Fractionally charged Laughlin quasihole 2026-10-18
A quasihole adds one zero at per Electron; its local deficit carries positive electric charge .[ref]
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations by Robert Laughlin. pp. 1396–1397, Eqs. (13), (15) and screening argument
Here is a transport counting outline, conditional on an incompressible quantum Hall fluid. Inserting one magnetic flux quantum slowly compared with , where is the excitation energy gap, produces a circulating electric field by Faraday's law. The transverse sheet conductivity sends a radial electric current whose time integral has magnitudeThe opposite electric charge moves to the boundary, so the total electric charge remains conserved. The counted deficit belongs to a collective quasiparticle; no individual Electron has been cut into pieces. The argument assumes the gapped fluid and its Hall response, and is not a consequence of the finite two-Electron normalization integral.
Incompressible quantum Hall fluid 2026-10-18
An incompressible quantum Hall fluid has a bulk spectral gap against charged excitations; disorder can localize excess quasiparticles.[ref]
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations by Robert Laughlin. pp. 1397–1398, incompressibility and impurity localization