fractional quantum Hall effect
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| fractional quantum Hall effect | |
|---|---|
| Name | Fractional quantum Hall effect |
| Discovered | 1982 |
| Discoverers | Horst L. Störmer, Daniel C. Tsui, Robert B. Laughlin |
| Awards | Nobel Prize in Physics |
| Field | Condensed matter physics |
fractional quantum Hall effect
The fractional quantum Hall effect is a quantum phenomenon observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, where the Hall conductance exhibits plateaus at fractional values of e^2/h. It revealed novel correlated states of matter linked to quasiparticles with fractional charge and fractional statistics, spurring developments in solid-state physics, quantum field theory, and topological phases of matter. The discovery led to major recognition including the Nobel Prize in Physics for the experimental discovery and theoretical explanation.
Introduction
The 1982 experimental report by Horst L. Störmer and Daniel C. Tsui at Bell Labs and the subsequent theoretical work by Robert B. Laughlin established the fractional quantum Hall regime as a paradigm of strongly correlated electrons in two dimensions. The phenomenon occurs in systems such as GaAs/AlGaAs heterostructure devices, graphene, and oxide interfaces at temperatures near millikelvin and magnetic fields of several tesla. Its study ties into research programs at institutions like Princeton University, Columbia University, Massachusetts Institute of Technology, and IBM Research. The effect sits among other quantum Hall phenomena including the integer quantum Hall effect observed by Klaus von Klitzing.
Experimental observations
Initial experiments used high-mobility two-dimensional electron gases in GaAs/AlGaAs heterostructure samples grown by molecular beam epitaxy at Bell Labs, revealing Hall resistance plateaus at filling fraction 1/3. Follow-up experiments in devices fabricated at Bell Laboratories, IBM Research, and Harvard University observed additional fractions such as 2/5, 3/7, and particle-hole conjugates like 2/3. Techniques from low-temperature physics developed at CERN and National Institute of Standards and Technology enabled precision transport measurements showing vanishing longitudinal resistivity at plateaus. Experiments in graphene by groups at University of Manchester and Columbia University extended observations to relativistic Landau levels; work at Stanford University and University of California, Santa Barbara explored fractional states in oxide interfaces like LaAlO3/SrTiO3.
High-resolution tunneling spectroscopy and shot-noise experiments by teams at Weizmann Institute of Science and Weizmann Institute measured quasiparticle charge e/3, while interferometry proposals tested fractional statistics in devices developed at Yale University and Microsoft Station Q. Observations of even-denominator fractions such as 5/2 spurred interest from groups at Princeton University and University of California, Berkeley because of potential non-Abelian excitations predicted by theorists at Microsoft Research and Caltech.
Theoretical foundations
The theoretical explanation began with Laughlin's variational wavefunction and was extended using concepts from many-body physics, quantum field theory, and topological quantum field theory. The understanding involves Landau quantization introduced by Lev Landau and connections to the Chern–Simons gauge theory developed by researchers at Institute for Advanced Study and University of Chicago. Conformal field theory approaches by scholars at University of Cambridge and University of California, Santa Barbara linked edge excitations to bulk topological order. The role of electron-electron interactions was emphasized by theorists at Harvard University and Massachusetts Institute of Technology, while numerical work using exact diagonalization and density-matrix-renormalization techniques came from groups at Los Alamos National Laboratory and University of Tokyo.
Fractional quantum Hall states and trial wavefunctions
Trial wavefunctions, foremost the Laughlin wavefunction proposed by Robert B. Laughlin, capture the 1/3 and related fractions; subsequent constructions include composite fermion wavefunctions developed by Jainendra K. Jain and paired states like the Moore–Read Pfaffian introduced by Gregory Moore and Nicholas Read. Hierarchical constructions following ideas of B. I. Halperin and Haldane produced daughter states, while trial functions based on conformal blocks from Conformal Field Theory were proposed by Eric Verlinde and collaborators. Variational Monte Carlo and exact diagonalization studies at Caltech, Rutgers University, and University of Illinois Urbana-Champaign tested overlaps with experimental energetics, and Bishop–Landau level mixing corrections were analyzed by groups at University of Maryland and University of Florida.
Hierarchy and composite fermion theories
Two primary frameworks explain the sequence of observed fractions: the Haldane–Halperin hierarchy developed by F. D. M. Haldane and B. I. Halperin and the composite fermion picture proposed by Jainendra K. Jain. The hierarchy envisions successive condensations of quasiparticles into daughter Laughlin-like states, while composite fermion theory maps interacting electrons in high magnetic field to weakly interacting composite fermions in reduced effective field, explaining sequences like n/(2pn±1). Computational advances from Argonne National Laboratory and Sandia National Laboratories supported the composite fermion energetics; experimental validation came from measurements at Bell Labs and Princeton University.
Excitations, anyons, and topological order
Quasiparticle excitations in fractional quantum Hall states carry fractional electric charge (measured e/3, e/5, etc.) and obey fractional statistics, or anyonic braiding, a concept explored by researchers at Microsoft Research, Weizmann Institute of Science, and University of California, Santa Barbara. Theoretical classification uses topological quantum field theory (Chern–Simons theory) and modular tensor categories studied at Institute for Advanced Study and Max Planck Institute for Physics. The non-Abelian Moore–Read state at filling 5/2 supports Majorana-like modes relevant to proposals from A. Kitaev and Chetan Nayak for topological quantum computation pursued at Microsoft Station Q and University of Maryland. Edge-state theory developed by Xiao-Gang Wen and collaborators connects bulk topological order to chiral Luttinger liquids, informing interferometry experiments at Yale University.
Applications and open questions
Applications center on potential platforms for fault-tolerant quantum computation using non-Abelian anyons as proposed by Alexei Kitaev and others; experimental efforts at Microsoft Research and Station Q aim to harness 5/2 states. Open questions include the precise nature of the 5/2 state debated by theorists at Princeton University and University of California, Berkeley, the role of disorder and Landau level mixing studied at University of Cambridge and University of Tokyo, and the realization of exotic fractions in graphene and transition metal dichalcogenide heterostructures investigated at Columbia University and MIT. Future progress depends on material advances from groups at IBM Research and National High Magnetic Field Laboratory and on experimental probes refined at Bell Labs and Harvard University.