Manipulating Anomalous Transport via Crystal Symmetry in 2D Altermagnets

Anomalous transports, including the anomalous Hall effect (AHE) and anomalous Nernst effect (ANE), are typical manifestations of time-reversal-symmetry-breaking responses in materials. In general, the two Hall states with opposite Hall conductivities can be regarded as time-reversal pairs coupled to magnetic order, and switching between them relies on reversing the magnetization via an external magnetic field or electric current. Here, we introduce a approach for manipulating anomalous transport through crystal symmetry engineering in two-dimensional (2D) altermagnetic systems. Based on symmetry analysis, we demonstrate that 2D altermagnets (AM) with out-of-plane N\'eel vectors will not host any anomalous Hall transport. Remarkably, breaking the symmetry connecting the two magnetic sublattices, an anomalous Hall response can emerge immediately, and the signs of the anomalous Hall and anomalous Nernst conductivities can be flexibly controlled by the symmetry-breaking term, thereby realizing tunable sign-reversible anomalous transport. Furthermore, the feasibility of the theoretical scheme is further verified by explicit lattice-model construction. Using first-principles calculations, we investigate the realization of crystal symmetry-controlled anomalous transport in a 2D AM material Cr$_{2}$O$_{2}$. The results indicate that Cr$_{2}$O$_{2}$ with out-of-plane N\'eel vectors can sequentially exhibit the AHE and quantum anomalous Hall effect (QAHE) under continuous uniaxial strain. Interestingly, the sign reversal between these two effects can be achieved by simply rotating the strain direction by C$_{4z}$ symmetry. The corresponding ANE and its sign reversal are also revealed. Our findings provide a new strategy to manipulate anomalous transport, and should have significant potential applications.