Bogoliubov-de Gennes Method and Its Applications by Jian-Xin Zhu

Author:Jian-Xin Zhu
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.4a)

(4.4b)

​​where

(4.5)

and

(4.6a)

(4.6b)

​​with n i as the density of nonmagnetic impurities. We note that . We can solve Eq. (4.4) to obtain

(4.7a)

(4.7b)

On substitution of Eq.(̇4.7) into Eq. (4.6), we find

(4.8a)

(4.8b)

​​Here we have dropped the contribution to the integral from the term linear in in the numerator of . The pair potential is subjected to the self-consistency:

(4.9)

In the weak-coupling limit, the pairing interaction is limited to a small range near the Fermi surface. As we discussed in the early chapter, for the s-wave pairing symmetry, the pairing interaction is approximated as

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