The Antiferromagnetic Quantum Critical Metal: A nonperturbative approach

Abstract

The superconductivity in heavy-fermion compounds, iron pnictides and cuprates has been intensively studied for over thirty years. Amongst some of these materials, the common denominator is the presence of strong antiferromagnetic fluctuations in their normal state, signaling an underlying quantum phase transition between a paramagnetic metal and a metal with antiferromagnetic long-range order. Although the quantum critical point is experimentally inaccessible due to the presence of superconducting order, it determines the physical properties of the normal state of the metal in a wide range of temperatures. In this thesis we study the low-energy theory for the critical metallic state that arises at the aforementioned quantum critical point. We present a nonperturbative study of the theory in spatial dimensions between two and three. We pay special attention to two dimensions where we show that our physical predictions are in qualitative agreement with experiments in electron-doped cuprates. We further develop a field theoretic functional renormalization group scheme that is analytically tractable. It provides a general framework to study the low-energy theory of metallic states with or without a quasiparticle description. Within this formalism we characterize the single-particle properties of the antiferromagnetic quantum critical metal. This allows one to study the superconducting instability triggered by critical antiferromagnetic quantum fluctuations quantitatively.