Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure

The geometrical properties of electron Bloch wavefunctions are central to modern condensed matter physics. In particular, the studies of Berry curvature have led to countless breakthroughs, ranging from the quantum Hall effect in 2DEGs to the anomalous Hall effect in ferromagnets. Hence, an important open question is to search for quantum geometrical phenomena beyond Berry curvature. This is possible since Berry curvature is only the imaginary component of quantum geometry. By contrast, the real component is known as a quantum metric, which has been rarely explored and responses from quantum metric have remained largely missing. By interfacing even-layered MnBi₂Te₄ (a PT-symmetric antiferromagnet (AFM)) with black phosphorus, we observe a new nonlinear Hall current, which switches direction upon reversing the AFM spins and exhibits distinct scaling that suggests a non-dissipative nature. This antiferromagnetic nonlinear Hall response arises from the dipole moment of the quantum metric. Like the anomalous Hall effect brought Berry curvature under the spotlight, our results open the door to discovering manifestations of the quantum metric. Our observation bridges nonlinear electronics with AFM spintronics, suggesting intriguing possibilities such as using AFM spins to harvest electromagnetic radiation energies.