Abstract
We review field theoretical studies dedicated to understanding the effects of electron-electron interaction in graphene, which is characterized by gapless bands, strong electron-electron interactions, and emerging Lorentz invariance deep in the infrared. We consider the influence of interactions on the transport properties of the system as well as their supposedly decisive influence on the potential dynamical generation of a gap.
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Notes
Usually the BPHZ procedure leads to the local form of singularities of Feynman diagrams, i.e. to their independence from external momenta (see, e.g., [9]). The case of the optical conductivity is rather unusual, since the singularity of the subgraph (i.e. \(1{\text{/}}\varepsilon \) in dimensional regularization) is compensated by the contribution \( \sim \varepsilon \) of the second integration. So, the two-loop result for \(\mathcal{C}_{1}^{{({\text{bare}})}}\) is finite (\( = (11 - 3\pi )/6\)). But since the subgraph is singular, \(\mathcal{C}_{1}^{{({\text{bare}})}}\) should be supplemented with a counter-term related to subgraph renormalization. The corresponding pole is also compensated by the contribution \( \sim \varepsilon \) from the integration of the remainder. Thus, this additional contribution is also finite (\( = 1{\text{/}}4\)) and must be subtracted from the results of calculating the two-loop diagrams as shown in Eq. (4).
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ACKNOWLEDGMENTS
The author is grateful to Sofian Teber for help in preparing the paper. He also thanks the Organizing Committee of the International Conference “Modern problems of condensed matter theory” for the invitation.
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Kotikov, A.V. Short Review of Interaction Effects in Graphene. Phys. Part. Nuclei Lett. 20, 1108–1110 (2023). https://doi.org/10.1134/S1547477123050461
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DOI: https://doi.org/10.1134/S1547477123050461