Breakdown of Universal Transport in Correlated $d$-Wave Superconductors

The prediction and observation of low-temperature universal thermal conductivity in cuprates has served as a keystone of theoretical approaches to the superconducting state, but recent measurements on underdoped samples show strong violations of this apparently fundamental property of $d$-wave nodal quasiparticles. Here, we show that the breakdown of universality may be understood as the consequence of disorder-induced magnetic droplets arising from enhanced antiferromagnetic correlations in the underdoped state, even as these same correlations protect the nodal density of states.

Figure 1

(a) Spatially averaged DOS in the uncorrelated $d$-wave superconductor ($U=0$) for different concentrations of disorder $n_i$. One clearly sees the pileup of low-energy impurity states. (b) Same as (a) but for the correlated $d$-wave superconductor with $U=2.5t$. (c) A line cut through the system showing the total charge density (top black lines) and the $d$-wave order parameter (lower red lines). The dashed (solid) lines display the results without (with) correlations. (d) DOS for 2.5% strong scatterers ($V^{\mathrm{imp}}/t=10$) as a function of $U$. The inset shows a zoom of the low-energy region $\omega \in [-0.35t,0.35t]$.

Figure 2

(a), (b) $\kappa (T)/T$ versus $T$ as a function of increased $U$. (a) shows the case of 2.5% strong scatterers with $V^{\mathrm{imp}}/t=10.0$, and (b) has 15.0% weaker impurities of $V^{\mathrm{imp}}/t=3.0$. (c), (d) show the disorder-induced magnetization in real space for the case in (a) with $U/t=3.2$ (c) and $U/t=3.6$ (d). The inset in (d) shows the DOS ($\omega \in [-0.3t,0.3t]$) for the clean system (dashed line), and the disordered case (solid lines) with (top to bottom) $U=0$, $U/t=3.2$ , and $U/t=3.6$.