even-layered MnBi2Te4 (a PT-symmetricantiferromagnet (AFM)) with black phosphorus. This novel nonlinear Hall effectswitches direction upon reversing the AFM spins and exhibits distinct scalingthat suggests a non-dissipative nature. Like the AHE brought Berry curvatureunder the spotlight, our results open the door to discovering quantum metricresponses. Moreover, we demonstrate that the AFM can harvest wirelesselectromagnetic energy via the new nonlinear Hall effect, therefore enablingintriguing applications that bridges nonlinear electronics with AFMspintronics.

Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure