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TMF, 2019, Volume 200, Number 2, Pages 343–360 (Mi tmf9678)  

Review of electron–electron interaction effects in planar Dirac liquids

S. Tebera, A. V. Kotikovb

a Sorbonne Universités, Laboratoire de Physique Théorique et Hautes Energies, LPTHE, Paris, France
b Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

Abstract: We review field theory studies devoted to understanding electron–electron interaction effects in condensed matter systems such as planar Dirac liquids, for example, graphene and graphene-like systems, surface states of some topological insulators, and possibly half-filled fractional quantum Hall systems. These liquids are characterized by gapless bands, strong electron–electron interactions, and emergent Lorentz invariance deep in the infrared. We address several important issues raised by experiments on these systems covering subjects of wide current interest in low-energy (condensed matter) and also high-energy (particle) physics. In particular, we consider the subtle influence of interactions on transport properties and their supposedly crucial influence on a potential dynamical mass generation. The resolution of these problems guide us from a thorough examination of the perturbative structure of gauge field theories to the development and application of nonperturbative approaches known from quantum electro/chromo-dynamics to address strong coupling issues.

Keywords: graphene, perturbation theory, electron–electron interaction.

DOI: https://doi.org/10.4213/tmf9678

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English version:
Theoretical and Mathematical Physics, 2019, 200:2, 1222–1236

Bibliographic databases:

Received: 14.12.2018
Revised: 12.02.2019

Citation: S. Teber, A. V. Kotikov, “Review of electron–electron interaction effects in planar Dirac liquids”, TMF, 200:2 (2019), 343–360; Theoret. and Math. Phys., 200:2 (2019), 1222–1236

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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