Spin-Triplet $p$-Wave Superconductivity Revealed under High Pressure in ${\mathrm{UBe}}_{13}$

To unravel the nature of the superconducting symmetry of the enigmatic $5f$ heavy-fermion ${\mathrm{UBe}}_{13}$, the pressure dependence of the upper critical field and of the normal state are studied up to 10 GPa. Remarkably, the pressure evolution of the anomalous $H_{c2}(T,P)$ over the entire pressure range up to 5.9 GPa can be successfully explained by the gradual admixture of a field-pressure-induced $E_u$ component in an $A_{1u}$ spin-triplet ground state. This result provides strong evidence for parallel-spin pairing in ${\mathrm{UBe}}_{13}$, which is also supported by the recently observed fully gapped excitation spectrum at ambient pressure. Moreover, we have also found a novel non-Fermi-liquid behavior of the resistivity, $\rho (T)\sim T^n$ ($n\lesssim 1$), which disappears with the collapse of the negative magnetoresistance behavior and the existence of a superconducting ground state around $P=6\mathrm{GPa}$, suggesting a close interplay between Kondo scattering and superconductivity.

Figure 1

$H\text{−}T$ SC phase diagram at 0 GPa with a contour plot of the exponent ($n$) of the resistivity $\rho (T)$. The markers indicate $H_{c2}$, determined by temperature $\rho (T)$ (circles) and field $\rho (H)$ (triangle) scans.

Figure 2

$C_{\mathrm{ac}}/T$ (in arbitrary units) of ${\mathrm{UBe}}_{13}$ under high pressures, (a) 0.7, (b) 1.2, and (c) 2.9 GPa in zero and several fields. (d) ${\chi }_{\mathrm{ac}}(T)$ in ${\mathrm{UBe}}_{13}$, at zero field under pressures from 0.5 to 5.8 GPa. (e) $T\text{−}P$ phase diagram of ${\mathrm{UBe}}_{13}$. The SC transition temperatures were obtained from our $C_{\mathrm{ac}}$ and ${\chi }_{\mathrm{ac}}$ measurements along with $T_{\max }(P)$. Here, $T_{\mathrm{coh}}(P)$ is taken from Ref. [25]. The dashed and solid lines are guides to the eye.

Figure 3

(a) $H_{c2}(T)$ of ${\mathrm{UBe}}_{13}$, obtained from ac specific-heat (0, 0.7, 1.2, 2, and 2.9 GPa) and resistivity (0, 2.1, 2.8, 3.6, 4.3, 5.6, and 5.9 GPa) measurements; circle and triangle markers indicate data determined from $T$ and $H$ scans, respectively; solid lines are fits to the $A_{1u}\oplus E_u$ model; the inset is a focus above 2.9 GPa. (b) $1/{[v_F(P)]}^2$ used in the fits above, compared with the resulting $H_{c2}^{\prime }/T_c$, both normalized by their values at $P=0$. (c) Pressure dependence of $T_{c1}/T_{c0}$, controlling the admixture of $A_{1u}$ and $E_u$ in the fits. (d) Strong-coupling constant $\lambda (P)$ (left) reproducing $T_c(P)$, and the resulting $v_F(P)=v_F(0)\{[1+\lambda (0)]/[1+\lambda (P)]\}$ (right).

Figure 4

Resistivity of ${\mathrm{UBe}}_{13}$ at (a) 0 GPa and under high pressures (in arbitrary units) of (b) 2.8, (c) 3.6, and (d) 5.6 GPa in zero and several fields vs (left) $T$ and (right) $T^2$. (e) Resistivity as a function of $T^2$ obtained at 10.3 GPa and (f) the field dependence of the $A$ coefficient, obtained semiquantitatively for each pressure [29].