Fractional quantum Hall effect

The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values of . It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations have a fractional elementary charge and possibly also fractional statistics. The 1998 Nobel Prize in Physics was awarded to Robert Laughlin, Horst Störmer, and Daniel Tsui for the discovery and explanation of the fractional Hall effect.[1] However, Laughlin's explanation was a phenomenological guess and only applies to fillings where is an odd integer. The microscopic origin of the FQHE remains unknown and is a major research topic in condensed matter physics.

Introduction

Unsolved problem in physics:
What mechanism explains the existence of the ν=5/2 state in the fractional quantum Hall effect?
(more unsolved problems in physics)

The fractional quantum Hall effect (FQHE) is a collective behaviour in a two-dimensional system of electrons. In particular magnetic fields, the electron gas condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures. As in the integer quantum Hall effect, the Hall resistance undergoes certain quantum Hall transitions to form a series of plateaus. 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 several major steps in the theory of the FQHE.

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.

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.

Evidence for fractionally-charged quasiparticles

Experiments have reported results that specifically support 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.[5] 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.[6][7] Both of these experiments have been confirmed with certainty.

A more recent experiment,[8] which measures the quasiparticle charge extremely directly, appears beyond reproach.

Impact of fractional quantum Hall effect

The FQH effect shows the limits of Landau's symmetry breaking theory. Previously it was long believed that the symmetry breaking theory could explain all the important concepts and essential properties of all forms of matter. According to this view 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. For example, properties once deemed isotropic for all materials may be anisotropic in 2D planes.[9] 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.[10][11][12] 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

  1. Schwarzschild, Bertram (1998). "Physics Nobel Prize Goes to Tsui, Stormer and Laughlin for the Fractional Quantum Hall Effect". Physics Today. 51 (12): 17–19. Bibcode:1998PhT....51l..17S. doi:10.1063/1.882480. Retrieved 20 April 2012.
  2. An, Sanghun; Jiang, P.; Choi, H.; Kang, W.; Simon, S. H.; Pfeiffer, L. N.; West, K. W.; Baldwin, K. W. (2011). "Braiding of Abelian and Non-Abelian Anyons in the Fractional Quantum Hall Effect". arXiv:1112.3400Freely accessible [cond-mat.mes-hall].
  3. Greiter, M. (1994). "Microscopic formulation of the hierarchy of quantized Hall states". Physics Letters B. 336: 48. Bibcode:1994PhLB..336...48G. arXiv:cond-mat/9311062Freely accessible. doi:10.1016/0370-2693(94)00957-0. (Subscription required (help)).
  4. MacDonald, A.H.; Aers, G.C.; Dharma-wardana, M.W.C. (1985). "Hierarchy of plasmas for fractional quantum Hall states". Physical Review B. 31 (8): 5529. Bibcode:1985PhRvB..31.5529M. doi:10.1103/PhysRevB.31.5529. (Subscription required (help)).
  5. Goldman, V.J.; Su, B. (1995). "Resonant Tunneling in the Quantum Hall Regime: Measurement of Fractional Charge". Science. 267 (5200): 1010. Bibcode:1995Sci...267.1010G. PMID 17811442. doi:10.1126/science.267.5200.1010. (Subscription required (help)). Lay summary Stony Brook University, Quantum Transport Lab (2003).
  6. "Fractional charge carriers discovered". Physics World. 24 October 1997. Retrieved 2010-02-08.
  7. R. de-Picciotto; M. Reznikov; M. Heiblum; V. Umansky; G. Bunin; D. Mahalu (1997). "Direct observation of a fractional charge". Nature. 389 (6647): 162. Bibcode:1997Natur.389..162D. doi:10.1038/38241.
  8. J. Martin; S. Ilani; B. Verdene; J. Smet; V. Umansky; D. Mahalu; D. Schuh; G. Abstreiter; A. Yacoby (2004). "Localization of Fractionally Charged Quasi Particles". Science. 305 (5686): 980–3. Bibcode:2004Sci...305..980M. PMID 15310895. doi:10.1126/science.1099950.
  9. Selby, N. S.; Crawford, M.; Tracy, L.; Reno, J. L.; Pan, W. (2014-09-01). "In situ biaxial rotation at low-temperatures in high magnetic fields". Review of Scientific Instruments. 85 (9): 095116. ISSN 0034-6748. doi:10.1063/1.4896100.
  10. Rychkov VS, Borlenghi S, Jaffres H, Fert A, Waintal X (August 2009). "Spin torque and waviness in magnetic multilayers: a bridge between Valet-Fert theory and quantum approaches". Phys. Rev. Lett. 103 (6): 066602. Bibcode:2009PhRvL.103f6602R. PMID 19792592. arXiv:0902.4360Freely accessible. doi:10.1103/PhysRevLett.103.066602.
  11. Callaway DJE (April 1991). "Random matrices, fractional statistics, and the quantum Hall effect". Phys. Rev. B Condens. Matter. 43 (10): 8641–8643. Bibcode:1991PhRvB..43.8641C. PMID 9996505. doi:10.1103/PhysRevB.43.8641.
  12. Zumbühl DM, Miller JB, Marcus CM, Campman K, Gossard AC (December 2002). "Spin-orbit coupling, antilocalization, and parallel magnetic fields in quantum dots". Phys. Rev. Lett. 89 (27): 276803. Bibcode:2002PhRvL..89A6803Z. PMID 12513231. arXiv:cond-mat/0208436Freely accessible. doi:10.1103/PhysRevLett.89.276803.

References

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