Recent Developments in the Antiferromagnetic Quantum Critical Metal: Pairing Instability, Emergent Momentum-Spacetime Geometry and Kondo Effect

Abstract

This thesis is concerned with recent progress made for the antiferromagnetic quantum critical metal in two space dimensions. Firstly, we develop a field-theoretic functional renormalization group formalism for the low-energy effective field theories for non-Fermi liquids by using renormalizable field theories for metals. The formalism is applied to the antiferromagnetic quantum critical metal in two space dimensions. In the space of coupling functions, we identify the interacting fixed point with a vanishing nesting angle. For theories with non-zero nesting angles, the coupling functions acquire universal momentum dependent profiles controlled by the bare nesting angle before flowing towards a superconducting state in the low-energy limit. The superconducting instability is inevitable because “lukewarm” electrons that are coherent enough to be susceptible to pairing are subject to a universal attractive interaction mediated by the critical spin fluctuations. Despite the superconducting instability being unavoidable, theories with repulsive or weakly attractive four-fermion interaction at a UV scale must flow through a “bottleneck” where there is a slow RG flow due to the proximity to non-Hermitian fixed points. This bottleneck of the RG flow controls the scaling behaviour of the normal state and the “quasi-universal” pathway to superconductivity. Secondly, we show that momentum-dependent quantum corrections dynamically give rise to a curved momentum-spacetimes for quasiparticles. In the antiferromagnetic quantum critical metal, the curved momentum-spacetime geometry arises from a momentum-dependent red shift. With increasing nesting angle, the red shift near the hot spots becomes stronger while the hot region on the Fermi surface with the strong red shift shrinks. This creates the possibility of realizing a momentum-space black hole horizon where electrons are perpetually slowed down as they approach the hot spots. However, the singularity in the momentum-dependent red shift is cut off at finite temperatures above the superconducting transition temperature. Finally, we study a magnetic impurity immersed in the antiferromagnetic quantum critical metal. Critical spin fluctuations represented by bosonic fields compete with the conduction electrons to couple with the impurity spin. In the low-energy limit, the electron-impurity (Kondo) coupling dominates over the boson-impurity coupling. However, the Kondo screening is suppressed by the boson with an increasing severity when the hot spots connected by the antiferromagnetic ordering wavevector are better nested. The origin of this suppression of Kondo screening lies in the ultraviolet/infrared (UV/IR) mixing: bosons that carry large momenta up to the UV cutoff actively suppress the Kondo screening at low energies.