Density-wave states of nonzero angular momentum

We study the properties of states in which particle-hole pairs of nonzero angular momentum condense. These states generalize charge- and spin-density-wave states, in which s-wave particle-hole pairs condense. We show that the p-wave spin-singlet state of this type has Peierls ordering, while the d-wave spin-singlet state is the staggered flux state. We discuss model Hamiltonians which favor p- and d-wave density-wave order. There are analogous orderings for pure spin models, which generalize spin-Peierls order. The spin-triplet density-wave states are accompanied by spin-$1$ Goldstone bosons, but these excitations do not contribute to the spin-spin correlation function. Hence they must be detected with NQR or Raman-scattering experiments. Depending on the geometry and topology of the Fermi-surface, these states may admit gapless fermionic excitations. As the Fermi-surface geometry is changed, these excitations disappear at a transition which is third order in mean-field theory. The singlet d-wave- and triplet p-wave density-wave states are separated from the corresponding superconducting states by zero-temperature $O\left(4\right)\mathrm{}$-symmetric critical points.