Fig. 1.

Band structure symmetry-breaking and magnetic structures of the bilayer CrI₃. Schematics of band structures a with both inversion symmetry ($\mathcal{P}$) and the time-reversal symmetry ($\mathcal{T}$), b with only $\mathcal{T}$ but $\mathcal{P}$-breaking, and c with both $\mathcal{P}$- and $\mathcal{T}$-breaking. For both a, b, the light excitation (ħω) at +k and −k is symmetric to each other. However, such a symmetry is broken in c. As a consequence, excited electrons at +k and −k do not cancel each other in velocity, giving rise to a dc photocurrent. d The band structure of antiferromagnetic(AFM) bilayer CrI₃. Here both $\mathcal{P}$- and $\mathcal{T}$ are broken as the case of (c), violating the k to −k symmetry. The spin-orbit coupling is included. The Fermi energy is shifted to zero. e The AFM, ferromagnetic (FM) and reversed AFM phases display three distinct responses to a linearly polarized light – positive current state(1), zero current state (0) and negative current state(−1)