Attractive Haldane bilayers for trapping non-Abelian anyons

Abstract

We study the interplay between intrinsic topological order and superconductivity in a two-component Haldane bilayer, where the two layers are coupled by an attractive force. We obtain the phase diagram of the model with exact diagonalization in finite size, and develop arguments to assess the stability of the observed phases in the thermodynamic limit. Our main result is that a finite critical attraction strength is needed to pair fermions forming a fractional topological order. This behavior can be harnessed to create clean interfaces between a fractional topological insulator and a superconductor by gating, wherein non-Abelian parafermionic modes are trapped. We discuss realization of such interfaces in the bulk of double bilayers of transition metal dichalcogenides by inhomogenous electrostatic gating, which should mitigate the spurious effects of disorder and crystalline defects present on physical edges.

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Cited by in corpus (9)

• Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers
• Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Twist-angle evolution of the intervalley-coherent antiferromagnet in twisted WSe${}_2$
• Theory of intervalley-coherent AFM order and topological superconductivity in tWSe${}_2$
• Topologically protected flatness in chiral moiré heterostructures
• Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• Efficient prediction of topological superlattice bands with spin-orbit coupling
• Tuning between a fractional topological insulator and competing phases at ${\nu }_{\mathrm{T}}=2/3$