CMTopic

Fractional Chern insulators beyond Landau levels

Fractional Chern insulators are states in a crystal where electrons act together as particles carrying a fraction of the electron charge, as in the fractional quantum Hall effect, but produced by band topology instead of a strong magnetic field.

Why it matters

They could bring anyons to zero field and higher temperatures, and they test which electron bands support fractional charge.

Review

Z. Liu, E. J. Bergholtz, Recent developments in fractional Chern insulators, arXiv:2208.08449, 2022. https://arxiv.org/abs/2208.08449 reference checked

Proof

Signed record: 99dc6b2de04e…
Public log: Entry 136, in checkpoint 2,123
Bitcoin date: Block 969,698, 2026-10-03

Download proof How this works

3 problems

Direct detection of fractional charge in zero-field fractional states
Open

Quasiparticles in these fractional states should carry one third of an electron's charge, but in the zero-field states found since 2023 this has been inferred only indirectly.
Superconductivity from doping a fractional Chern insulator
Open

Adding a few extra electrons to a fractional state may produce a superconductor whose carriers are anyons, and the superconductivity seen next to fractional states in twisted MoTe2 could be the first example.
Band-geometry criterion for fractional Chern insulator stability
Partially resolved

Theory says a band that closely mimics a Landau level favours fractional states, but nobody can yet predict from a band's properties alone whether a real material will form a fractional state or an electron crystal.

Fractional Chern insulators beyond Landau levels

Why it matters

Review

Proof

3 problems

Direct detection of fractional charge in zero-field fractional states

Superconductivity from doping a fractional Chern insulator

Band-geometry criterion for fractional Chern insulator stability