Odd-parity altermagnetism through sublattice currents: From Haldane-Hubbard model to general bipartite lattices

We propose the sublattice currents in a compensated collinear magnetic system as a feasible route to odd-parity altermagnetism (ALM), where nonrelativistic collinear spin splitting occurs in the bands as an odd function of momentum. In contrast to previously classified ALMs, the sublattice currents break the time-reversal symmetry in the nonmagnetic crystal structure and allow for such odd-parity spin splitting. A representative example is the Haldane-Hubbard model at half filling. Although the compensated collinear magnetic ground state was previously recognized as antiferromagnetism, we show that it is actually an odd-parity ALM. Interestingly, its topological version serves as an example of an ALM Chern insulator. We further generalize the Haldane-Hubbard model to common two- and three-dimensional bipartite lattices. With spin splitting allowed by sublattice currents, the compensated collinear magnetic ground states at half filling are generally odd-parity ALM.