Low temperature thermal conductivity in a d-wave superconductor with coexisting charge order: Effect of self-consistent disorder and vertex corrections

TL;DR

This paper investigates how coexisting charge order affects low-temperature thermal conductivity in a d-wave superconductor, considering disorder and vertex corrections, revealing that disorder treatment alters the charge order threshold for gapping.

Contribution

It introduces a self-consistent approach to disorder in a charge-ordered d-wave superconductor, showing how it modifies thermal transport properties and the charge order threshold.

Findings

Vertex corrections are negligible in the ladder approximation.

Self-consistent disorder treatment reduces the charge order needed for effective gapping.

Charge order influences the thermal conductivity tensor significantly.

Abstract

Given the experimental evidence of charge order in the underdoped cuprate superconductors, we consider the effect of coexisting charge order on low-temperature thermal transport in a d-wave superconductor. Using a phenomenological Hamiltonian that describes a two-dimensional system in the presence of a Q=(\pi,0) charge density wave and d-wave superconducting order, and including the effects of weak impurity scattering, we compute the self-energy of the quasiparticles within the self-consistent Born approximation, and calculate the zero-temperature thermal conductivity using linear response formalism. We find that vertex corrections within the ladder approximation do not significantly modify the bare-bubble result that was previously calculated. However, self-consistent treatment of the disorder does modify the charge-order-dependence of the thermal conductivity tensor, in that the magnitude of charge order required for the system to become effectively gapped is renormalized, generally to a smaller value.