Recently, it has been reported that the low-temperature high-magnetic field superconducting phase in ${\mathrm{CeCoIn}}_5$ ($Q$ phase), has spin-density wave (SDW) order that only exists within this phase. This indicates that the SDW order is the result of the development of pair density wave (PDW) order in the superconducting phase that coexists with $d$-wave superconductivity. Here we develop a phenomenological theory for these coexisting orders. This provides selection rules for the PDW order and further shows that the detailed structure of this order is highly constrained. We then apply our theory to the vortex phase. This reveals vortex phases in which the $d$-wave vortex cores exhibit charge density wave order and further reveals that the SDW order provides detailed information about the vortex phase.

• Received 12 February 2009

DOI:https://doi.org/10.1103/PhysRevLett.102.207004