Mechanism of skyrmion condensation and pairing for twisted bilayer graphene

Dian Jing, Alexander Conkey Tyner, Pallab Goswami

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 (σxyf) controls the degeneracy of topologically protected, fermion zero-modes, localized on hedgehogs. The overlap between zero-mode eigenfunctions or 't Hooft vertex is shown to control the nature of the paired states. Employing this formalism for the N=2 model of twisted bilayer graphene, we describe the competition among flavor Hall orders, charge 4e- superconductivity, and various charge 2e- paired states in BCS and paired-density-wave channels. At charge neutrality, we show that the competition between flavor Hall insulators and charge 2e- states can be captured by SO(9) nonlinear sigma models. If the topological pairing mechanism can dominate over the conventional pairing mechanism, our work predicts the flavor-symmetry-preserving charge 4e- superconductivity as a natural candidate for the paired state in the vicinity of the charge neutral point.

Original languageEnglish (US)
Article number184505
JournalPhysical Review B
Issue number18
StatePublished - May 1 2022

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


Dive into the research topics of 'Mechanism of skyrmion condensation and pairing for twisted bilayer graphene'. Together they form a unique fingerprint.

Cite this