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The formation of a heavy Fermi liquid in metals with local moments ischaracterized by multiple energy and temperature scales, most prominently theKondo temperature and the coherence temperature, characterizing the onset ofKondo screening and the emergence of Fermi-liquid coherence, respectively. Inthe standard setting of a wide conduction band, both scales dependexponentially on the Kondo coupling. Here we discuss how the presence of flat,i.e., dispersionless, conduction bands modifies this situation. Focussing onthe case of the kagome Kondo-lattice model, we utilize a parton mean-fieldapproach to determine the Kondo temperature and the coherence temperature asfunction of the conduction-band filling $n_c$, both numerically andanalytically. For $n_c$ values corresponding to the flat conduction bandlocated at the Fermi level, we show that the exponential is replaced by alinear dependence for the Kondo temperature and a quadratic dependence for thecoherence temperature, while a cubic law emerges for the coherence temperatureat $n_c$ corresponding to the band edge between the flat and dispersive bands.We discuss implications of our results for pertinent experimental data.

Kondo screening and coherence in kagome local-moment metals: Energy scales of heavy fermions in the presence of flat bands