The fractional quantum Hall effect (FQHE) is a physical phenomenon in which a certain system behaves as if it were composed of particles with charge smaller than the elementary charge. Its discovery and explanation were recognized by the 1998 Nobel Prize in Physics.
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Introduction
The fractional quantum Hall effect (FQHE) is a manifestation of simple collective behaviour in a two-dimensional system of strongly interacting electrons. At particular magnetic fields, the electron gas condenses into a remarkable state with liquid-like properties. This state is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures. As in the integer quantum Hall effect, a series of plateaus forms in the Hall resistance. Each particular value of the magnetic field corresponds to a filling factor (the ratio of electrons to magnetic flux quanta)
where p and q are integers with no common factors. Here q turns out to be an odd number with the exception of two filling factors 5/2 and 7/2. The principal series of such fractions are
and
There were two major steps in the theory of the FQHE.
- Fractionally-charged quasiparticles: this theory, proposed by Laughlin, is based on accurate trial wave functions for the ground state at fraction 1 / q as well as its quasiparticle and quasihole excitations. The excitations have fractional charge of magnitude
.
- Composite fermions: this theory was proposed by Jain, and Halperin, Lee and Read. As a result of the repulsive interactions, two (or, in general, an even number) flux quanta
are captured by each electron, forming integer-charged quasiparticles called composite fermions. The fractional states are mapped to the integer QHE. This makes electrons at a filling factor 1/3, for example, behave in the same way as at filing factor 1. A remarkable result is that filling factor 1/2 corresponds to zero magnetic field. Experiments support composite fermion theory.
The FQHE was experimentally discovered in 1982 by Daniel Tsui and Horst Störmer, in experiments performed on gallium arsenide heterostructures developed by Arthur Gossard. Tsui, Störmer, and Laughlin were awarded the 1998 Nobel Prize for their work.
Laughlin's original plasma model was extended to other fractionally charged systems by MacDonald and others[1]. An approach based on the idea of composite Fermions[2] given by Jain has now emerged as a basic paradigm encompassing most of the earlier approaches.
Fractionally charged quasiparticles are neither bosons nor fermions and exhibit anyonic statistics. The fractional quantum Hall effect continues to be influential in theories about topological order. Certain fractional quantum Hall phases appear to have the right properties for building a topological quantum computer.
Other evidence for fractionally-charged quasiparticles
Apart from the FQHE itself, further evidence has continued to emerge that specifically supports the understanding that there are fractionally-charged quasiparticles in an electron gas under FQHE conditions.
In 1995, the fractional charge of Laughlin quasiparticles was measured directly in a quantum antidot electrometer at Stony Brook University, New York.[3] In 1997, two groups of physicists at the Weizmann Institute of Science in Rehovot, Israel, and at the Commissariat à l'énergie atomique laboratory near Paris, detected such quasiparticles carrying an electric current, through measuring quantum shot noise.[4][5]
Impact of fractional quantum Hall effect
For a long time, people believe that all phases and phase transitions are described by Landau symmetry breaking theory. It has become a common belief that we have figured out the important concepts and understood the essential properties of all forms of matter. The theory for phases of matter has reached its end and is a more or less complete theory. The only thing to be done is to apply the symmetry breaking theory to all different kinds of phases and phase transitions. From this perspective, we can understand the importance of the FQHE discovered by Tsui, Stormer, and Gossard.
Different FQH states all have the same symmetry and cannot be described by symmetry breaking theory. Thus FQH states represent new states of matter that contain a completely new kind of order—topological order. The existence of FQH liquids indicates that there is a whole new world beyond the paradigm of symmetry breaking, waiting to be explored. The FQH effect opened up a new chapter in condensed matter physics. The new type of orders represented by FQH states greatly enrich our understanding of quantum phases and quantum phase transitions. The associated fractional charge, fractional statistics, non-Abelian statistics, chiral edge states, etc demonstrate the power and the fascination of emergence in many-body systems.
See also
Notes
- ^ A.H. MacDonald, G.C. Aers and M.W.C. Dharma-wardana, A Hierarchy of Plasmas for Fractional Quantum Hall States, Phys. Rev. B 31, 5529 (1985).
- ^ J. Jain, Composite Fermions (Cambridge University press) 2007
- ^ "Measurement of fractional charge" (Science Report) 1995. See also Description on the researcher's website.
- ^ "Fractional charge carriers discovered" - Physics Web article 1997-10-24.
- ^ R. de-Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin and D. Mahalu, Nature 389, 162-164 (1997) doi:10.1038/38241
References
- University of Cambridge, Semiconductor Physics Group Research.
- D.C. Tsui, H.L. Stormer, and A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982) doi:10.1103/PhysRevLett.48.1559
- R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983) doi:10.1103/PhysRevLett.50.1395
- Fractional quantum Hall effect( List of Authority Articles)
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