Stripe-like orbital order resulting from pure orientaional orbital motion

We introduce an elementary model based upon the orientational nature of orbitals, which may arise from the influence of a cubic-symmetric crystal field. We focus on orbital ordering induced by correlated charge motion: a phenomenon often ignored. Motivated by the Nagaoka ferromagnetism, we seek the analogue single-hole result for our model in the strong-coupling regime. For two-fold degenerate orbitals on the square lattice, we show that the system promotes stripe phases as energetically favourable. In such phases, the system breaks the symmetry, with lines of one species of fermion being periodically separated and the other species filling in the gaps. For the simplest form of stripe, all periodicities are exactly degenerate, but we can show rigorously that such states are actually higher in energy than a small number of more exotic states which show the same long-range behaviour but are locally disrupted from the simplest case. Such states have a preferred periodicity of three.