Geodesic
Vacuum charge and current densities in the supercritical two-dimensional Dirac–Coulomb system in a magnetic field with an axial-vector potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 1, pp. 122-144 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider nonperturbative vacuum polarization effects in the supercritical region for a planar Dirac–Coulomb system with a supercritical extended axially symmetric Coulomb source with a charge $Z > Z_{{\rm cr},1}$ and radius $R_0$ in the magnetic field with an axial-vector potential. We study the behavior of the vacuum charge and vacuum current densities, $\rho_{\scriptscriptstyle\mathrm{VP}}(\vec r\,)$ and $\vec{j}_{\scriptscriptstyle\mathrm{VP}}(\vec r\,)$. We focus on the divergence in the theory corresponding to the renormalization and convergence of partial series for $\rho_{\scriptscriptstyle\mathrm{VP}}(\vec r\,)$ and $\vec{j}_{\scriptscriptstyle\mathrm{VP}}(\vec r\,)$. We stress that in contrast to the vacuum charge density, the partial channels with large values of the third projection of the total angular momentum $|m_j|$ must be taken into account in calculating the vacuum current density in the presence of an external magnetic field localized in the range $R_1>R_0$. We show that in the presence of a supercritical Coulomb source, the induced magnetic field can enhance the original magnetic field for certain values of parameters of the external vector potential.
Mots-clés : planar Dirac–Coulomb system
Keywords: vacuum polarization, essentially nonperturbative effects for $Z>Z_{\rm cr}$, magnetic vacuum effects, vacuum charge density, vacuum current density. 
@article{TMF_2021_208_1_a8,
     author = {A. S. Davydov and A. A. Krasnov and V. A. Kuzmin},
     title = {Vacuum charge and current densities in the~supercritical two-dimensional {Dirac{\textendash}Coulomb} system in a~magnetic field with an axial-vector potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {122--144},
     year = {2021},
     volume = {208},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_208_1_a8/}
}
TY  - JOUR
AU  - A. S. Davydov
AU  - A. A. Krasnov
AU  - V. A. Kuzmin
TI  - Vacuum charge and current densities in the supercritical two-dimensional Dirac–Coulomb system in a magnetic field with an axial-vector potential
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2021
SP  - 122
EP  - 144
VL  - 208
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2021_208_1_a8/
LA  - ru
ID  - TMF_2021_208_1_a8
ER  - 
%0 Journal Article
%A A. S. Davydov
%A A. A. Krasnov
%A V. A. Kuzmin
%T Vacuum charge and current densities in the supercritical two-dimensional Dirac–Coulomb system in a magnetic field with an axial-vector potential
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2021
%P 122-144
%V 208
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2021_208_1_a8/
%G ru
%F TMF_2021_208_1_a8
A. S. Davydov; A. A. Krasnov; V. A. Kuzmin. Vacuum charge and current densities in the supercritical two-dimensional Dirac–Coulomb system in a magnetic field with an axial-vector potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 1, pp. 122-144. http://geodesic.mathdoc.fr/item/TMF_2021_208_1_a8/

[1] A. K. Geim, K. S. Novoselov, “The rise of graphene”, Nature Mater., 6:3 (2007), 183–191 | DOI

[2] A. V. Shytov, M. I. Katsnelson, L. S. Levitov, “Vacuum polarization and screening of supercritical impurities in graphene”, Phys. Rev. Lett., 99:23 (2007), 236801, 4 pp. | DOI

[3] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene”, Nature, 438:7065 (2005), 197–200 | DOI

[4] S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, A. K. Geim, “Giant intrinsic carrier mobilities in graphene and its bilayer”, Phys. Rev. Lett., 100:1 (2008), 016602, 4 pp. | DOI

[5] V. M. Kuleshov, V. D. Mur, N. B. Narozhnyi, A. M. Fedotov, Yu. E. Lozovik, “O kulonovskoi zadache v grafene so schelyu v elektronnom spektre”, Pisma v ZhETF, 101:4 (2015), 282–288 | DOI | DOI

[6] V. M. Kuleshov, V. D. Mur, N. B. Narozhnyi, A. M. Fedotov, Yu. E. Lozovik, V. S. Popov, “Kulonovskaya zadacha s zaryadom yadra $Z>Z_\mathrm{cr}$”, UFN, 185:8, 845–852 | DOI

