Strong electron correlations can give rise to extraordinary properties of metals with renormalized quasiparticles which are at the basis of Landaus Fermi liquid theory. Near a quantum critical point, these quasiparticles can be destroyed and non-Fermi liquid behavior ensues. YbRh$_2$Si$_2$ is a prototypical correlated metal as it exhibits quasiparticles formation, formation of Kondo lattice coherence and quasiparticle destruction at a field-induced quantum critical point. Here we show how, upon lowering the temperature, the Kondo lattice coherence develops and finally gives way to non-Fermi liquid electronic excitations. By measuring the single-particle excitations through scanning tunneling spectroscopy down to 0.3 K, we find the Kondo lattice peak emerging below the Kondo temperature $T_{rm K} sim$ 25 K, yet this peak displays a non-trivial temperature dependence with a strong increase around 3.3 K. At the lowest temperature and as a function of an external magnetic field, the width of this peak is minimized in the quantum critical regime. Our results provide a striking demonstration of the non-Fermi liquid electronic excitations in quantum critical metals, thereby elucidating the strange-metal phenomena that have been ubiquitously observed in strongly correlated electron materials.
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