Evidence for the Coexistence of an Anisotropic Superconducting Gap and Nonlocal Effects in the Nonmagnetic Superconductor ${\mathrm{LuNi}}_2{\mathrm{B}}_2\mathrm{C}$

A study of the dependence of the heat capacity $C_p(\alpha )$ on the field angle in ${\mathrm{LuNi}}_2{\mathrm{B}}_2\mathrm{C}$ reveals an anomalous disorder effect. For pure samples, $C_p(\alpha )$ exhibits a fourfold variation as the field $H<H_{c2}$ is rotated in the $[001]$ plane, with minima along $⟨100⟩$ ($\alpha =0$). A slightly disordered sample, however, develops anomalous secondary minima along $⟨110⟩$ for ${\mu }_{0}H>1\mathrm{T}$, leading to an eightfold pattern at 2 K and 1.5 T. The anomalous pattern is discussed in terms of coexisting superconducting gap anisotropy and nonlocal effects.

Figure 1

(a) Heat capacity of sample $C$ at 2.5 K for $H\parallel [110]$. (b)–(d) Heat capacity of sample $A$ at 2.5, 4, and 8 K, respectively, for $H\parallel [110]$. Dashed lines are $H^{1/2}$ fit and arrows indicate the deviation point from $H^{1/2}$.

Figure 2

(a) Normalized heat capacity of sample $C$ at 2.5 K and a fourfold oscillation (solid line), $\Delta C(\alpha )/c=1+\Gamma |\sin 2\alpha |$. (b) Field-induced heat capacity of sample $A$ at 2 K, $\Delta C=C_{\mathrm{total}}-C_{\mathrm{bkg}}$, and a $4+4$ pattern (solid line) (see text).

Figure 3

Oscillation amplitude $\Gamma$ of sample $C$ (circles) and sample $N$ (squares). The dashed line is from the 3D nodal quasiparticle theory with $v_F=1.5\times {10}^7\mathrm{cm}/\mathrm{s}$ [8]. The bottom panel contrasts the oscillation amplitude due to the nonlocal effect (circles) and gap anisotropy (squares).

Figure 4

$H-T$ phase diagram of sample $A$ with lowest $T_c$. $H_{s1}$ is the FLL transition for $H\parallel [110]$ and $H_{s1}$ for $H\parallel [100]$. The dotted lines are a guide to the eye. Triangles and squares were sketched to show the corresponding FLL.