Manipulating anyons through gate and environment engineering

Motivated by recent experimental advances demonstrating clean interfaces between distinct topological orders via inhomogeneous gating [1], and between superconductors and fractional topological phases through metallization [2], I will discuss how gate and environment engineering can be used to trap and manipulate anyons. To illustrate these ideas concretely, I first introduce and analyze a two-component Haldane bilayer model with interlayer attraction. Finite-size studies and extrapolation to the thermodynamic limit reveal that a critical attraction strength is required to pair fermions into a fractional topological order [3]. This mechanism enables the creation of clean interfaces between a fractional topological insulator and a superconductor, where non-Abelian parafermionic modes can be localized. I will discuss how such interfaces can be realized in the bulk of double bilayers of transition metal dichalcogenides using inhomogeneous electrostatic gating, which avoids the disorder and crystalline defects typically present at physical edges. Finally, I will describe strategies to manipulate the anyons trapped at these interfaces and, time permitting, outline prospects for observing their braiding.

[1] Ji, Z., Park, H., Barber, M. E., Hu, C., ... & Shen, Z. X. (2024). Local probe of bulk and edge states in a fractional Chern insulator. Nature, 635(8039), 578-583.

[2] Jia, Y., Yu, G., Song, T., Yuan, ... & Wu, S. (2024). Superconductivity from on-chip metallization on 2D topological chalcogenides. Physical Review X, 14(2), 021051.

[3] Crépel, V., & Regnault, N. (2024). Attractive Haldane bilayers for trapping non-Abelian anyons. Physical Review B, 110(11), 115109.