| quantum Hall effect | |
|---|---|
| Name | Quantum Hall effect |
| Caption | Schematic of Landau levels and edge states in a two-dimensional electron gas |
| Field | Condensed matter physics |
| Discovered | 1980s |
| Discoverer | Klaus von Klitzing (integer), Daniel C. Tsui and Horst L. Störmer (fractional) |
| Institutions | Max Planck Institute, Bell Labs, Princeton University, Columbia University |
quantum Hall effect
The quantum Hall effect is a set of quantum phenomena observed in two-dimensional electron systems subjected to low temperatures and strong perpendicular magnetic field. It manifests as quantized plateaus in the transverse (Hall) conductance and vanishing longitudinal resistance, revealing precise, robust integer or fractional values of the von Klitzing constant and elementary charge ratios. The effect is foundational in quantum mechanics and condensed matter physics for illustrating macroscopic quantum coherence, enabling precision metrology standards, and motivating the modern theory of topological order.
The effect arises from quantization of cyclotron orbits into discrete Landau levels and formation of one-dimensional chiral edge states at sample boundaries. The single-particle description by Landau quantization combines with disorder-driven localization to produce wide conductance plateaus; key theoretical ingredients include the quantum Hamiltonian of electrons in a magnetic field, gauge choices like the Landau gauge and the role of the Aharonov–Bohm effect. Electron–electron interactions introduce correlated many-body states described by trial wavefunctions such as the Laughlin wavefunction and field-theory approaches like Chern–Simons theory. Concepts from Berry phase, Berry curvature, and the TKNN invariant (Thouless–Kohmoto–Nightingale–den Nijs) relate the quantization to topological invariants.
The integer quantum Hall effect (IQHE), discovered by Klaus von Klitzing, can be explained largely by noninteracting electrons filling Landau levels; Hall conductance is quantized in units of e^2/h. The fractional quantum Hall effect (FQHE), discovered by Daniel Tsui and Horst Störmer with theoretical advances by Robert Laughlin, emerges from strong correlations producing quasiparticles with fractional charge and anyonic statistics. Subsequent theoretical and experimental work uncovered hierarchical states (Haldane–Halperin hierarchy), composite fermion theory by Jainendra Jain and non-Abelian candidate states like the Moore–Read state. Important figures and works include F. D. M. Haldane's insight into topological aspects and experiments at Bell Labs and leading university laboratories.
Realizations use high-mobility two-dimensional electron gases (2DEGs) in GaAs/AlGaAs heterostructures, graphene monolayers, and oxide interfaces like LaAlO3/SrTiO3. Typical experimental setup includes cryogenic systems (dilution refrigerators), high-magnetic-field facilities such as the National High Magnetic Field Laboratory and precise electronic instrumentation (lock-in amplifiers, low-noise amplifiers). Transport measurements record Hall and longitudinal resistivities via four-terminal techniques; scanning probe methods (scanning tunneling microscopy, scanning gate microscopy) and shot-noise experiments probe edge reconstruction and quasiparticle charge. Key experimental advances stem from groups at Columbia University, Harvard University, Princeton University, University of Cambridge, and industrial labs like IBM Research.
The integer quantum Hall effect underpins the realization of a resistance standard tied to fundamental constants; the von Klitzing constant R_K = h/e^2 provides an exact reference used by national metrology institutes such as NIST and the BIPM. Developments in graphene-based quantum Hall devices promise improved operating conditions. Beyond metrology, the FQHE's anyonic excitations offer routes toward fault-tolerant topological quantum computation; programs exploring non-Abelian anyons connect to efforts at companies and institutes pursuing quantum information, including Microsoft Research and university consortia. The effect also influences nanoelectronics, spintronics, and research into strongly correlated electron systems, with social implications for equitable access to measurement standards and technologies.
The quantum Hall effect inaugurated the role of topology in condensed matter, with the IQHE exemplifying a topological invariant (TKNN integer) immune to local perturbations. The FQHE introduced topological order as a new class of quantum phases beyond symmetry-breaking paradigms described by Landau theory. Mathematical structures invoked include Chern number, modular tensor categorys for anyon fusion rules, and effective field theories like Chern–Simons gauge theory. Connections extend to topological insulators and quantum anomalous Hall effect, and to theoretical frameworks advanced by researchers such as Xiao-Gang Wen, Shou-Cheng Zhang, and A. H. MacDonald. The interplay of topology, interactions, and disorder remains active research fertile ground with implications for material justice—prioritizing open access, diversity in research participation, and equitable distribution of technology stemming from these discoveries.
Category:Condensed matter physics Category:Quantum mechanics Category:Topological phases of matter