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Electromagnetism of one-component plasmas of massless fermions

Published online by Cambridge University Press:  11 August 2023

V.M. Rylyuk Open the ORCID record for V.M. Rylyuk [Opens in a new window]  and
I.M. Tkachenko Open the ORCID record for I.M. Tkachenko [Opens in a new window]
V.M. Rylyuk*
Affiliation:
National Academy of Sciences of Ukraine “Center for Problems of Marine Geology, Geoecology and Sedimentary Ore Formation of the NAS of Ukraine”, Kyiv, 01054, Ukraine
I.M. Tkachenko
Affiliation:
Departament de Matemàtica Aplicada, Universitat Poliècnica de València, Valencia, 46022, Spain Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
*
†Email address for correspondence: rvm@onu.edu.ua
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Abstract

We present a theoretical study of two- and three-dimensional massless Dirac one-component plasmas embedded in a constant uniform magnetic field. We determine the wavefunctions and Landau energy levels of a massless Dirac fermion in a constant magnetic field. On this basis we consider magnetism of Fermi fluids of massless charged particles. We show that such a three-dimensional Dirac plasma consisting of fermions with the same helicity has its own magnetic moment. We also consider the limit of strong magnetic fields and investigate the De Haas–van Alphen effect. We derive the Kubo formula for the electrical conductivity tensor of massless Dirac plasmas and consider the Shubnikov–de Haas effect. In addition, we propose a model of the static conductivity tensor and employ the matrix version of the classical method of moments to derive a Drude-like formula for the dynamic conductivity tensor for massless Dirac plasmas. We find that the electrical conductivity tensor for Dirac fermions with the right helicity is not isotropic in the plane perpendicular to the magnetic field.

Keywords

quantum plasmastrongly coupled plasmasplasma properties
Type
Research Article
Information
Journal of Plasma Physics , Volume 89 , Issue 4 , August 2023 , 905890415
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press

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