Kondo effect in $f$-electron superlattices

We demonstrate the importance of the Kondo effect in artificially created $f$-electron superlattices. We show that the Kondo effect does not only change the density of states of the $f$-electron layers, but is also the cause of pronounced resonances at the Fermi energy in the density of states of the noninteracting layers in the superlattice, which are between the $f$-electron layers. Remarkably, these resonances strongly depend on the structure of the superlattice; due to interference, the density of states at the Fermi energy can be strongly enhanced or even shows no changes at all. Furthermore, we show that by inserting the Kondo lattice layer into a three-dimensional metal, the gap of the Kondo insulating state changes from a full gap to a pseudogap with quadratically vanishing spectral weight around the Fermi energy. Due to the formation of the Kondo insulating state in the $f$-electron layer, the superlattice becomes strongly anisotropic below the Kondo temperature. We prove this by calculating the in-plane and the out-of-plane conductivity of the superlattice.

Figure 1

Schematic picture of a (1,2) superlattice, consisting of a periodic arrangement of one $f$-electron layer and two noninteracting layers.

Figure 2

Results of a single KLL, $J=0.5W_2$, within a 3D noninteracting host. Upper panel: DOS of the KLL for different hopping amplitudes, $t_z$, between the KLL and the NIL. The insets show magnifications around the Fermi energy. Lower panel: DOS of different layers. (a) DOS of the KLL, (b) nearest-neighbor layer, (c) next-nearest-neighbor layer, (d) third-nearest-neighbor layer, (e) 10 layers away.

Figure 3

DOS of a (1,1) superlattice for different temperatures. The insets show magnifications around the Fermi energy.

Figure 4

DOS at the Fermi energy and crossover temperature for the (1,1) superlattice. Left: DOS at the Fermi energy, ${\rho }_{\mathrm{Fermi}}$, for different temperatures and interaction strengths. The lower (upper) lines correspond to the KLL (NIL). Right: Crossover temperature over inverse interaction strength, proving the exponential dependence.

Figure 5

DOS of a (1,2) superlattice for different temperatures. Due to symmetry, both NILs are identical.

Figure 6

DOS of a (1,3) superlattice for different temperatures.

Figure 7

Upper panel: DOS at the Fermi energy over temperature for $J/W_2=0.3$, and for a variety of superlattice configurations. We only show the Kondo lattice layer and the nearest-neighbor NIL. Lower panel: Each panel shows the normalized DOS at the Fermi energy for all different layers in the superlattice. The arrows at the layer index denote the KLLs.

Figure 8

Spectral functions at $T=0$ for the $(1,1)$ and $(1,2)$ superlattice for different interlayer couplings, $t_z$.

Figure 9

Real part of the conductivity within the layers, ${\sigma }_x$, and perpendicular to the superlattice structure, ${\sigma }_z$, for $J/W_2=0.5$. The lower panel shows the excitations in the local DOS corresponding to the peaks in the conductivity.

Figure 10

DOS for the (1,2) superlattice in a doped system $J/W_2=0.65$.