Universal Transport at Lifshitz Metal-Insulator Transitions in Two Dimensions

We study the charge transport across a band-tuned metal-insulator transition in two dimensions. For high temperatures T and chemical potentials μ 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 semiclassical behavior and study the quantum regime beyond, where scaling breaks down. We analytically evaluate the simplest Feynman diagram of the linear-response conductivity σ=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} moiré 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 (μ=T=0) has the universal value, R_{L}=(2πh)/e^{2}, per degree of freedom, in congruence 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 come up with an, in principle, complete assignment of the transition mechanism.