Topologically Protected Two-Fluid Edge States

Edge states exhibit the nontrivial topology of energy band in the bulk. As localized states at boundaries, many-particle edge states may obey a special symmetry that is broken in the bulk. When local particle-particle interaction is induced, they may support a particular property. We consider an anisotropic two-dimensional Su-Schrieffer-Heeger Hubbard model and examine the appearance of $\eta$-pairing edge states. In the absence of Hubbard interaction, the energy band is characterized by topologically invariant polarization in association with edge states. In the presence of on-site Hubbard interaction, $\eta$-pairing edge states with an off-diagonal long-range order appear in the nontrivial topological phase, resulting in the condensation of pairs at the boundary. In addition, as Hamiltonian eigenstates, the edge states contain one paired component and one unpaired component. Neither affects the other; they act as two-fluid states. From numerical simulations of many-particle scattering processes, a clear manifestation and experimental detection scheme of topologically protected two-fluid edge states are provided.