Universal electrical transport of composite Fermi liquid to Metal transition in Moir\'e systems

TL;DR

This paper develops a universal theoretical framework for electrical transport near continuous phase transitions between a composite Fermi liquid and a metal in moire systems, predicting specific conductivities and scaling behaviors.

Contribution

It introduces a novel QED-Chern-Simons critical theory and a controlled large-N expansion to compute universal transport properties at the transition.

Findings

Derived explicit resistivity tensor composition rule.

Calculated finite DC conductivities at criticality.

Identified a Chern-Simons filtering mechanism affecting Landau damping.

Abstract

We compute universal electrical transport near continuous transitions between a composite Fermi liquid (CFL) and a metallic phase in moire Chern bands, focusing on fillings $\nu=-1/2$ and $\nu=-3/4$. The critical theory represents a novel QED-Chern-Simons framework: a charged sector at a bosonic Laughlin-superfluid critical point is coupled, via emergent gauge fields and Chern-Simons mixing, to a neutral spinon Fermi surface. Integrating out matter fields to quadratic order yields an explicit Ioffe-Larkin composition rule for the full resistivity tensor, showing how longitudinal channels add in series while Chern-Simons terms generate Hall response. To obtain the DC limit in the quantum critical fan, we develop a controlled large-N expansion where both fermion flavors and Chern-Simons levels scale with $N$, and solve a quantum Boltzmann equation at leading nontrivial order $1/N$. Gauge-mediated inelastic scattering removes the collisionless Drude singularity and produces a universal scaling function $\Sigma(\omega/T)$ and finite DC conductivities $\sigma(0) \approx 0.033 e^2/\hbar$ ($\nu=-1/2$) and $0.047 e^2/\hbar$ ($\nu=-3/4$). We also identify a Chern-Simons "filtering" mechanism that suppresses transmission of Landau damping from the spinon Fermi surface to the critical gauge mode. Our approach provides concrete transport diagnostics for detecting quantum criticality in moire superlattices.