Thermal Conductivity Evidence for a $d_{x^2-y^2}$ Pairing Symmetry in the Heavy-Fermion ${\mathrm{CeIrIn}}_5$ Superconductor

The phase diagram of the quasi-2D $\mathrm{Ce}(\mathrm{Ir},\mathrm{Rh}){\mathrm{In}}_5$ system contains two distinct superconducting domes. By the thermal transport measurements in rotating magnetic fields $\mathit{H}$, we pinned down the superconducting gap structure of ${\mathrm{CeIrIn}}_5$ in the second dome, located distant from the first dome in proximity to an antiferromagnetic quantum critical point. Clear fourfold oscillation was observed when $\mathit{H}$ is rotated within the $ab$ plane, while no oscillation was observed within the $bc$ plane. In sharp contrast to previous reports, our results are most consistent with $d_{x^2-y^2}$ symmetry, implying that the superconductivity in the second phase is also mediated by antiferromagnetic spin fluctuations.

Figure 1

Temperature dependence of $\kappa /T$ as a function of $T^2$ in zero field and above $H_{c2}^c$ ($H=2\mathrm{T}$). The solid line represents $\kappa /T={\kappa }_{00}/T+A{T}^2$; the dashed line shows $\kappa /T$ obtained from the resistivity using the Wiedemann-Franz law. Inset: phase diagram of $\mathrm{Ce}(\mathrm{Ir},\mathrm{Rh}){\mathrm{In}}_5$ as a function of Ir concentration and pressure, from Refs. 7, 8.

Figure 2

Angular variation of the thermal conductivity $\Delta \kappa \equiv \kappa -{\kappa }_0$at $T=200\mathrm{mK}$ with rotating $\mathit{H}$ (a) within the $bc$ plane as a function of polar angle $\theta$ for $|\mathit{H}|=0.05\mathrm{T}$ (filled circles) and 0.10 T (open circles) and (b) within the 2D $ab$ plane as a function of azimuthal angle $\varphi$ for $|\mathit{H}|=0.10\mathrm{T}$. Here ${\kappa }_0$ is the angular average of $\kappa$. The thermal current $\mathit{q}$ is applied parallel to the $a$ axis. The dashed line shows the twofold ($\cos 2\varphi$) variation. The solid line is the fit by $\kappa (\varphi )={\kappa }_0+C_{2\varphi }\cos 2\varphi +C_{4\varphi }\cos 4\varphi$, where $C_{2\varphi }$, and $C_{4\varphi }$ are constants.

Figure 3

(a)–(d) The fourfold component ${\kappa }_{4\varphi }$normalized by ${\kappa }_n$ with $\mathit{H}$ rotated in the $ab$ plane at $T=200\mathrm{mK}$ at $|\mathit{H}|=0.69$, 0.5, 0.25, and 0.1 T, respectively. The upper critical field is $H_{c2}^{ab}\gtrsim 0.7\mathrm{T}$ at this temperature. The solid lines represent the fit by $C_{4\varphi }\cos 4\varphi$. (e) $C_{4\varphi }/{\kappa }_n$ at $T=200\mathrm{mK}$ as a function of $H/H_{c2}^{ab}$. (f) $C_{4\varphi }/{\kappa }_n$ at $H=0.1$ and 0.25 T as a function of $T/T_c$.

Figure 4

$H\mathrm{\text{−}}T$ phase diagram for the fourfold term ${\kappa }_{4\varphi }$ in $\mathit{H}$ rotated within the $ab$ plane. Solid (open) circles indicate points with maxima (minima) of ${\kappa }_{4\varphi }$ at $\varphi =0°$. The shaded (unshaded) regions correspond to minima (maxima) of ${\kappa }_{4\varphi }$ for $\mathit{H}$ along the nodal directions [35].