Effect of coexisting order of various form and wave vector on low-temperature thermal conductivity in d-wave superconductors

In light of recent experimental evidence of density wave order in the cuprates, we consider a phenomenological model of a d-wave superconductor with coexisting charge-, spin-, or pair-density wave order of various form and wave vector. We study the evolution of the nodal structure of the quasiparticle energy spectrum as a function of the amplitude of the coexisting order and perform diagrammatic linear-response calculations of the low-temperature (universal-limit) thermal conductivity. The work described herein expands upon our past studies, which focused on a particular unit-cell-doubling charge-density wave, generalizing our techniques to a wider class of coexisting order. We find that the question of whether the nodes of the d-wave superconductor survive amidst a reasonable level of coexisting order is sensitive to the form and wave vector of the order. However, in cases where the nodes do become gapped, we identify a signature of the approach to this nodal transition, in the low-temperature thermal conductivity, that appears to be quite general. The amplitude of this signature is found to be disorder dependent, which suggests a connection between the presence of coexisting order in the underdoped cuprates and recent observations of deviations from universal (disorder-independent) thermal conductivity in the underdoped regime.