Determination of Gap Symmetry from Angle-Dependent $H_{c2}$ Measurements on ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$

The tetragonal heavy-fermion compound ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ exhibits a superconducting ground state ($S$ type, $T_c=0.67\mathrm{K}$) close to a magnetic instability. Here, we present angle-resolved resistivity measurements of the upper critical field $H_{c2}$. In-plane rotation of $S$-type ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ single crystals reveals a fourfold oscillation of $H_{c2}$. An extended weak-coupling BCS model for a $d$-wave symmetry including strong Pauli-limiting effects confirms the aforementioned angular dependence and points towards $d_{xy}$ symmetry of the order parameter.

Figure 1

(a) $H\mathrm{\text{−}}T$ phase diagram for ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$. The solid red curve indicates the theoretical calculation for a $d$-wave symmetry (see text). Note the nonmonotonicity of $H_{c2}$ at lower temperatures, both in the data and the fit, due to the Pauli-limiting effect [16]. Resistivity $\rho$ as a function of magnetic field $H$ (b) and temperature $T$ (c) for $S$-type ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ from which the $H\mathrm{\text{−}}T$ diagram was obtained.

Figure 2

Resistivity $\rho$ as a function of field $H$ for different angles at 40 mK. Here $\theta$ is the angle between the magnetic field and the crystalline $a$ axis.

Figure 3

Angular dependence of the upper critical field $H_{c2}$ at 40 mK after subtraction of a 5° misalignment component

Figure 4

(a) In-plane angular dependence of $H_{c2}$ normalized with respect to the upper critical field along [110]. The theoretical model for a $d_{xy}$ wave superconductor at 100 mK is presented with (solid red curve) and without (dashed blue curve) Fermi velocity anisotropy. The fourfold modulation and the amplitude of the oscillation are well reproduced by the calculation. (b) The admixing parameter $C$ as a function of $\theta$ (anisotropic case). (c) In-plane angular dependence of $H_{c2}$ when assuming a $d_{x^2\mathrm{\text{−}}{y}^2}$ symmetry (anisotropic case). Note the 45° shift compared to the experimental data.