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Thermodynamic functions of a relativistic electron gas on a tube in a magnetic field

N. V. Gleizer

Ukrainian State University of Railway Transport, Fejerbaha Sq. 7, Kharkiv 61050, Ukraine

E-mail Address: natalya.gleyzer@gmail.com

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A. M. Ermolaev

Kharkiv National University, Svobody Sq. 4, Kharkiv 61022, Ukraine

E-mail Address: alexander.m.ermolaev@univer.kharkov.ua

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G. I. Rashba

Kharkiv National University, Svobody Sq. 4, Kharkiv 61022, Ukraine

E-mail Address: georgiy.i.rashba@gmail.com

Corresponding author.

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https://doi.org/10.1142/S0217979219502539Cited by:0 (Source: Crossref)

Abstract

On the basis of the one-particle Dirac equation, an exact solution for the problem of the energy spectrum of a relativistic electron on the surface of a tube in a magnetic field is obtained. The spectra of a relativistic rotator and a relativistic electron in a two-dimensional electron gas are obtained in limiting cases. The density of electron states and the main thermodynamic functions of a relativistic electron gas on a tube in a magnetic field are calculated. These values experience Aharonov–Bohm oscillations and oscillations of the de Haas–van Alphen type with a change of the magnetic field and parameters of the problem. The asymptotics of thermodynamic functions at low- and high-temperatures are obtained. The results can be used in studies of nanotubes of a two-dimensional electron gas and in astrophysics.

Keywords:

PACS: 73.63.Fg, 65.80.

$+$ n, 51.30.

$+$ i, 05.30.-d, 71.10.Ca

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