Quantum geometric-induced third-order nonlinear transport in antiferromagnetic topological insulator MnBi2Te4

Discovering the nonlinear transport features in antiferromagnets is of fundamental interest in condensed matter physics as it offers a new frontier of the understanding deep connections between multiple degrees of freedom, including magnetic orders, symmetries, and band geometric properties. Antiferromagnetic topological insulator MnBi${_2}$Te${_4}$ has provided a highly tunable platform for experimental explorations due to its rich magnetic structures and striking topological band structures. Here, we experimentally investigate the third-order nonlinear transport properties in bulk MnBi${_2}$Te${_4}$ flakes. The measured third-harmonic longitudinal ($V_{xx}^{3{\omega}}$) and transverse ($V_{xy}^{3{\omega}}$) voltages show intimate connection with magnetic transitions of MnBi${_2}$Te${_4}$ flakes and their magnitudes change abruptly as MnBi${_2}$Te${_4}$ flakes go through magnetic transitions with varying temperature and magnetic fields. In addition, the measured $V_{xx}^{3{\omega}}$ exhibits an even-symmetric feature with changing magnetic field direction and the $V_{xy}^{3{\omega}}$ shows an odd-symmetric property, which are believed to be related to the quantum metric and the emergency of non-zero Berry curvature quadrupole with broken ${PT}$ symmetry and non-degenerate band structures under external magnetic fields, respectively. Our work shows great advances in the understanding of the underlying interactions between multiple geometric quantities.