Thermal conductance of a two-channel Kondo model

A theory of thermal transport in a two-channel Kondo system, such as the one formed by a small quantum dot coupled to two leads and to a larger dot, is formulated. The interplay of the two screening constants allow an exploration of the Fermi liquid and non-Fermi liquid regimes. By using analytical, as well as numerical, renormalization group methods, we study the temperature dependence of the thermal conductance and the Lorentz number. We find that in the low-temperature limit, the Lorentz number attains its universal value, irrespective of the nature of the ground state.

Figure 1

The universal behavior of the thermal conductance of a 2CK model (corresponding to channel 1). Three regimes are clearly visible when $J_1\ne J_2$. For $T\ll T^{\star }$ the system is in the Fermi liquid regime, followed by a crossover ($T^{\star }<T<T_K$) to the perturbative ($T\gg T_K$) regime. The non-Fermi fixed point is realized for $J_1=J_2$. $\alpha$ and $\gamma$ are two numerical constants of order 1, and $G_0$ is the universal conductance $G_0=2\hspace{0.5em}{e}^2/h$.

Figure 2

Thermal conductance as function of $T/T_K$ on a logarithmic scale. The NFL fixed point result, $J_1=J_2$, corresponds to the solid line, while dashed and dash-dotted lines correspond to $J_1\ne J_2$. $K$ is the anisotropy factor $(J_1-J_2)/J^2$. In both cases the average coupling is $J=(J_1+J_2)/2=0.2$.

Figure 3

The thermal conductance in the FL regime for $K>0$ (top panel) and for $K<0$ (bottom panel). $\kappa (T)/T$ given by Eq. (1) is plotted as a function of $T/T^{*}$ on a scaled temperature axis.

Figure 4

The universal behavior of the Lorentz number as function of $T/T^{\star }$ in the FL regime. In the low-temperature limit $T\ll T^{\star }$, $L(T)$ converges to $L_0$. The inset presents $L(T)$ as function of $T/T_K$. At the NFL fixed point, for $T\ll T_K$ the same universality is recovered.