Flat bands and strongly correlated Fermi systems

Abstract

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 . 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 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.