Vortex Fermi Liquid and Strongly Correlated Quantum Bad Metal

TL;DR

This paper explores a new theoretical framework for strongly correlated bad metals that exceed the Mott-Ioffe-Regal limit, using a vortex-based dual description to explain their large resistivity and emergent charge dynamics.

Contribution

It introduces a vortex fermion model for strongly correlated bad metals, providing a dual perspective beyond quasiparticle descriptions and explaining large resistivity and doping effects.

Findings

Resistivity can be exceptionally large at zero temperature.

Doping introduces a small Drude weight proportional to the square of doping level.

The vortex fermion model captures key features of strongly correlated bad metals.

Abstract

The semiclassical description of two-dimensional ($2d$) metals based on the quasiparticle picture suggests that there is a universal threshold of the resistivity: the resistivity of a $2d$ metal is bounded by the so called Mott-Ioffe-Regal (MIR) limit, which is at the order of $h/e^2$. If a system remains metallic while its resistivity is beyond the MIR limit, it is referred to as a "bad metal", which challenges our theoretical understanding as the very notion of quasiparticles is invalidated. The description of the system becomes even more challenging when there is also strong correlation between the electrons. Partly motivated by the recent experiment on transition metal dichalcogenides moir\'{e} heterostructure, we seek for understanding of strongly correlated bad metals whose resistivity far exceeds the MIR limit. For some strongly correlated bad metals, though a microscopic description based on electron quasiparticles fails, a tractable dual description based on the "vortex of charge" is still possible. We construct a concrete example of such strongly correlated bad metals where vortices are fermions with a Fermi surface, and we demonstrate that its resistivity can be exceptionally large at zero temperature. And when extra charge $\delta n_e$ is doped into the system away from half-filling, a small Drude weight proportional to $(\delta n_e)^2$ will emerge in the optical conductivity .