  Some materials can have the dispersionless parts in their electronic spectra.
These parts are usually called flat bands and generate the corps of unusual
physical properties of such materials. These flat bands are induced by the
condensation of fermionic quasiparticles, being very similar to the Bose
condensation. The difference is that fermions to condense, the Fermi surface
should change its topology, leading to violation of time-reversal (T) and
particle-hole (C) symmetries. Thus, the famous Landau theory of Fermi liquids
does not work for the systems with fermion condensate (FC) so that several
experimentally observable anomalies have not been explained so far. Here we use
FC approach to explain recent observations of the asymmetric tunneling
conductivity in heavy-fermion compounds and graphene and its restoration in
magnetic fields, as well as the violation of Leggett theorem, recently observed
experimentally in overdoped cuprates, and recent observation of the challenging
universal scaling connecting linear-$T$-dependent resistivity to the
superconducting superfluid density.
