Chern insulator phase transition in valley-dependent altermagnet

We investigate the possibility of a Chern insulator phase transition in two-dimensional altermagnetic (AM) metals by incorporating the effects of Rashba spin–orbit coupling (RSOC) and an additional exchange field. We present a phase diagram of the system as a function of the AM and exchange field strengths, and demonstrate that when the AM exchange strength exceeds a critical value of the exchange field, the system shows a nonzero Chern number. Moreover, we find that not only do the RSOC and exchange field significantly affect the topological properties, but the AM exchange energy and band energy also play essential roles. Specifically, when the AM exchange energy exceeds the AM band energy and the spin-momentum coupling exhibits clear valley separation, a bulk energy gap opens, and the system transitions into the quantum anomalous Hall insulator regime. Conversely, when the AM exhibits only anisotropic spin-momentum coupling, the system retains the same Chern number but lacks corresponding chiral edge states. We further compute the transport properties of a valley-dependent AM ribbon structure, confirming the existence of possible chiral edge states and their robustness.