Preformed heavy-electrons at the Quantum Critical Point in heavy fermion compounds

The existence of multiple energy scales is regarded as a signature of the Kondo breakdown mechanism for explaining the quantum critical behavior of certain heavy fermion compounds, like YbRh$_{2}$Si$_{2}$. The nature of the intermediate state between the heavy Fermi liquid and the quantum critical region, however, remains elusive. In this study we suggest an incoherent heavy-fermion scenario, where inelastic scattering with novel soft modes of the dynamical exponent $z = 3$ gives rise to non-Fermi liquid physics for thermodynamics and transport despite the formation of the heavy-fermion band. We discuss a crossover from $z = 3$ to $z = 1$ for quantum phase fluctuations.