Landau's Fermi liquid theory and Bardeen-Cooper-Schrieffer theory, which respectively describe the physics of conventional metals in the normal state and the instability toward superconductivity, are among the most successful theories in condensed matter physics. However, these theories do not apply to strongly correlated metals where quantum fluctuations destroy the coherence of quasiparticles. Those unconventional metals called non-Fermi liquids often arise near quantum critical points at which quantum fluctuations melt long-range orders. Despite their ubiquity, the theoretical effort to understand non-Fermi liquids and their superconducting instabilities has long been hindered by a lack of a theoretical framework for describing the physics of infinitely many low-energy electrons residing on the Fermi surface subject to strong quantum fluctuations. In this talk, I will discuss the recent progress made in understanding the normal state and its pathway toward the superconducting state for the non-Fermi liquid realized at the antiferromagnetic quantum critical point in two space dimensions.
