Exciton condensation in an extended spinless Falicov Kimball model in the presence of orbital magnetic fields

An extended, spinless Falicov-Kimball model in the presence of perpendicular magnetic field is investigated employing Hartree-Fock self-consistent mean-field theory in two dimensions. In the presence of an orbital field the hybridization-dependence of the excitonic average ${ \Delta =<{{d_i}^\dagger} {f_i}>}$ is modified. The exciton responses in subtle different ways for different chosen values of the magnetic flux consistent with Hofstadter's well-known spectrum. The excitonic average is suppressed by the application of magnetic field. We further examine the effect of Coulomb interaction and $f$-electron hopping on the condensation of exciton for some rational values of the applied magnetic field. The interband Coulomb interaction enhances the $\Delta$ exponentially, while a non-zero $f$-electron hopping reduces it. A strong commensurability effect of the magnetic flux on the behaviour of the excitons is observed.