GENERALIZED FLUX STATES ON 3-DIMENSIONAL LATTICE

Electrons on three dimensional lattice in external magnetic fields are investigated. If the field is applied in the (1, 1, 1) direction with the flux per plaquette in each plane phi = p/q, the density of state at the chemical potential of electron filling v = phi is found to be zero for phi-c < phi < 1-phi-c. For the simple cubic lattice phi-c almost-equal-to 1/8. The total energy of electrons is lowered by applying the uniform magnetic field along the (1, 1, 1) direction with one flux unit par particle through each plane if the condition, v(c) < v < 1-v(c)(v(c) almost-equal-to phi-c), is satisfied.