https://doi.org/10.1140/epjb/s10051-023-00599-8
Regular Article - Statistical and Nonlinear Physics
Phase transitions in three-dimensional Dirac semi-metals using Schwinger–Dyson equations
1
Department of Physics, Brandon University, R7A 6A9, Brandon, MB, Canada
2
Winnipeg Institute for Theoretical Physics, Winnipeg, MB, Canada
3
Department of Physics & Astronomy, University of Manitoba, R3T 2N2, Winnipeg, MB, Canada
Received:
10
July
2023
Accepted:
25
September
2023
Published online:
9
October
2023
We study the semi-metal/insulator quantum phase transition in three-dimensional Dirac semi-metals by solving a set of Schwinger–Dyson equations. We study the effect of an anisotropic fermion velocity on the critical coupling of the transition. We consider the influence of several different approximations that are commonly used in the literature and show that results for the critical coupling change considerably when some of these approximations are relaxed. Most importantly, the nature of the dependence of the critical coupling on the anisotropy depends strongly on the approximations that are used for the photon polarization tensor. On the one hand, this means that calculations that include full photon dynamics are necessary to answer even the basic question of whether the critical coupling increases or decreases with anisotropy. On the other hand, our results mean that it is possible that anisotropy could provide a mechanism to promote dynamical gap generation in realistic three-dimensional Dirac semi-metallic materials.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
