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The Physics of NanoelectronicsTransport and Fluctuation Phenomena at Low Temperatures$
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Tero T. Heikkilä

Print publication date: 2013

Print ISBN-13: 9780199592449

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199592449.001.0001

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Scattering approach to quantum transport

Scattering approach to quantum transport

Chapter:
(p.37) 3 Scattering approach to quantum transport
Source:
The Physics of Nanoelectronics
Author(s):

Tero T. Heikkilä

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199592449.003.0003

This chapter introduces the scattering approach to electron transport in mesoscopic conductors. The scattering approach relates the current to the scattering properties of electrons inside the sample and is able to treat arbitrary quantum-mechanical effects. The chapter first derives the Landauer-Büttiker formula for the conductance of a mesoscopic conductor and introduces the quantum point contacts where one can measure quantized conductance. It also explains the main properties of scattering matrices and relates them to the currents in mesoscopic systems. Resonant tunnelling is introduced as an important effect that can be straightforwardly discussed with the scattering approach. The chapter also indicates how inelastic scattering can be included in the scattering approach, and gives a few examples of more recent developments concerning time-dependent transport, non-linear effects, and the scattering theory of current-driven spin transfer torque.

Keywords:   scattering approach, Landauer-Büttiker formula, quantum transport, resonant tunnelling, quantum point contact

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