Chang-An Li
Altermagnetic Josephson junctions (AMJJs) can host unconventional \pi phase and \varphi phase despite vanishing net magnetizations. Whether these phases are stable against disorder existing in real materials remains an open question. Here, we investigate impact of disorder on exotic phases in two-dimensional AMJJs consisting of two conventional superconductors mediated by a d-wave altermagnet. We show that disorder is able to drive phase transitions from the exotic \pi phase to conventional 0 phase, accompanied by a substantial suppression of critical current. This behavior is attributed to modifications of the tunneling Cooper-pair phase shift and superconducting decoherence. Remarkably, the anomalous \varphi phase is highly fragile in presence of disorder and can be driven to either a \pi phase or 0 phase in a nonreciprocal way. Across such transitions, the first harmonic of current-phase relation changes its sign, while the higher-order harmonics are rapidly suppressed. Our findings reveal the crucial role of disorder in tailoring distinct phases of AMJJs and shed new light on their potential functionalities.