Universal electrical transport of composite Fermi liquid to Metal transition in Moiré systems

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 $ν=-1/2$ and $ν=-3/4$. 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 $Σ(ω/T)$ and finite DC conductivities $σ(0) \approx 0.033 e^2/\hbar$ ($ν=-1/2$) and $0.047 e^2/\hbar$ ($ν=-3/4$). 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.

Figures (5)

• Figure 1: (Adapted from Ref. PhaseTransitionsOutsong2024)The resistivity as a function of temperature. The blue curves are for the FL, the black for the CFL, and the red for the quantum critical points. We compute the universal jump $r_{xx}, r_{xy}$ in the quantum critical regime($T\sim 0$), which are of order $h/e^2$.
• Figure 2: The leading terms of 1-loop diagram where straight line is Dirac $\psi$ Fermion and wavy line is gauge $b$ boson. Wavy lines represent gauge propagator while solid lines represent free propagator of Dirac fermions. Diagram (a) is of order $N$ since each flavor can form a loop, while diagram (b) is of order $N^{-1}$ and thus suppressed
• Figure 3: Real part of the scaling function $\Sigma(\omega/T)$ of $\nu=-1/2$ case.
• Figure 4: Real part of the scaling function of $\nu = -3/4$ case.
• Figure 5: Density plot of $-\mathrm{Im}[1/\Psi_T(\Omega,q)]$.