Mechanism of skyrmion condensation and pairing for twisted bi-layer graphene

TL;DR

This paper explores how skyrmion condensation in quantum flavor Hall insulators can induce various forms of superconductivity, including charge 2e and 4e states, with implications for twisted bilayer graphene.

Contribution

It introduces a mechanism linking skyrmion condensation and pairing via Weyl fermion interactions and flavor Hall conductivity, revealing new superconducting phases.

Findings

Flavor Hall conductivity controls zero-mode degeneracy.

Different flavor Hall insulators lead to distinct superconducting states.

Implications for charge 2e and 4e superconductivity in twisted bilayer graphene.

Abstract

When quantum flavor Hall insulator phases of itinerant fermions are disordered by strong quantum fluctuations, the condensation of skyrmion textures of order parameter fields can lead to superconductivity. In this work, we address the mechanism of skyrmion condensation by considering the scattering between (2+1)-dimensional, Weyl fermions and hedgehog type tunneling configurations of order parameters that violate the skyrmion-number conservation law. We show the quantized, flavor Hall conductivity ($\sigma^f_{xy}$) controls the degeneracy of topologically protected, fermion zero-modes, localized on hedgehogs, and the overlap between zero-mode eigenfunctions or 't Hooft vertex determines the nature of pairing. We demonstrate the quantum-disordered, flavor Hall insulators with $\sigma^f_{xy}= 2 N$ lead to different types of charge $2 N e^-$ superconductivity. Some implications for the competition among flavor Hall insulators, the charge $2e^-$ paired states in BCS and pair-density-wave channels, and the composite, charge $4e^-$ superconductors for twisted bilayer graphene are outlined.