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

Abstract: We propose the sublattice currents 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 nonmagnetic crystal structures 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 sublattice currents induce spin splitting in the bands and therefore turn it into an odd-parity ALM. Interestingly, its topological version serves as an example of ALM Chern insulator. We further generalize the Haldane-Hubbard model to common two- and three-dimensional bipartite lattices. With spin splitting from sublattice currents, the compensated collinear magnetic ground states at half filling are generally odd-parity ALM.