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 3, Page 384 (1988)
Mesoscopic Phenomena and Nanolithographic ...
  Full article: arrowPDF   arrowCopyright info





   

What is measured when you measure a resistance?—The Landauer formula revisited

by A. D. Stone, A. Szafer
We re-examine the question of what constitutes the physically relevant quantum-mechanical expression for the resistance of a disordered conductor in light of recent experimental and theoretical advances in our understanding of the conducting properties of mesoscopic systems. It is shown that in the absence of a magnetic field, the formula proposed by Büttiker, which expresses the current response of a multi-port conductor in terms of transmission matrices, is derivable straightforwardly from linear response theory. We also present a general formalism for solving these equations for the resistance given the scattering matrix. This Landauer-type formula reduces to g=(e2/h)Tr(tt), where g is the conductance and t is the transmission matrix, for the two-probe case. It is suggested that this formula provides the best description of the present class of experiments performed in two-probe or multi-probe measuring configurations, and that the subtleties leading to various different Landauer formulae are not relevant to these experiments. This is not because of the large number of channels in real conductors, but is due to the fact that apparently no present experiment probes a "local chemical potential" in the conductor. Certain standard objections to deriving a Landauer-type formula from linear response theory are answered. Applications of this formula to fluctuations in disordered multi-probe conductors are discussed.
Related Subjects: Carrier transport in small structures; Mesoscopic phenomena; Physics, solid state