*Review* **Peculiar Physics of Heavy-Fermion Metals: Theory versus Experiment**

**Vasily R. Shaginyan 1,2,\*, Alfred Z. Msezane 2 and George S. Japaridze 2**

	- george.japaridze@gmail.com (G.S.J.) **\***Correspondence: vrshag@thd.pnpi.spb.ru

**Abstract:** This review considers the topological fermion condensation quantum phase transition (FCQPT) that leads to flat bands and allows the elucidation of the special behavior of heavy-fermion (HF) metals that is not exhibited by common metals described within the framework of the Landau Fermi liquid (LFL) theory. We bring together theoretical consideration within the framework of the fermion condensation theory based on the FCQPT with experimental data collected on HF metals. We show that very different HF metals demonstrate universal behavior induced by the FCQPT and demonstrate that Fermi systems near the FCQPT are controlled by the Fermi quasiparticles with the effective mass *M*∗ strongly depending on temperature *T*, magnetic field *B*, pressure *P*, etc. Within the framework of our analysis, the experimental data regarding the thermodynamic, transport and relaxation properties of HF metal are naturally described. Based on the theory, we explain a number of experimental data and show that the considered HF metals exhibit peculiar properties such as: (1) the universal *T*/*B* scaling behavior; (2) the linear dependence of the resistivity on *T*, *ρ*(*T*) ∝ *A*1*T* (with *A*1 is a temperature-independent coefficient), and the negative magnetoresistance; (3) asymmetrical dependence of the tunneling differential conductivity (resistivity) on the bias voltage; (4) in the case of a flat band, the superconducting critical temperature *Tc* ∝ *g* with *g* being the coupling constant, while the *M*∗ becomes finite; (5) we show that the so called Planckian limit exhibited by HF metals with *ρ*(*T*) ∝ *T* is defined by the presence of flat bands.

**Keywords:** topology; quantum phase transition; flat bands; fermion condensation; HF metals; thermodynamic; transport properties

**PACS:** 64.70.Tg; 75.40.Gb; 78.20.-e; 71.10.Hf
