Symmetry, disorder and transport through altermagnetic quantum dots and their antiferromagnetic twins

Altermagnetic crystals resemble antiferromagnets in that they have no macroscopic magnetization, but unlike antiferromagnets they exhibit spin-split band structures. Here the transport properties of altermagnetic quantum dots and their antiferromagnetic twins are explored theoretically for the first time with the help of Landauer-Büttiker theory, symmetry considerations and tight-binding models. The influence of the symmetries of the quantum dots, their parent crystal lattices, their shapes and edges, lead arrangements and disorder on the anomalous Hall effect, the spin-Hall effect and spin filtering by the quantum dots are investigated. Novel findings presented here include vanishing of the anomalous Hall resistances of altermagnetic quantum dots that (with leads) have C4Tsymmetry and giant anomalous Hall resistances of antiferromagnetic quantum dots. These findings differ radically from the predictions of theories of macroscopic altermagnetic and antiferromagnetic crystals.