Magnetic-field effect on excitonic condensation emergent in extended Falicov-Kimball model

Abstract: We investigate the effects of magnetic fields on excitonic condensation in the extended Falicov-Kimball model, which is a spinless two-orbital Hubbard model with orbital splitting. In lattice systems under magnetic fields up to several tens of teslas, Zeeman effects on electron spins have been extensively studied, while the impact on orbital motion has often been considered negligible. However, the recent capability to generate ultra-high magnetic fields exceeding 1000 T has renewed interest in understanding their influence on ordered phases in correlated electron systems, beyond spin-related phenomena. To examine these effects, we incorporate a magnetic field into the extended Falicov-Kimball model by introducing the Peierls phase into the transfer integrals, enabling the study of orbital motion. Using the Hartree-Fock approximation, we reveal a nonmonotonic response of the excitonic order parameter to increasing magnetic fields. At sufficiently high fields, the excitonic order is suppressed, resulting in a disordered insulating state characterized by partial occupation of the two orbitals with nonzero Chern numbers. This state is distinct from a fully orbital-polarized configuration. Furthermore, our analysis of an excitonic supersolid phase, in which excitonic and orbital orders coexist, demonstrates that orbital order remains robust under magnetic fields, while excitonic condensation is suppressed. These findings provide insights into the interplay between orbital motion and magnetic fields in multi-orbital correlated electron systems.