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Finkel’stein Nonlinear Sigma Model: Interplay of Disorder and Interaction in 2D Electron Systems

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Abstract

In this paper, I briefly review recent theoretical results derived within the Finkel’stein nonlinear sigma model approach for description of two-dimensional interacting disordered electron systems. The examples include an electron system with two valleys, electrons in a double quantum well, electrons on the surface of a topological insulator, an electron system with superconducting correlations, and the integer quantum Hall effect.

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Notes

  1. It is instructive for the experts to highlight the difference between Eqs. (37a)–(37e) and that of [83]. First of all, the right hand side of the RG equation for γs in [83] (see Eq. (A12) there) is not proportional to the factor 1 + γs contrary to our Eq. (37b). This means that the Coulomb interaction, γs = –1, is not the fixed point of RG equations of [83] in contradiction with the \(\mathcal{F}\)-invariance of the FNLSM action. Secondly, the RG equation for γt of [83] does not contain the term proportional to t\(\gamma _{c}^{2}\), in contrast to our Eq. (37b). Finally, the RG equation for γc in [83] contains an additional term proportional to tγcln(1 + γs) which is absent in our Eq. (37d). A similar term was reported by Belitz and Kirkpatrick [32] (see Eq. (6.8g) there). This term was criticized by Finkel’stein in [84]: the origin of this term has been attributed to an improper treatment of the gauge invariance in the RG scheme. We note that such terms, divergent for the case of Coulomb interaction, γs = –1, cannot appear in the course of renormalization of \(\mathcal{F}\)-invariant operators, a particular example of which is the Cooper-channel interaction term SC.

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ACKNOWLEDGMENTS

I am grateful to my coauthors M. Baranov, N. Chtchelkatchev, I. Gornyi, E. König, A. Levchenko, A. Mirlin, P. Ostrovsky, I. Protopopov, A. Pruisken, K. Tikhonov for fruitful collaboration on the problems discussed in this review. I am indebted to A. Germanenko, D. Knyazev, A. Kuntsevich, D. de Lang, G. Minkov, L. Ponomarenko, V. Pudalov, and A. Sherstobitov for detailed discussions of their experimental results. I thank M. Feigel’man, A. Finkelstein, Y. Fominov, A. Ioselevich, Y. Makhlin, M. Skvortsov and the other members of Landau Institute for useful discussions and comments.

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Contribution for the JETP special issue in honor of I. M. Khalatnikov’s 100th anniversary

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Burmistrov, I.S. Finkel’stein Nonlinear Sigma Model: Interplay of Disorder and Interaction in 2D Electron Systems. J. Exp. Theor. Phys. 129, 669–679 (2019). https://doi.org/10.1134/S1063776119100029

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