| quantum Hall effect | |
|---|---|
| Name | Quantum Hall effect |
| Caption | Schematic of a two-dimensional electron gas in a magnetic field showing edge states |
| Field | Condensed matter physics |
| Discovered | 1980 |
| Discoverer | Klaus von Klitzing |
| Institutions | IBM, Max Planck Society |
| Related | topological insulator, fractional statistics |
quantum Hall effect
The quantum Hall effect is a quantum phenomenon in two-dimensional electron systems subject to low temperatures and strong perpendicular magnetic fields, where the transverse Hall conductance becomes quantized in units of e^2/h. It reveals topological aspects of electronic states and has profound implications for precision metrology, condensed matter physics, and the study of strongly correlated quantum phases.
The quantum Hall effect was first observed by Klaus von Klitzing in 1980 while working at an IBM research laboratory, who measured exact plateaus in the Hall resistance of a two-dimensional electron gas (2DEG) formed in a GaAs/AlGaAs heterostructure at cryogenic temperatures and high magnetic fields. This observation led to the identification of the Integer quantum Hall effect and earned von Klitzing the Nobel Prize in Physics in 1985. Later, in 1982, experimental discovery of the Fractional quantum Hall effect by Daniel Tsui and Horst Störmer (with theoretical interpretation by Robert Laughlin) revealed electron correlation effects and led to further Nobel recognition in 1998. The phenomenon bridges experimental techniques developed at institutions such as Bell Labs and Bell Telephone Laboratories with theoretical advances from Princeton University, MIT, and the Institute for Advanced Study.
The Integer quantum Hall effect (IQHE) occurs when noninteracting or weakly interacting electrons in a 2DEG occupy discrete Landau levels produced by a perpendicular magnetic field. The Hall conductance σ_xy is quantized as n e^2/h, where n is an integer linked to filled Landau levels and to a topological invariant known as the Chern number in the Berry phase formalism. The robustness of plateaus against disorder is explained by localization theory and by chiral edge state transport described in approaches related to the Landauer–Büttiker formalism. IQHE experiments often use high-mobility heterostructures grown by molecular beam epitaxy at facilities like Bell Labs and measurement standards traceable to the International System of Units.
The Fractional quantum Hall effect (FQHE) emerges when strong Coulomb interactions drive electrons into correlated many-body states at fractional filling factors (e.g., 1/3, 2/5). Robert Laughlin proposed a variational many-body wavefunction (the Laughlin wavefunction) that captures the 1/3 state and explains quasiparticles carrying fractional charge and fractional statistics (anyons). Subsequent theoretical constructs include the composite fermion picture by Jainendra Jain and hierarchical schemes by Haldane and others. Experimental signatures include fractional plateaus in σ_xy and quasiparticle charge detected by shot noise experiments at institutions such as CERN and specialized low-temperature labs.
The quantum Hall effect is understood through a combination of single-particle and many-body theories. Key frameworks include Landau quantization, topological band theory (e.g., Chern insulators), and field-theoretic descriptions using Chern–Simons theory that encode braiding statistics of excitations. The role of topology connects to topological order and the concept of protected edge states via the bulk–boundary correspondence. Exactly solvable models, numerical methods such as exact diagonalization and density-matrix renormalization group (DMRG), and conformal field theory (CFT) techniques are applied to study FQHE states, non-Abelian anyons (proposed in the Moore–Read Pfaffian state), and possible realizations for topological quantum computation.
Experiments require high-quality 2DEGs or graphene devices, strong magnetic fields from superconducting magnets or pulsed-field facilities, and temperatures often below 1 K achieved with dilution refrigerators. Fabrication methods include molecular beam epitaxy and lithography to make Hall bars and mesoscopic devices. Observables comprise quantized Hall resistance, longitudinal resistance minima, activation energy gaps, magneto-transport oscillations (Shubnikov–de Haas), and tunneling spectroscopy. Advanced techniques—scanning probe microscopy, shot noise measurement for fractional charge, and interferometry for anyon statistics—have been pursued at centers like University of Cambridge, Columbia University, Yale University, and national labs.
The quantum Hall effect underpins resistance metrology: the quantized Hall resistance defines a reproducible standard of resistance linked to fundamental constants e and h, adopted by metrology institutes such as the International Bureau of Weights and Measures (BIPM). Beyond standards, research into non-Abelian FQHE states informs proposals for fault-tolerant quantum computation using anyonic braiding. Realizations in materials such as graphene and engineered systems (cold atoms, photonic crystals) expand technological prospects for low-dissipation interconnects and devices leveraging topological protection.
The quantum Hall effect sits at the intersection of quantum mechanics, many-body physics, and topology. It exemplifies quantization emergent from global properties of quantum states (Chern numbers, Berry curvature) rather than local order parameters, influencing the development of topological insulator theory and research on quantum spin Hall effect and fractional statistics. The interplay of disorder, interactions, and topology in the quantum Hall regime continues to inform studies in strongly correlated systems, quantum criticality, and proposals for implementing exotic quasiparticles in platforms pursued by groups at Microsoft Research, IBM Research, and leading university laboratories.
Category:Condensed matter physics Category:Quantum phenomena