A Composite Fermion Hofstader Problem: Partially Polarized Density Wave States in the 2/5 FQHE

It is well-known that the 2/5 state is unpolarized at zero Zeeman energy, while it is fully polarized at large Zeeman energies. A novel state with charge/spin density wave order for Composite Fermions is proposed to exist at intermediate values of the Zeeman coupling for 2/5. This state has half the maximum possible polarization, and can be extended to other incompressible fractions. A Hartree-Fock calculation based on the new approach for all fractional quantum Hall states developed by R.Shankar and the author is used to demonstrate the stability of this state to single-particle excitations, and compute gaps. We compare our results with a very recent experiment which shows direct evidence for the existence of such a state, and also with more indirect evidence from past experiments.