Strongly inhomogeneous phases and non-Fermi-liquid behavior in randomly depleted Kondo lattices

We investigate the low-temperature behavior of paramagnetic Kondo lattices upon random depletion of the local $f$ moments by using strong-coupling arguments and solving SU$\left(N\right)$ saddle-point equations on large lattices. For a large range of intermediate doping levels, between the coherent Fermi-liquid of the dense lattice and the single-impurity Fermi liquid of the dilute limit, we find strongly inhomogeneous states that exhibit distinct non-Fermi-liquid characteristics. The interplay of dopant disorder and strong interactions leads to rare weakly screened moments which dominate the bulk susceptibility. Our results are relevant to compounds like ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}\mathrm{Co}{\mathrm{In}}_5$ and ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{Pb}}_3$.

Figure 1

Schematic phase diagram of paramagnetic depleted Kondo lattices. In the dense limit, $n_f\lesssim 1$, a coherent heavy FL is formed below $T_{\mathrm{coh}}$ (dashed line), whereas in the dilute limit, $n_f\to 0$, single-impurity physics prevails, with local FL behavior below $T_K^{\left(1\right)}$ (dash-dotted line). There is a large regime of intermediate $n_f$ where low-energy properties are strongly inhomogeneous and FL behavior is suppressed.

Figure 2

(Color online) Summary of the mean-field results: (a) $T^{*}=⟨b_r^2⟩∕D$ as function of the local-moment concentration $n_f$ for $J_K∕D=1.25$ and different band fillings $n_c$. Note the sharp change around $n_c=n_f$. The inset shows the distribution of $b_r^2∕⟨b_r^2⟩$ for the different $n_c$ at fixed $n_f=0.5$. The strongly inhomogeneous regime is characterized by a bimodal distribution; here most pronounced at $n_c=0.4$. (b) Evolution (from top to bottom) of the mean-field density of states from the HFL to the dilute impurity limit at fixed $n_c=0.4$.

Figure 3

(Color online) Spatial distribution of the slave boson amplitudes ($b_r$, left), the low-energy LDOS [$A_r(\omega =0)$, middle], and the local susceptibilities [${\chi }_{\mathrm{loc},r}(T={10}^{-3})$, right] for different $n_f=0.05$, 0.5, and 0.95 at a band filling of $n_c=0.8$. The Kondo coupling is $J_K∕D=1.25$.

Figure 4

(Color online) Spatial distribution of the LDOS, $A_r(\omega =0)$, for a specific disorder realization with $n_f=0.2$, but for varying conduction electron filling $n_c=0.1$, 0.2, and 0.8. The crossover from the single-vacancy (a) to the single-impurity (c) regime can be nicely seen, with a tendency toward island formation in between. The $f$-moment locations can be identified from the dark sites in (c).

Figure 5

(Color online) Temperature dependence of $\chi$ and mean-field parameters. (a) $f$-moment susceptibility ${\chi }_{ff}$; in the inhomogeneous regime, $n_f\approx n_c=0.4$, ${\chi }_{ff}$ does not saturate to the lowest $T$ studied. (b) Local susceptibility, ${\chi }_{\mathrm{loc}}\left(T\right)$, at three different sites, illustrating the broad range of behavior. (c) and (d) Mean-field parameters $b_r\left(T\right)$ and ${\mu }_r\left(T\right)$ at the same sites. $J_K∕D=1.25$ and for (b)–(d) $n_f=n_c=0.4$.