Giant nonlinear photocurrent in $\mathcal{PT}$-symmetric magnetic topological quantum materials

Nonlinear photocurrent in time-reversal invariant noncentrosymmetric systems have attracted substantial interest. Here we propose two new types of second-order nonlinear direct photocurrent as the counterpart of normal shift photocurrent (NSC) and normal injection photocurrent (NIC), namely magnetic shift photocurrent (MSC) and magnetic injection photocurrent (MIC) in time-reversal symmetry and inversion symmetry broken system. We show that MSC is mainly governed by shift vector and interband Berry curvature, and MIC is dominated by absorption strength and asymmetry of the group velocity difference at time-reversed $\pm$$\textbf{k}$ points. MSC and MIC can be induced by circularly and linearly polarized light, respectively, in $\mathcal{PT}$-symmetric systems with $\mathcal{P}$ and $\mathcal{T}$ being individually broken. Taking $\mathcal{PT}$-symmetric magnetic topological quantum material bilayer antiferromagnetic (AFM) MnBi$_2$Te$_4$ as an example, we predict the presence of large MIC in the terahertz frequency regime which can be magnetically switched between two AFM states with time-reversed spin orderings. While NSC vanishes in $\mathcal{T}$-symmetric systems, external electric field breaks $\mathcal{PT}$ symmetry and enables large NSC response which can be electrically switched. MIC and NSC are perpendicular to each other upon linearly $x$/$y$-polarized light, and are highly tunable under electric field, resulting in giant nonlinear photocurrent response down to a few THz regime. It suggests bilayer AFM MnBi$_2$Te$_4$ as a tunable platform with rich THz and magneto-optoelectronic applications. The present work reveals that nonlinear photocurrent provides a powerful tool for deciphering magnetic structures and interactions, particularly fruitful for probing and understanding magnetic topological quantum materials.