  In quantum materials, electrons that have strong correlations tend to
localize, leading to quantum spins as the building blocks for low-energy
physics. When strongly correlated electrons coexist with more weakly-correlated
conduction electrons, multiple channels of effective interactions develop and
compete with each other. The competition creates quantum fluctuations having a
large spectral weight, with the associated entropies reaching significant
fractions of $R\ln 2$ per electron. Advancing a framework to understand how the
fluctuating local moments influence unconventional superconductivity is both
pressing and challenging. Here we do so in the exemplary setting of
heavy-fermion metals, where the amplified quantum fluctuations manifest in the
form of Kondo destruction and large-to-small Fermi-surface fluctuations. These
fluctuations lead to unconventional superconductivity whose transition
temperature is exceptionally high relative to the effective Fermi temperature,
reaching several percent of the Kondo temperature scale. Our results provide a
natural understanding of the enigmatic superconductivity in a host of
heavy-fermion metals. Moreover, the qualitative physics underlying our findings
and their implications for the formation of unconventional superconductivity
apply to a variety of highly correlated metals with strong Fermi surface
fluctuations.

Strongly Correlated Electrons;Superconductivity