Flat Bands and Salient Experimental Features Supportingthe Fermion Condensation Theory of Strongly Correlated Fermi Systems

The physics of strongly correlated Fermi systems, being the mainstream topic for more than half a century, still remains elusive. Recent advancements in experimental techniques permit to collect important data, which, in turn, allow us to make the conclusive statements about the underlying physics of strongly correlated Fermi systems. Such systems are close to a special quantum critical point represented by topological fermion-condensation quantum phase transition which separates normal Fermi liquid and that with a fermion condensate, forming flat bands. Our review paper considers recent exciting experimental observations of universal scattering rate related to linear temperature dependence of resistivity in a large number of strongly correlated Fermi systems as well as normal metals. We show that the observed scattering rate is explained by the emergence of flat bands, while the so-called Planckian limit occurs accidentally since the normal metals exhibit the same scattering rate behavior. We also analyze recent challenging experimental data on tunneling differential conductivity collected under the application of magnetic field on the twisted graphene and the archetypical heavy fermion metal YbRh $${}_{2}$$ Si $${}_{2}$$ . Also we describe recent empirical observations of scaling properties related to universal linear-temperature resistivity for a large number of strongly correlated high-temperature superconductors. We show that these observations support the fermion condensation theory. Our theoretical results are in good agreement with corps of different and seemingly unrelated experimental facts. They show that the fermion-condensation quantum phase transition is an intrinsic property of strongly correlated Fermi systems and can be viewed as the universal agent explaining their core physics.