UC Santa Cruz

The Extremely Correlated Fermi Liquids (ECFL) theory is reviewed as a framework for understanding the $t$-$J$ model in metallic systems close to the Mott insulating limit. This overview presents the underlying ideas and the resulting equations in a form accessible to nonexperts. We compare theoretical results with all available resistivity data for single-layer High-T$_{c}$ systems, and with some spectral data. The highlighted results include a density dependent quasilinear T-dependence in resistivity, an unusually small quasiparticle weight, and distinct low-temperature emergent scales that dominate transport, thermodynamics and spectral properties of single-layer High T$_c$ systems. Suggestions are made for further experiments to probe the physics of these challenging quantum many-body systems.