  In solids containing elements with f orbitals, the interaction between
f-electron spins and those of itinerant electrons leads to the development of
low-energy fermionic excitations with a heavy effective mass. These excitations
are fundamental to the appearance of unconventional superconductivity and
non-Fermi-liquid behaviour observed in actinide- and lanthanide-based
compounds. Here we use spectroscopic mapping with the scanning tunnelling
microscope to detect the emergence of heavy excitations with lowering of
temperature in a prototypical family of cerium-based heavy-fermion compounds.
We demonstrate the sensitivity of the tunnelling process to the composite
nature of these heavy quasiparticles, which arises from quantum entanglement of
itinerant conduction and f electrons. Scattering and interference of the
composite quasiparticles is used to resolve their energy-momentum structure and
to extract their mass enhancement, which develops with decreasing temperature.
The lifetime of the emergent heavy quasiparticles reveals signatures of
enhanced scattering and their spectral lineshape shows evidence of
energy-temperature scaling. These findings demonstrate that proximity to a
quantum critical point results in critical damping of the emergent heavy
excitation of our Kondo lattice system.
