Universal transport at Lifshitz metal-insulator transitions in two dimensions

TL;DR

This paper investigates charge transport near Lifshitz metal-insulator transitions in two dimensions, deriving an analytical formula for conductivity, confirming experimental results, and predicting a universal resistance value at the quantum-critical point.

Contribution

It introduces an analytical formula for conductivity in 2D systems near Lifshitz transitions, explaining quantum effects and proposing a universal resistance at the critical point.

Findings

Analytical formula matches experimental data for MoTe2/WSe2 bilayers.

Quantum effects break classical scaling relations.

Universal resistance value at the Lifshitz critical point is consistent with experiments.

Abstract

We study the charge transport across a band-tuned metal-insulator transition in two dimensions. For high temperatures $T$ and chemical potentials $\mu$ far from the transition point, conduction is ballistic and the resistance $R(T)$ verifies a simple one-parameter scaling relation. Here, we explore the limits of this semi-classical behaviour and study the quantum regime beyond, where scaling breaks down. We derive an analytical formula for the simplest Feynman diagram of the linear-response conductivity $\sigma=1/R$ of a parabolic band endowed with a finite lifetime. Our formula shows excellent agreement for experiments for a field-tuned MoTe$_2$/WSe$_2$ moir\'e bilayer, and can capture the quantum effects responsible for breaking the one-parameter scaling. We go on to discuss a fascinating prediction of our model: The resistance at the quantum-critical band-tuned Lifshitz point ($\mu=T=0$) has the universal value, $R_L=(2 \pi h)/e^2$, per degree of freedom and this value is found to be compatible with experiment. Furthermore, we investigate whether two dimensional metal-insulator transitions driven by strong electron correlations or disorder can also be classified by their quantum-critical resistance and find that $R_L$ may be useful in identifying predominantly interaction driven transitions.