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.