Probing the Nodal Gap in the Pressure-Induced Heavy Fermion Superconductor ${\mathrm{CeRhIn}}_5$

We report field-orientation specific heat studies of the pressure-induced heavy-fermion superconductor ${\mathrm{CeRhIn}}_5$. These experiments provide the momentum-dependent superconducting gap function for the first time in any pressure-induced superconductor. In the coexisting phase of superconductivity and antiferromagnetism, field rotation within the Ce-In plane reveals fourfold modulation in the density of states, which favors a $d$-wave order parameter and constrains a theory of the interplay between superconductivity and magnetism.

Figure 1

(a) Phase diagram of ${\mathrm{CeRhIn}}_5$ as a function of pressure [15]. Pressure induces a bulk superconducting (SC) state at 0.5 GPa that coexists with the antiferromagnetic (AFM) phase up to $P1$, where $T_c$ becomes equal to $T_N$. The critical pressure marked by $P2$ is the field-tuned quantum critical point hidden by the SC dome. (b) Heat capacity of ${\mathrm{CeRhIn}}_5$ at 1.47 GPa (see text for details).

Figure 2

(a) Low-temperature heat capacity ($C_p$) of ${\mathrm{CeRhIn}}_5$ at 1.47 GPa and in low applied fields indicated in the legend. Solid and open symbols represent $C_P/T$ for field along [100] and [001], respectively. (b) Temperature dependence of the upper critical field $H_{c2}$. Squares, circles, and diamond symbols correspond to fields along [100], [110], and [001], respectively. The dotted (or dash-dotted) line is a guide for a linear-$H$ dependence. (c) Magnetic field dependence of $C/T$ at 300 mK for $H\parallel [100]$ at 1.47 GPa (squares) and 2.3 GPa (circles). Here, $H_{c2}$ is 1.2 and 7.7 T for 1.4 and 2.3 GPa, respectively. The solid line describes least-squares fitting by $\Delta C/T=C/T-C(0T)/T=A{H}^n$ with $n=0.68$, while the dashed line is for $n=0.5$.

Figure 3

Field-rotation specific heat of ${\mathrm{CeRhIn}}_5$ at 1.47 GPa. (a) Azimuthal rotation ($\varphi$) of the magnetic field (0.5 T) within the Ce-In plane both in the AFM (1.8 K) and the coexisting phase of AFM and SC (0.3 K). (b) Polar rotation ($\theta$) of the magnetic field (0.5 T) perpendicular to the Ce-In plane in the coexisting phase at 0.3 K. The solid line is a least-squares fit to a twofold modulation model: $C=C_0+A(1+A_2|\cos \varphi |)$ with $C_0=265$, $A=59.3$, and $A_2=0.30$, where the oscillation arises from $H_{c2}$ anisotropy.

Figure 4

(a) Field-rotation specific heat of ${\mathrm{CeRhIn}}_5$ at 0.3 K for 0.2 (squares) and 0.9 T (triangles). Dashed lines are least-squares fits by a sinusoidal form of the angular dependence (see text). (b) Oscillation amplitude $A_4$ as a function of the normalized field $h(=H/H_{c2})$ with $H_{c2}=1.2\mathrm{T}$ at 0.3 K.