Fractional quantum Hall effect
Strongly interacting electrons can form incompressible liquids with fractionally charged excitations.
$$\nu=\frac{1}{m}\quad(m\ \text{odd for fermionic Laughlin states})$$
What this means
Strongly interacting electrons can form incompressible liquids with fractionally charged excitations.
Deep dive: mathematical and physical mechanism
At filling $\nu=1/m$, the Laughlin wavefunction is $\Psi_m=\prod_{i Fractional Hall states in high-mobility two-dimensional electron gases. For context, see the Interacting Topological Phases topic guide and the reading references.How it appears in quantum phenomena
Assumptions, caveats and limitations
Fractional filling does not automatically imply a Laughlin phase; interactions and sample conditions matter.Connect the ideas