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.