Exotic Superconducting Properties in the Electron-Hole-Compensated Heavy-Fermion “Semimetal” ${\mathrm{URu}}_2{\mathrm{Si}}_2$

We show that the charge and thermal transport measurements on ultraclean crystals of ${\mathrm{URu}}_2{\mathrm{Si}}_2$ reveal a number of unprecedented superconducting properties. The uniqueness is best highlighted by the peculiar field dependence of thermal conductivity including the first-order transition at $H_{c2}$ with a reduction of entropy flow. This is a consequence of multiband superconductivity with compensated electronic structure in the hidden order state of this system. We provide strong evidence for a new type of unconventional superconductivity with two distinct gaps having different nodal topology.

Figure 1

Main panel: Temperature dependence of $\rho$ (solid lines) along the $a$ axis in zero and finite magnetic fields ($\mathit{H}||c$) and Hall coefficient $R_H$ (solid circles). Inset: The MR at $T\to 0\mathrm{K}$ as a function of $H^2$.

Figure 2

Main panel: $\kappa /T$ plotted as a function of $T^2$ at very low temperatures. The data in magnetic fields ($\mathit{H}||c$) are obtained under field cooling conditions. The lines are guides for the eyes. Inset: $\kappa /T$ vs $T$ at high temperatures.

Figure 3

(a) The field dependence of $\kappa /T$ for $\mathit{H}||c$ [blue (or dark gray) circles] and $\mathit{H}||a$ [red (or gray) circles] as a function of $H/H_{c2}^c$ and $H/H_{c2}^a$, respectively. The dashed blue (or dark gray) and dotted red (or gray) lines represent the expected $\kappa (H)/T$ by the WF law for ($\mathit{H}||c$) and ($\mathit{H}||a$), respectively. (b) $\kappa (H)/T$ at low fields as a function of $\sqrt{H}$. The characteristic field, $H_s=0.4\mathrm{T}$ is indicated by the arrow. (c) The field derivative of $\kappa (H)/T$ for $\mathit{H}||c$ plotted as a function of $H$. (d) The $H\mathrm{\text{−}}T$ phase diagram for $\mathit{H}||c$. The transition between superconducting (SC) and normal (N) states is of first order below $\sim 0.4\mathrm{K}$.

Figure 4

The schematic figure of the Fermi surface (opaque) and superconducting gap structure (transparent) inferred from the present experiments [21].