New State of Matter: Heavy Fermion Systems, Quantum Spin Liquids, Quasicrystals, Cold Gases, and High-Temperature Superconductors

We report on a new state of matter manifested by strongly correlated Fermi systems including various heavy fermion (HF) metals, two-dimensional quantum liquids such as \(^3\)He films, certain quasicrystals, and systems behaving as quantum spin liquids. Generically, these systems can be viewed as HF systems or HF compounds, in that they exhibit typical behavior of HF metals. At zero temperature, such systems can experience a so-called fermion condensation quantum phase transition (FCQPT). Combining analytical considerations with arguments based entirely on experimental grounds, we argue and demonstrate that the class of HF systems is characterized by universal scaling behavior of their thermodynamic, transport, and relaxation properties. That is, the quantum physics of different HF compounds is found to be universal, emerging irrespective of the individual details of their symmetries, interactions, and microscopic structure. This observed universal behavior reveals the existence of a new state of matter manifest in HF compounds. We propose a simple, realistic model to study the appearance of flat bands in two-dimensional ensembles of ultracold fermionic atoms, interacting with coherent resonant light. It is shown that signatures of these flat bands may be found in peculiarities in their thermodynamic and spectroscopic properties. We also show that the FCQPT, in generating flat bands and altering Fermi surface topology, is an essential progenitor of the exotic behavior of the overdoped high-temperature superconductors represented by \(\hbox {La}_{2-x}\hbox {Sr}_{x}x\hbox {CuO}_4\), whose superconductivity differs from that predicted by the classical Bardeen–Cooper–Schrieffer theory. The theoretical results presented are in good agreement with recent experimental observations, closing the colossal gap between these empirical findings and Bardeen–Cooper–Schrieffer-like theories.