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Excitons and Cooper PairsTwo Composite Bosons in Many-Body Physics$
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Monique Combescot and Shiue-Yuan Shiau

Print publication date: 2015

Print ISBN-13: 9780198753735

Published to Oxford Scholarship Online: March 2016

DOI: 10.1093/acprof:oso/9780198753735.001.0001

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The Gorkov Approach

The Gorkov Approach

Chapter:
(p.238) 9 The Gorkov Approach
Source:
Excitons and Cooper Pairs
Author(s):

Monique Combescot

Shiue-Yuan Shiau

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198753735.003.0009

Chapter 9 deals with the mean-field approach proposed by Gorkov to the BCS problem. Like the Bogoliubov approach, the Gorkov approach transforms the two-body reduced BCS potential into a one-body operator. However, in the Gorkov approach, the expectation values introduced in the mean-field Hamiltonian are self-consistently determined through the Gorkov equations, which couple standard Green functions and anomalous Green functions. The zero-temperature gap equation is obtained by solving the two coupled Gorkov equations for T = 0 Green functions. This approach can be easily extended to finite temperature. The finite-temperature gap equation provides a direct link between the T = 0 superconductor gap and the critical temperature for gap disappearance. Electromagnetic effects are also easy to include within this approach.

Keywords:   BCS problem, Gorkov equation, standard Green function, anomalous Green function, critical temperature, gap equation, mean-field approach

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