Strain engineering of quantum geometry in magnetic topological insulators*

Quantum metric, the real part of the quantum geometric tensor, is an important but often overlooked aspect of the Bloch wavefunction. The PT (P=inversion, T=time reversal ) symmetric magnets, which naturally suppress the Berry curvature-induced anomalous Hall effect, are suitable candidates for exploring the quantum metric-induced effects. Using density functional theory based ab initio calculations and low energy models, we explore the quantum metric dipole-induced intrinsic non-linear Hall effect (INHE) in MnBi$_{2n}$Te$_{3n+1}$ thin films. By applying uniaxial strain along various directions of the crystal structure, we break the threefold rotational symmetry and predict the existence of large INHE (~mA/V$^2$) in this family of materials. We show that INHE has large values near the band anti-crossing points, and it strongly depends on the strain and the Neel vector orientation. Our work promotes the MnBi$_{2n}$Te$_{3n+1}$ series of compounds as an exciting material platform for exploring and engineering various quantum geometry-induced effects.