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Incoming links: Quantum Hall effect
Andre Geim, Konstantin Novoselov and collaborators mechanically cleaved graphite, identified thin flakes, and fabricated multi-terminal Hall bars on oxidized silicon. A substrate gate changed the carrier density; longitudinal electrical resistance and the Hall coefficient supplied different checks. The 2004 report included one-, two- and three-layer devices and described a few-layer semimetal interpretation. Layer identification and electrical control were separate experimental achievements.[ref]
Electric Field Effect in Atomically Thin Carbon Films by Konstantin Novoselov and others. pp.1–2 and Figs.1–2: preparation, thickness selection and electrical measurements
The 2005 monolayer study used an optical microscope, electron microscopy and atomic force microscopy to select monolayers. It then measured Shubnikov-de Haas oscillations as temperature, gate voltage and magnetic field varied. Their damping inferred a density-dependent cyclotron effective mass; comparison with oscillation frequency tested a linear dispersion relation. A comparison with two-layer devices also distinguished their quantum Hall effect sequences. These are complementary tests of the monolayer model, rather than consequences of finding a thin-looking flake alone.[ref]
Two-Dimensional Gas of Massless Dirac Fermions in Graphene by Konstantin Novoselov and others. pp.1–3, Figs.2–4: monolayer selection, oscillation damping and bilayer comparison
Longitudinal resistance in a Hall bar 2026-10-18
Voltage contacts separated along the current direction measure longitudinal resistance, even when the device is called a Hall bar. For an approximately uniform rectangular strip, . Transverse contacts measure instead. Shubnikov-de Haas effect oscillations in need not be Hall-resistance plateaus; in the integer quantum Hall effect, longitudinal minima accompany quantized transverse plateaus.
Nobel Prize in Physics in 1985 2026-10-18
Awarded to Klaus von Klitzing for discovering the quantum Hall effect.[ref]
The Nobel Prize in Physics 1985 by Nobel Prize Outreach. Individual official 1985 summary: sole laureate, quantized Hall-effect discovery.
Quantum Hall effect 2026-10-18
The quantum Hall effect connects an electrical measurement to a quantum counting rule: a two-dimensional electron gas in a perpendicular magnetic field can exhibit plateaus of transverse electrical resistance. The integer case supplies a resistance scale built from the Planck constant and elementary charge, rather than the sample's dimensions. The fractional quantum Hall effect involves additional many-Electron physics.