Thermal Transport in Superconductors with coexisting Spin Density Wave Order

Thermal conductivity measurements are a very useful probe of superconductivity as it can reveal the gap structure of unconventional superconductors. Here we study thermal transport in a two-dimensional system with coexisting Superconducting (SC) and Spin Density Wave (SDW) orders. We find that the coexistence phase of the d_x²-y² pairing state is fully gapped, whereas new zero energy excitations appear in the case of d_xy and s-wave pairing states. These exications are not gapped by the SC order in the coexistence phase. The occurrence of these zero energy excitations is related to the symmetry properties of the pairing states. We compute the electronic thermal conductivity within the framework of Boltzmann kinetic theory, using Born approximation for the impurity scattering collision integral. We describe the influence of the Fermi surface (FS) topology, the competition between the SC and SDW order parameters, the presence or absence of zero energy excitations in the coexistence phase, on the low temperature behaviour of thermal conductivity of the various paring states. We present numerical results that show that the heat transport signatures of these paring states are quite distinct.