Universal Theory of Incoherent Metals

TL;DR

This paper develops a microscopic model for incoherent metallic transport in unconventional superconductors, explaining phenomena beyond Fermi-liquid theory with non-perturbative methods.

Contribution

It introduces the two-dimensional Yukawa-SYK model to describe quantum-critical incoherent metals and their transport properties.

Findings

Provides a non-Boltzmann transport formula relating resistivity and quasi-particle lifetime.

Shows violation of the Mott-Ioffe-Regel resistivity bound.

Demonstrates violation of the Kovtun-Son-Starinets shear viscosity bound.

Abstract

Numerous unconventional superconductors such as cuprates, heavy-fermions, and twisted-bilayer graphene exhibit incoherent metallic transport above the superconducting critical temperature. This phenomenon cannot be described with Fermi-liquid theory and has presented a significant theoretical challenge to overcome. We utilize the two-dimensional Yukawa-SYK model of fermions with spatially random coupling to quantum-critical bosons to study transport in a manner which is non-perturbative in the coupling strength. Our work provides a microscopic model of quantum-critical incoherent metals and their concomitant properties, including a non-Boltzmann transport formula between resistivity and quasi-particle lifetime, violation of the Mott-Ioffe-Regel resistivity bound, and violation of the Kovtun-Son-Starinets shear viscosity to entropy density bound.