Engineering Competing Fractional Topological States in a BHZ Superlattice

Abstract

Scalar superlattices offer a route from simple topological bands to fractionalized states, while multicomponent systems raise the additional question of which fractional order is energetically selected. We show that a scalar superlattice applied to the Qi-Wu-Zhang (QWZ) Chern-insulator model produces an isolated C = +1 miniband with strongly improved Berry-curvature and quantum metric uniformity. Exact diagonalization of the projected interaction identifies a 1/3 fractional Chern insulator in this miniband. Restoring the time-reversed partner to form the Bernevig-Hughes-Zhang (BHZ) superlattice yields, at total filling 2/3, a balanced fractional quantum spin Hall (FQSH)-like state and a fully polarized 2/3 fractional Chern insulator. Their competition separates two aspects of fractional-state control: the finite-momentum intercomponent coupling governs the stability of the balanced FQSH-like state, whereas a uniform pseudospin anisotropy shifts the relative energies of conserved sectors and can switch the global ground state between the balanced and polarized states. These results establish a minimal lattice setting that connects topological-miniband reconstruction, fractional-state formation, and fractional-state selection, illustrating how distinct levels of control can be combined to navigate competing fractional topological states.