quantum Hall effect

quantum Hall effect
Name	quantum Hall effect
Discoverer	Klaus von Klitzing
Year	1980
Field	Condensed matter physics

quantum Hall effect is a quantum phenomenon observed in two-dimensional electron systems subjected to low temperatures and strong perpendicular magnetic fields, producing quantized plateaus in transverse (Hall) conductance and vanishing longitudinal resistance. First revealed experimentally by Klaus von Klitzing in 1980 and further extended by discoveries attributed to Robert Laughlin and others, the effect links topology, many-body physics, and metrology through precise values tied to fundamental constants. Research into the effect has engaged institutions such as Bell Labs, IBM, Max Planck Society, and collaborations at facilities like CERN and national laboratories.

Introduction

The discovery by Klaus von Klitzing at an International Conference on the Physics of Semiconductors experiment using a silicon MOSFET led to a Nobel Prize in 1985 and sparked investigations at centers including Bell Labs, IBM Thomas J. Watson Research Center, and University of Manchester. The phenomenon occurs in heterostructures such as GaAs/AlGaAs interfaces and in two-dimensional materials like graphene and MoS2, often realized in devices fabricated at Bell Labs or university cleanrooms associated with MIT and Stanford University. Measurements require cryogenic environments provided by apparatus from Oxford Instruments and Bluefors and high magnetic fields generated by facilities such as the National High Magnetic Field Laboratory. The quantization observed—linking to the von Klitzing constant—made the effect central to discussions at standards organizations including the International Bureau of Weights and Measures.

Integer quantum Hall effect

The integer quantum Hall effect (IQHE) was explained using noninteracting electron models and concepts from the Landau level spectrum introduced in early work by Lev Landau and observed in semiconductor heterostructures by experimentalists at Bell Labs and academic groups at Harvard University and Princeton University. Plateaus occur at transverse conductance values equal to integer multiples of e^2/h, a relation that became important in debates at the International Committee for Weights and Measures and in precision metrology labs such as Physikalisch-Technische Bundesanstalt. Theoretical descriptions drew on ideas from David Thouless and collaborators, connecting quantization to topological invariants described in papers from groups at University of Cambridge and Rutgers University. Measurements of IQHE informed research at National Institute of Standards and Technology and spurred further experiments at Bell Labs and IBM Research.

Fractional quantum Hall effect

The fractional quantum Hall effect (FQHE) was discovered in 1982 in experiments by Horst L. Störmer and Daniel C. Tsui at Bell Labs, leading to a Nobel Prize in 1998 shared with Robert Laughlin, who proposed a many-body wavefunction to explain observed fractionalization. The FQHE manifests at fractional values of transverse conductance and introduces quasi-particles with fractional charge and fractional statistics, concepts elaborated in theoretical work from groups at Princeton University, University of California, Berkeley, and Yale University. Studies in materials like GaAs heterostructures and in fractional Chern insulator realizations by groups at ETH Zurich and Caltech connected the FQHE to research on anyons pertinent to proposals by Alexei Kitaev and experimental efforts at Microsoft Research and Delft University of Technology. The FQHE links to early topology work by Michael Berry and to conformal field theory developments by researchers at Imperial College London and University of California, Santa Barbara.

Experimental techniques and observations

Experiments employ low-temperature cryostats at institutions such as Kavli Institute for Theoretical Physics and Laboratory for Physical Sciences, using dilution refrigerators and superconducting magnets from vendors like Oxford Instruments and labs including National High Magnetic Field Laboratory and Los Alamos National Laboratory. Sample fabrication leverages molecular beam epitaxy methods developed at Bell Labs and IBM Research and lithography facilities at Sandia National Laboratories and Argonne National Laboratory. Transport measurements use lock-in amplifiers and electronics from companies tied to research at MIT Lincoln Laboratory and Brookhaven National Laboratory, while scanning probe techniques developed at IBM Almaden Research Center and IBM Research provide local probes. Optical probes, terahertz spectroscopy, and microwave techniques used by groups at Max Planck Institute for Solid State Research and University of Tokyo complement magnetotransport, with experiments reported in journals associated with American Physical Society and Nature Publishing Group.

Theoretical frameworks and models

Frameworks include Landau quantization by Lev Landau, topological band theory advanced by researchers at University of Washington and University of Chicago, and many-body approaches by Robert Laughlin and collaborators. The Chern number formalism introduced in mathematical physics by work related to Atiyah–Singer index theorem and developed by groups at Imperial College London and University of Oxford links to topological phases studied at Microsoft Research and Perimeter Institute for Theoretical Physics. Composite fermion theory originated in research at Princeton University and Harvard University, while numerical methods from Los Alamos National Laboratory and Lawrence Berkeley National Laboratory enabled exact diagonalization and density matrix renormalization group studies. Field-theoretic descriptions draw on path-integral techniques used at Institute for Advanced Study and conformal field theory frameworks pursued at California Institute of Technology.

Applications and technological implications

The precision of the effect underpins resistance standards maintained by National Physical Laboratory and Physikalisch-Technische Bundesanstalt, influencing metrology work at International Bureau of Weights and Measures. Potential applications include topological quantum computing inspired by proposals from Alexei Kitaev and pursued in part at Microsoft Research, Delft University of Technology, and start-ups linked to QuTech. Spintronics and low-dissipation electronics explored at Samsung Advanced Institute of Technology and Intel Labs draw on principles related to edge-state transport studied at Nokia Bell Labs and IBM Research. Ongoing interdisciplinary research at universities such as Stanford University, University of California, Berkeley, and ETH Zurich investigates integration with graphene and van der Waals heterostructures for future quantum devices.

Category:Condensed matter physics