Enhancement of the Nonlinear Hall Effect from Inversion Symmetry Breaking

The nonlinear Hall effect (NHE) can have two topological origins: the Berry curvature dipole and quantum metric dipole. The quantum metric and Berry curvature are the real and imaginary parts of the quantum geometric tensor, respectively. The quantum metric induced NHE has recently been observed in PT symmetric MnBi₂Te₄ thin films, where the Berry curvature dipole is forbidden. Here we propose that when the PT symmetry is broken by an external electric field, the Kramers pairs can give rise to a much larger quantum metric dipole, compared to the PT symmetric scenario where the degeneracy of the Kramers pairs forbids such contributions. Therefore, we expect a great enhancement of the quantum metric induced NHE from the symmetry breaking.