IBM Journal of Research and Development
IBM Skip to main content
  Home     Products & services     Support & downloads     My account  

  Select a country  
Journals Home  
  Systems Journal  
Journal of Research
and Development
    Current Issue  
    Recent Issues  
    Papers in Progress  
    Search/Index  
    Orders  
    Description  
    Patents  
    Recent publications  
    Author's Guide  
  Staff  
  Contact Us  
  Related links:  
     IBM Research  

IBM Journal of Research and Development  
Volume 32, Number 1, Page 52 (1988)
Basic Concepts in Quantum and Stochastic T...
  Full article: arrowPDF   arrowCopyright info





   

Bloch electron in a magnetic field: Mixed dimensionality and the magnetic-field-induced generalized quantum Hall effect

by M. Y. Azbel
The energy spectrum of a Bloch electron in a magnetic field is one-dimensional. This leads to the Peierls instability and the magnetic-field-induced transition to the quantized Hall effect. The wave function is two-dimensional. This decreases the Peierls gap and makes it exponentially vanishing with magnetic field. Disorder lifts the degeneracy and one-dimensionality of the spectrum. High disorder yields a metallic behavior. Intermediate disorder leads to the generalized quantized Hall effect. The latter has a finite magnetoresistance as a semimetal, and Hall plateaus similar to the quantized ones, but they may have any value of the effective charge.
Related Subjects: Carrier transport in small structures; Hall effect; Mesoscopic phenomena; Physics, solid state; Quantum theory and effects