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Study of temperature Green’s functions of graphene-like systems in a half-space

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Abstract

We consider the formalism of temperature Green’s functions to study the electronic properties of a semiinfinite two-dimensional graphene lattice at a given temperature. Under most general assumptions about the graphene boundary structure, we calculate the propagator in the corresponding diagram technique. The obtained propagator survives limit transitions between physically different states of the system boundary, i.e., a zig-zag edge and a boundary condition in the “infinite mass” approximation, and also correctly describes the problem where the electron–hole symmetry is violated because of the presence of an external potential applied to the graphene boundary. We illustrate the use of the propagator, its analytic properties, and specific features of calculating with it in the example of determining the dependence of the electron density on the distance to the system boundary.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    I. A. D’yakonov, M. V. Komarova & M. Yu. Nalimov

Authors
  1. I. A. D’yakonov
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  2. M. V. Komarova
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  3. M. Yu. Nalimov
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Corresponding author

Correspondence to I. A. D’yakonov.

Additional information

This research is supported by St. Petersburg State University (Research Grant No. 11.38.185.2014).

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 190, No. 3, pp. 426–439, March, 2017.

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D’yakonov, I.A., Komarova, M.V. & Nalimov, M.Y. Study of temperature Green’s functions of graphene-like systems in a half-space. Theor Math Phys 190, 366–377 (2017). https://doi.org/10.1134/S0040577917030060

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