Verification of the Wiedemann-Franz Law in ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ at a Quantum Critical Point

The thermal conductivity measurements are performed on the heavy-fermion compound ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ down to 0.04 K and under magnetic fields through a quantum critical point (QCP) at $B_c=0.66\mathrm{T}\parallel c$ axis. In the limit as $T\to 0$, we find that the Wiedemann-Franz law is satisfied within experimental error at the QCP despite the destruction of the standard signature of Fermi liquid. Our results place strong constraints on models that attempt to describe the nature of the unconventional quantum criticality of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$.

Figure 1

Temperature dependence of the thermal conductivity divided by temperature $\kappa (T)/T$ of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ at various magnetic fields with the enlarged plot around the Néel ordering temperature $T_N$ (upper inset), in semilogarithmic plots. Lower inset: Field dependence of $\kappa (B)/T$ at 0.051 K. $B_c=0.66\mathrm{T}$ denotes the critical field.

Figure 2

Temperature dependence of the heat resistivity $w(T)$ and the charge resistivity $\rho (T)$ of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ at (a) $B_c=0.66$ and 1 T and at (b) 0 T plotted vs $T$, and at (c) 5 T plotted vs $T^2$, respectively. The dashed lines represent linear fits to the data. An arrow in (c) indicates the upper bound of $T^2$ dependence of $\rho (T)$. For comparison, $w(T)$ and $\rho (T)$ at $B_c=0.06\mathrm{T}$ for $B\parallel ab$ adapted from Ref. 22 are plotted in (a). Inset: $\rho (T)$ as a function of $T$ under 0, 0.66, and 5 T.

Figure 3

Temperature dependence of the Lorenz ratio $L(T)/L_0$ of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ above the critical field $B_c=0.66\mathrm{T}$. Arrows denote minima $T_{\min }$ in $L(T)/L_0$ at each field. Inset: $B$-$T$ phase diagram of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$, including the Néel ordering temperature $T_N$, the upper bound of $T^2$ electrical resistivity $T_{\mathrm{FL}}$, and the positions of minimum $T_{\min }$ of the Lorenz ratio $L(T)/L_0$, respectively, together with $T_N$ and $T_{\mathrm{FL}}$ (open symbols) from Ref. 18.

Figure 4

Field dependence of the Lorenz ratio $L(B)/L_0$ of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ in the zero temperature limit and at finite temperatures.