Unconventional Superconductivity from Local Spin Fluctuations in the Kondo Lattice

The explanation of heavy-fermion superconductivity is a long-standing challenge to theory. It is commonly thought to be connected to nonlocal fluctuations of either spin or charge degrees of freedom and therefore of unconventional type. Here we present results for the Kondo-lattice model, a paradigmatic model to describe heavy-fermion compounds, obtained from dynamical mean-field theory which captures local correlation effects only. Unexpectedly, we find robust $s$-wave superconductivity in the heavy-fermion state. We argue that this novel type of pairing is tightly connected to the formation of heavy quasiparticle bands and the presence of strong local spin fluctuations.

Figure 1

Left-hand panel: $N$ DOS (dashed red lines) and SC DOS (full lines) for $n=0.9$ and various $J$. Right-hand panel: Real part of the corresponding gap functions.

Figure 2

Anomalous expectation value $\Phi$ as a function of $J/W$ between quarter and half filling. The white dashed lines indicate the cuts along a fixed $J$ and $n$ shown in Figs. 3a, 3b.

Figure 3

$\Phi$ (circles) and $T_0$ (squares) as a function of $J$ at fixed $n=0.9$ (a), or as a function of $n$ at fixed $J/W=0.2$ (b). The full lines represent approximate dependencies of $T_0$ on $J$ and $n$ (see text).

Figure 4

Evolution of the DOS with increasing temperature for $n=0.9$ and $J=0.25\mathrm{W}$, where $T_0/W=0.0105$ at $T\to 0$. Inset: $\Phi$ as a function of temperature. Pair correlations are fully suppressed for $T>T_c$.

Figure 5

Second-order process responsible for pairing in the limit of large $J/W$. Shown are the $c$ electron and local-moment ($f$) configurations on adjacent lattice sites; the ellipses denote a singlet bond of two electrons. Here, two hoppings effectively move a down-spin hole by two sites across an up-spin hole, with a triplet intermediate state (bold red arrows).