Quick search Find article
Quick search
Find article

Topological aspects of the quantum Hall effect

REVIEW ARTICLE

Y Hatsugai

Show affiliations


REVIEW ARTICLE

The quantum Hall effect is a typical realization of topological effects in condensed matter physics. In this article, some of the topological aspects of the quantum Hall effect are reviewed. For the lattice fermions, the Hall conductance of the system is expressed in terms of two different topological invariants. One is the famous TKNN integer which is related to the bulk state. The other is the winding number of the edge state on the complex-energy surface which is generally a high-genus Riemann surface. We will describe them in detail.

Therefore we have two topological expressions for the Hall conductance. Actually these two expressions give the same integer, although they look quite different. This means that one can explain the quantum Hall effect by using either the edge states or the bulk states, that is, .


PACS

73.43.Cd Theory and modeling

Subjects

Surfaces, interfaces and thin films

Dates

Issue 12 (24 March 1997)

Received 12 August 1996, in final form 30 December 1996



  1. Topological aspects of the quantum Hall effect

    Y Hatsugai 1997 J. Phys.: Condens. Matter 9 2507

  2. Fabrication of GaAs quantum dots by droplet epitaxy on Si/Ge virtual substrate

    S Bietti et al 2009 IOP Conf. Ser.: Mater. Sci. Eng. 6 012009

  3. The Berry phase for spin in the Majorana representation

    J H Hannay 1998 J. Phys. A: Math. Gen. 31 L53

  4. Multi-peakons and a theorem of Stieltjes

    R Beals et al 1999 Inverse Problems 15 L1

  5. Electronic structure based on the local atomic environment for tight-binding bands

    R Haydock et al 1972 J. Phys. C: Solid State Phys. 5 2845

  6. Electronic structure based on the local atomic environment for tight-binding bands. II

    R Haydock et al 1975 J. Phys. C: Solid State Phys. 8 2591

  7. Self-assembled crystalline semiconductor optoelectronics on glass and plastic

    E Saeedi et al 2008 J. Micromech. Microeng. 18 075019

  8. Theoretical uncertainties in sparticle mass predictions from computational tools

    Benjamin C. Allanach et al JHEP03(2003)016

  9. Near-field photonics: tip-enhanced microscopy and spectroscopy on the nanoscale

    Neil Anderson et al 2006 J. Opt. A: Pure Appl. Opt. 8 S227

  10. Fluctuation patterns in high-frequency financial asset returns

    T. Preis et al 2008 EPL 82 68005

Users also read

What's this?
This innovative new feature generates a list of articles 'also read' by other users based on them reading the original article. Article abstracts citations and references are all considered and weighted accordingly. We hope that this will help you find relevant papers for your research.

  1. Composite fermions in the quantum Hall effect
  2. Quantised Hall effect

Related review articles

What's this?
View review articles related to this research to gain an insight into the key trends in this subject area. Related review articles are selected based on PACS/MSC codes, and are no more than three years old.

  1. Electron dynamics in inhomogeneous magnetic fields
  2. Quantum Hall effects in graphene-based two-dimensional electron systems
  3. Disordered topological insulators: a non-commutative geometry perspective
More

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.