  The heavy-fermion superconductor CeCu$_{2}$Si$_{2}$ exhibits two-band,
$d$-wave superconductivity with a finite energy gap over the whole Fermi
surface around the magnetic instability where 4$f$ antiferrerromagnetic order
is suppressed. In contrast, in YbRh$_{2}$Si$_{2}$ heavy-fermion
superconductivity appears only when 4$f$-electronic antiferromagnetic order is
replaced at ultra-low temperatures by a combined nuclear and 4$f$-spin order.
Whereas both compounds exhibit different variants of antiferromagnetic
instabilities, i.e., a spin-density-wave quantum critical point in
CeCu$_{2}$Si$_{2}$ and one of "partial-Mott" type in YbRh$_{2}$Si$_{2}$, in
both cases the Cooper pairing, as well as the pronounced "strange-metal"
behavior in YbRh$_{2}$Si$_{2}$, appear to be driven by large-to-small Fermi
surface fluctuations. The transport properties and scanning tunneling
spectroscopy (STS) for these materials are dominated by single-ion Kondo
scatterings down to very low temperatures. Further open problems of the Kondo
lattice include both the interplay between superconductivity and
antiferromagnetic order as well as the onset of lattice coherence. While
microscopic coexistence of superconductivity and antiferromagnetism seems to
require a sufficiently large staggered moment, the onset of lattice coherence
in transport measurements and STS is associated solely with the
crystal-field-doublet ground state, while it involves the fully degenerate
Hund's rule multiplet in ARPES.
