Spin-biased quantum spin Hall effect in altermagnetic Lieb lattice

Altermagnetic (AM) order, a recently discovered magnetic state, has attracted intense research interest for its potential applications in spintronic and quantum technologies. Here, we theoretically investigate the AM state in the Lieb lattice, a prototypical two-dimensional lattice, using the Hubbard model. We show that AM order emerges with only moderate electronic correlations. Strikingly, spin-orbit coupling drives the system into a topological phase exhibiting a new quantum spin Hall effect (QSHE) with spin-biased topological edge states in one-dimensional nanoribbons. These edge states possess different localizations and velocities, and hence may produce spin and charge currents, fundamentally distinct from that in conventional topological insulators with spin degeneracy. This novel spin-biased QSHE in the AM Lieb lattice unveils exciting opportunities for both fundamental studies and innovative device concepts, motivating immediate experimental exploration.