[7] V. N. Kotov, V. M. Pereira, B. Uchoa, “Polarization charge distribution in gapped graphene: Perturbation theory and exact diagonalization analysis”, Phys. Rev. B, 78:7 (2008), 075433, 5 pp. | DOI

[8] V. N. Kotov, B. Uchoa, V. M. Pereira, F. Guinea, A. H. C. Neto, “Electron-electron interactions in graphene: Current status and perspectives”, Rev. Modern Phys., 84:3 (2012), 1067–1125 | DOI

[9] A. Bubnov, N. Gubina, V. Zhukovsky, “Vacuum current induced by an axial-vector condensate and electron anomalous magnetic moment in a magnetic field”, Phys. Rev. D, 96:1 (2017), 016011, 10 pp. | DOI

[10] P. Górnicki, “Aharonov–Bohm effect and vacuum polarization”, Ann. Phys., 202:2 (1990), 271–296 | DOI

[11] H.-N. Li, D. A. Coker, A. S. Goldhaber, “Self-consistent solutions for vacuum currents around a magnetic flux string”, Phys. Rev. D, 47:2 (1993), 694–702 | DOI

[12] R. Jackiw, A. I. Milstein, S.-Y. Pi, I. S. Terekhov, “Induced current and Aharonov–Bohm effect in graphene”, Phys. Rev. B, 80:3 (2009), 033413, 3 pp. | DOI

[13] Y. Nishida, “Vacuum polarization of graphene with a supercritical coulomb impurity: Low-energy universality and discrete scale invariance”, Phys. Rev. B, 90:16 (2014), 165414, 6 pp. | DOI

[14] V. Khalilov, I. Mamsurov, “Planar density of vacuum charge induced by a supercritical coulomb potential”, Phys. Lett. B, 769 (2017), 152–158 | DOI

[15] V. R. Khalilov, K. E. Lee, “Planar massless fermions in couloumb and Aharonov–Bohm potentials”, Internat. J. Modern Phys. A, 27:29 (2012), 1250169, 14 pp. | DOI | MR

[16] A. I. Milstein, I. S. Terekhov, “Induced charge generated by a potential well in graphene”, Phys. Rev. B, 81:12 (2010), 125419, 5 pp. | DOI

[17] A. I. Milstein, I. S. Terekhov, “Induced current in the presence of a magnetic flux tube of small radius”, Phys. Rev. B, 83:7 (2011), 075420, 5 pp. | DOI

[18] Yu. A. Sitenko, N. D. Vlasii, “Vacuum polarization effects on graphitic nanocones”, J. Phys.: Conf. Ser., 129 (2008), 012008, 9 pp. | DOI

[19] A. Davydov, K. Sveshnikov, Yu. Voronina, “Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system I. Vacuum charge density”, Internat. J. Modern Phys. A, 33:01 (2018), 1850004, 25 pp., arXiv: 1712.02704 | DOI

[20] Yu. S. Voronina, A. S. Davydov, K. A. Sveshnikov, “Vakuumnye effekty dlya odnomernogo “atoma vodoroda” pri $Z>Z_{\mathrm{cr}}$”, TMF, 193:2 (2017), 276–308 | DOI | DOI

[21] K. A. Sveshnikov, Yu. S. Voronina, A. S. Davydov, P. A. Grashin, “Suschestvenno neperturbativnye effekty polyarizatsii vakuuma v dvumernoi cisteme Diraka–Kulona pri $Z>Z_\mathrm{cr}$. Vakuumnaya plotnost zaryada”, TMF, 198:3 (2019), 381–417 | DOI | DOI | MR

[22] K. A. Sveshnikov, Yu. S. Voronina, A. S. Davydov, P. A. Grashin, “Suschestvenno neperturbativnye effekty polyarizatsii vakuuma v dvumernoi sisteme Diraka–Kulona pri $Z>Z_{\mathrm{cr}}$. Energiya polyarizatsii vakuuma”, TMF, 199:1 (2019), 69–103 | DOI | DOI | MR

[23] A. Davydov, K. Sveshnikov, Yu. Voronina, “Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system II. Vacuum energy”, Internat. J. Modern Phys. A, 33:01 (2018), 1850005, arXiv: 1712.02703 | DOI

[24] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. 1, Gipergeometricheskaya funktsiya. Funktsii Lezhandra, Nauka, M., 1973 | MR

[25] P. A. Grashin, K. A. Sveshnikov, “Ferromagnetic phase in graphene-based planar heterostructures induced by charged impurity”, Ann. Phys., 532:1 (2020), 1900351, 12 pp. | DOI | MR