Hidden weak-pairing superconductivity of non-interacting anyons obeying $\frac{1}{3}$ statistics

TL;DR

This paper demonstrates that a non-interacting gas of charge-$e/3$ anyons with specific exchange statistics can become superconducting through a hidden weak-pairing mechanism, connecting fractional Chern insulators to unconventional superconductivity.

Contribution

It introduces a flux-attachment construction mapping the problem to composite fermions, revealing a novel weak-pairing superconducting phase driven by anyon statistics.

Findings

The anyon gas can superconduct via a hidden weak-pairing mechanism.

The resulting superconductor has a chiral edge with central charge $c_-=-1/2$.

The theory explains recent experimental observations near fractional Chern insulators.

Abstract

We show that a non-interacting gas of charge-$e/3$ anyons with exchange statistics $\theta=-\pi/3$ can superconduct through a hidden weak-pairing mechanism. Such an anyon gas arises naturally in doped fractional Chern insulators at filling $1/3$ or $2/3$, where projective lattice translations enforce three degenerate anyon pockets. Exploiting this three-pocket structure, we develop a flux-attachment construction in which the average statistical flux vanishes, thereby mapping the problem to three species of composite fermions (CFs) in zero effective magnetic field. We show that the anyon statistics itself, encoded in statistical gauge field fluctuations, supplies the pairing glue and drives the CFs into a $p-\mathrm{i}p$ paired state, which corresponds to a $f-\mathrm{i}f$ physical superconductor. The CF strong-pairing phase is adiabatically connected to Laughlin's picture of anyon superconductivity, where charge-$e/3$ anyons bind into charge-$2e/3$ molecules, which then lead to superconductivity. By contrast, the more natural weak-pairing phase of CFs realizes a distinct superconducting phase - its edge is characterized by a chiral central charge $c_-=-1/2$, in contrast to the prediction of integer $c_-$ for the anyon superconductor based on Laughlin's picture, thereby resolving the discrepancy between previous theories and recent numerical results. Our theory provides a natural framework for understanding superconductivity near fractional Chern insulators, as observed in recent experiments. Finally, we discuss extensions of our theory that predict new chiral superconductors adjacent to FCIs at other fillings.