  Quantum geometry - the geometry of electron Bloch wavefunctions - is central
to modern condensed matter physics. Due to the quantum nature, quantum geometry
has two parts, the real part quantum metric and the imaginary part Berry
curvature. 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 quantum
metric has rarely been explored. Here, we report a new nonlinear Hall effect
induced by quantum metric by interfacing even-layered MnBi2Te4 (a PT-symmetric
antiferromagnet (AFM)) with black phosphorus. This novel nonlinear Hall effect
switches direction upon reversing the AFM spins and exhibits distinct scaling
that suggests a non-dissipative nature. Like the AHE brought Berry curvature
under the spotlight, our results open the door to discovering quantum metric
responses. Moreover, we demonstrate that the AFM can harvest wireless
electromagnetic energy via the new nonlinear Hall effect, therefore enabling
intriguing applications that bridges nonlinear electronics with AFM
spintronics.
