https://scholarlywiki.org/index.php?action=history&feed=atom&title=Physics%3AQuantum_fractional_Hall_effectPhysics:Quantum fractional Hall effect - Revision history2026-05-22T20:04:28ZRevision history for this page on the wikiMediaWiki 1.44.5https://scholarlywiki.org/index.php?title=Physics:Quantum_fractional_Hall_effect&diff=8883&oldid=prevMaintenance script: Add Quantum fractional Hall effect page2026-05-22T17:33:05Z<p>Add Quantum fractional Hall effect page</p>
<p><b>New page</b></p><div>{{Short description|Fractional quantization of Hall conductance in two-dimensional electron systems}}<br />
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|text='''Fractional Hall effect''' is a ScholarlyWiki page in the Quantum Collection about fractionally quantized Hall conductance, correlated electron states, and emergent quasiparticles in two-dimensional systems.<br />
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== Overview ==<br />
The '''fractional Hall effect''' is a collective quantum phenomenon observed in very clean two-dimensional electron systems placed in a strong perpendicular magnetic field at low temperature. In this regime the Hall conductance forms plateaus at fractional values of <math>e^2/h</math>, rather than only at integer values.<br />
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The effect is a landmark example of strongly correlated quantum matter. It cannot be explained by treating electrons as independent particles filling single-particle Landau levels. Instead, interactions between electrons produce new many-body states with unusual excitations, including fractionally charged quasiparticles and anyonic exchange statistics.<br />
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== Key ideas ==<br />
In the ordinary Hall effect, a transverse voltage appears when charge carriers move through a magnetic field. In the integer quantum Hall effect, the conductance is quantized because the electron motion is organized into [[Physics:Quantum Landau levels|Landau levels]]. The fractional Hall effect appears when a Landau level is only partially filled and electron-electron interactions dominate the physics.<br />
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The filling factor is commonly written as<br />
<br />
<math display="block"><br />
\nu = \frac{n h}{eB},<br />
</math><br />
<br />
where <math>n</math> is the two-dimensional electron density and <math>B</math> is the magnetic field. Fractional Hall plateaus occur at values such as <math>\nu=1/3</math>, <math>2/5</math>, and many related fractions.<br />
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== Laughlin states ==<br />
Robert Laughlin proposed a many-body wavefunction that explains the simplest fractional plateaus, especially <math>\nu=1/3</math>. The Laughlin state captures how electrons avoid one another while remaining in the lowest Landau level. This correlation lowers interaction energy and produces an incompressible quantum fluid.<br />
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The associated quasiparticle excitations can carry a fraction of the electron charge. For the <math>\nu=1/3</math> Laughlin state, the elementary quasiparticle charge is <math>e/3</math> in magnitude. These fractional charges have been probed experimentally through shot-noise and interferometry measurements.<br />
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== Composite fermions ==<br />
Many observed fractions are described by the composite-fermion picture. In this approach, an electron moving in a strong magnetic field is treated as binding an even number of magnetic flux quanta, forming an emergent composite particle. Composite fermions experience a reduced effective magnetic field and can fill effective Landau levels.<br />
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This idea organizes prominent sequences of fractions, such as<br />
<br />
<math display="block"><br />
\nu = \frac{p}{2p \pm 1},<br />
</math><br />
<br />
where <math>p</math> is an integer. The composite-fermion framework connects the fractional Hall effect to an effective integer quantum Hall effect of emergent quasiparticles.<br />
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== Topological order ==<br />
Fractional Hall states are examples of [[Physics:Quantum Topological phases of matter|topological phases of matter]]. Their essential properties are not described by a local order parameter in the usual symmetry-breaking sense. Instead, they show topological order, robust edge modes, ground-state degeneracy on nontrivial geometries, and quasiparticle statistics that depend on braiding.<br />
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Some fractional Hall states support Abelian anyons, while more exotic candidates may support non-Abelian anyons. These possibilities connect the fractional Hall effect with [[Physics:Quantum anyon|anyons]], topological quantum matter, and proposals for fault-tolerant quantum information processing.<br />
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== Physical setting ==<br />
The effect is typically observed in high-mobility semiconductor heterostructures or other two-dimensional materials where disorder is low enough for interaction-driven states to form. Low temperatures reduce thermal smearing, and strong magnetic fields separate the Landau levels.<br />
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Although the basic measurements are transport measurements, the physics is deeply many-body. Edge channels carry current along the boundary, while the bulk remains incompressible at a plateau. Deviations from the plateau reveal quasiparticle excitations, disorder effects, and transitions between quantum Hall states.<br />
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== See also ==<br />
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}<br />
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== References ==<br />
{{reflist|3}}<br />
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* {{Cite journal |last1=Tsui |first1=D. C. |last2=Stormer |first2=H. L. |last3=Gossard |first3=A. C. |title=Two-Dimensional Magnetotransport in the Extreme Quantum Limit |journal=Physical Review Letters |volume=48 |issue=22 |pages=1559-1562 |year=1982 |doi=10.1103/PhysRevLett.48.1559}}<br />
* {{Cite journal |last1=Laughlin |first1=R. B. |title=Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations |journal=Physical Review Letters |volume=50 |issue=18 |pages=1395-1398 |year=1983 |doi=10.1103/PhysRevLett.50.1395}}<br />
* {{Cite journal |last1=Jain |first1=J. K. |title=Composite-fermion approach for the fractional quantum Hall effect |journal=Physical Review Letters |volume=63 |issue=2 |pages=199-202 |year=1989 |doi=10.1103/PhysRevLett.63.199}}<br />
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{{Author|Harold Foppele}}<br />
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