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Volumn 64, Issue 11, 2001, Pages

Parquet approach to nonlocal vertex functions and electrical conductivity of disordered electrons

Author keywords

[No Author keywords available]

Indexed keywords

ALLOY;

EID: 0035884647     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.115115     Document Type: Article
Times cited : (42)

References (47)
  • 4
    • 85038326619 scopus 로고    scopus 로고
    • I. Turek, V. Drchal, J. Kudrnovský, M. Šob, and P. Weinberger, Electronic Structure of Disordered Alloys, Surfaces and Interfaces (Kluwer, Boston, 1997)
    • I. Turek, V. Drchal, J. Kudrnovský, M. Šob, and P. Weinberger, Electronic Structure of Disordered Alloys, Surfaces and Interfaces (Kluwer, Boston, 1997).
  • 9
    • 0003456797 scopus 로고
    • E. van Groessen and E. M. de Jager Studies in Mathematical Physics North-Holland, Amsterdam
    • A. Gonis, Green Functions for Ordered and Disordered Systems, edited by E. van Groessen and E. M. de Jager,Studies in Mathematical Physics (North-Holland, Amsterdam, 1992).
    • (1992) Green Functions for Ordered and Disordered Systems
    • Gonis, A.1
  • 16
    • 85038278413 scopus 로고    scopus 로고
    • D. Vollhardt and P. Wölfle, in Electronic Phase Transitions, edited by W. Hanke and Yu. V. Kopaev (Elsevier, Amsterdam, 1992), p. 1
    • D. Vollhardt and P. Wölfle, in Electronic Phase Transitions, edited by W. Hanke and Yu. V. Kopaev (Elsevier, Amsterdam, 1992), p. 1.
  • 27
    • 0000274183 scopus 로고
    • Systems with site-diagonal disorder within this approach were studied, e.g., in R. Vlaming and D. Vollhardt, Phys. Rev. B 45, 4637 (1992);
    • (1992) Phys. Rev. B , vol.45 , pp. 4637
    • Vlaming, R.1    Vollhardt, D.2
  • 31
    • 84983812716 scopus 로고
    • Details of the diagrammatic techniques in disordered electron systems can be found in the original papers, S. F. Edwards, Philos. Mag. 3, 1020 (1958);
    • (1958) Philos. Mag. , vol.3 , pp. 1020
    • Edwards, S.F.1
  • 32
    • 0000857706 scopus 로고
    • and in Refs. 3 14 15
    • J. S. Langer, Phys. Rev. 120, 714 (1960);and in Refs. 3, 14, and 15.
    • (1960) Phys. Rev. , vol.120 , pp. 714
    • Langer, J.S.1
  • 34
    • 85038290489 scopus 로고    scopus 로고
    • A two-particle function is called completely irreducible if it is irreducible in all two-particle channels, i.e., it can be disconnected by cutting at least three lines (one-particle propagators)
    • A two-particle function is called completely irreducible if it is irreducible in all two-particle channels, i.e., it can be disconnected by cutting at least three lines (one-particle propagators).
  • 37
    • 85038348166 scopus 로고    scopus 로고
    • We have not found any identity between one- and two-particle averaged Green functions that would lead to the most general form of identity (28) being a formal but straightforward result of a functional integration of the differential identity (10)
    • We have not found any identity between one- and two-particle averaged Green functions that would lead to the most general form of identity (28) being a formal but straightforward result of a functional integration of the differential identity (10).
  • 39
    • 85038269038 scopus 로고    scopus 로고
    • Note that not all diagrammatic approximations for the vertex function with the self-energy calculated via the Ward identity (29) allow for a closed set of self-energy diagrams. We actually do not need this property for a physically consistent picture, since no physical law is broken. The Feynman diagrams serve to control the approximation made in the entire phase space. This is done in the parquet approach at the two-particle level. The self-energy calculated via the Ward identity is defined only at the saddle point and does not have a variational character as a diagrammatically derived one
    • Note that not all diagrammatic approximations for the vertex function with the self-energy calculated via the Ward identity (29) allow for a closed set of self-energy diagrams. We actually do not need this property for a physically consistent picture, since no physical law is broken. The Feynman diagrams serve to control the approximation made in the entire phase space. This is done in the parquet approach at the two-particle level. The self-energy calculated via the Ward identity is defined only at the saddle point and does not have a variational character as a diagrammatically derived one.
  • 43
    • 85038276746 scopus 로고    scopus 로고
    • Rather insignificant differences in the mean-field conductivity with and without vertex corrections observed here are caused by the asymptotic limit (Formula presented). This limit is needed to keep global consistence between one-particle (CPA with local self-energy) and two-particle Green functions. When mean-field conductivity (41) is applied in three dimensions, the Ward identity (29) has to be used to adjust the self-energy. Even for the vertex function (40) the self-energy becomes nonlocal. The vertex corrections from Eq. (41) not only cause important changes in the conductivity but also in the band structure of finite-dimensional systems, in particular near band edges. In low dimensions, (Formula presented), the asymptotic expression for the irreducible vertex (40) becomes inapplicable due to diffusion and Cooperon poles and we have to leave the mean-field concept and solve the parquet Eqs. (19) with other means
    • Rather insignificant differences in the mean-field conductivity with and without vertex corrections observed here are caused by the asymptotic limit (Formula presented). This limit is needed to keep global consistence between one-particle (CPA with local self-energy) and two-particle Green functions. When mean-field conductivity (41) is applied in three dimensions, the Ward identity (29) has to be used to adjust the self-energy. Even for the vertex function (40) the self-energy becomes nonlocal. The vertex corrections from Eq. (41) not only cause important changes in the conductivity but also in the band structure of finite-dimensional systems, in particular near band edges. In low dimensions, (Formula presented), the asymptotic expression for the irreducible vertex (40) becomes inapplicable due to diffusion and Cooperon poles and we have to leave the mean-field concept and solve the parquet Eqs. (19) with other means.


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