Excitonic quantum criticality: from bilayer graphene to narrow Chern bands

TL;DR

This paper investigates excitonic quantum phase transitions in bilayer systems, revealing continuous transitions with unique non-Fermi liquid responses, applicable to graphene bilayers and narrow Chern bands in moiré materials.

Contribution

It introduces a controlled theoretical framework for excitonic quantum criticality, connecting bilayer graphene and narrow Chern bands, and predicts distinctive non-Fermi liquid counterflow behavior.

Findings

Continuous excitonic quantum phase transitions with non-Fermi liquid response.

Application to both graphene bilayers and narrow Chern bands in moiré materials.

Prediction of an exotic exciton insulator state with a charge neutral Fermi surface.

Abstract

We study a family of excitonic quantum phase transitions describing the evolution of a bilayer metallic state to an inter-layer coherent state where excitons condense. We argue that such transitions can be continuous and exhibit a non-Fermi liquid counterflow response ${\rho_{\mathrm{counterflow}}(\omega)\sim\omega^{2/z}}$ that directly encodes the dynamical critical exponent $z$. Our calculations are performed within a controlled expansion around $z = 2$. This physics is relevant to any system with spin, valley, or layer degrees of freedom. We consider two contexts for excitonic quantum criticality: (1) a weakly interacting graphene bilayer, and (2) a system of two narrow, half-filled Chern bands at zero external magnetic field, with total Chern number $C_{\mathrm{tot}}=0$, which may soon be realizable in moir\'{e} materials. The latter system hosts a time-reversed pair of composite Fermi liquid states, and the condensation of excitons of the composite fermions leads to an exotic exciton insulator* state with a charge neutral Fermi surface. Our work sheds new light on the physics of inter-layer coherence transitions in 2D materials.