Flat bands and strongly correlated Fermi systems

• Published in: Physica scripta 2019-06, Vol.94 (6), p.65801
• Main Authors: Shaginyan, V R, Msezane, A Z, Stephanovich, V A, Japaridze, G S, Kirichenko, E V
• Format: Article
• Language: English
• Subjects: flat bands; strongly correlated Fermi systems; tunneling conductance
• ISSN: 0031-8949; 1402-4896
• DOI: 10.1088/1402-4896/ab10b4

Many strongly correlated Fermi systems including heavy-fermion (HF) metals and high-Tc superconductors belong to that class of quantum many-body systems for which Landau Fermi-liquid (LFL) theory fails. Instead, these systems exhibit non-Fermi-liquid properties that arise from violation of time-reversal (T) and particle-hole (C) invariance. Measurements of tunneling conductance provide a powerful experimental tool for detecting violations of these basic symmetries inherent to LFLs, which guarantee that the measured differential conductivity dI/dV, where I is the current and V the bias voltage, is a symmetric function of V. Thus, it has been predicted that the conductivity becomes asymmetric for HF metals such as CeCoIn5 and YbRh 2 Si 2 . In these systems, the background electron liquid is considered to undergo a transformation that renders a portion of its excitation spectrum dispersionless, giving rise to so-called flat bands. The presence of a flat band indicates that the system is close to a special quantum critical point, namely a topological fermion-condensation quantum phase transition. An essential aspect of the behavior of a system hosting a flat band is that application of a magnetic field can restore its normal Fermi-liquid properties, including T- and C-invariance, with the differential conductivity again becoming a symmetric function of V. This behavior has been observed in recent measurements of tunneling conductivity in both YbRh 2 Si 2 and graphene. Also within the FC framework, we describe and explain 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 the observed scaling is explained by the emergence of flat bands formed by fermion condensation.