Supercritical Instability of Dirac Electrons in the Field of Two Oppositely Charged Nuclei
DOI:
https://doi.org/10.15407/ujpe61.09.0759Keywords:
supercritical instability, wave-function localization change, critical dipole moment, LCAO methodAbstract
The Dirac equation for an electron in a finite dipole potential has been studied within the method of linear combination of atomic orbitals (LCAO). The Coulomb potential of the nuclei that compose a dipole is regularized, by considering the finite nuclear size. It is shown that if the dipole momentum reaches a certain critical value, the novel type of supercriticality occurs; namely, the wave function of the highest occupied electron bound state changes its localization from the negatively charged nucleus to the positively charged one. This phenomenon can be interpreted as a spontaneous creation of an electron-positron pair in vacuum, with each of the created particles being in the bound state with the corresponding nucleus and partially screening it.
References
P.A.M. Dirac, The quantum theory of the electron. Part II, Proc. R. Soc. London, A 118, 351 (1928).
http://dx.doi.org/10.1098/rspa.1928.0056
C.G. Darwin, The wave equations of the electron, Proc. R. Soc. London, A 118, 654 (1928).
http://dx.doi.org/10.1098/rspa.1928.0076
W. Gordon, Die energieniveaus des wasserstoffatoms nachder diracschen quantentheorie des elektrons, Z. Phys. 48, 11 (1928).
http://dx.doi.org/10.1007/BF01351570
I.Ya. Pomeranchuk and Y.A. Smorodinsky, On energy levels in systems with > 137, J. Phys. USSR 9, 97 (1945).
Ya.B. Zeldovich and V.N. Popov, Electronic structure of superheavy atoms, Sov. Phys. Usp. 14, 673 (1972).
http://dx.doi.org/10.1070/PU1972v014n06ABEH004735
W. Greiner, B. M¨uller, and J. Rafelski, Quantum Electro-dynamics of Strong Fields (Springer, Berlin, 1985).
http://dx.doi.org/10.1007/978-3-642-82272-8
S.S. Gershtein and Ya.B. Zeldovich, Positron production during the mutual approach of heavy nuclei and the polarization of the vacuum, Sov. Phys. JETP 30, 358 (1970).
J. Rafelski, L.P. Fulcher, and W. Greiner, Superheavy elements and an upper limit to the electric field strength, Phys. Rev. Lett. 27, 958 (1971).
http://dx.doi.org/10.1103/PhysRevLett.27.958
B. M¨uller, H. Peitz, J. Rafelski, and W. Greiner, Solution of the Dirac equation for strong external fields, Phys. Rev. Lett. 28, 1235 (1972).
http://dx.doi.org/10.1103/PhysRevLett.28.1235
M.S. Marinov and V.S. Popov, Critical distance in collision of heavy ions, Sov. Phys. JETP 41, 205 (1975).
K.S. Novoselov, A.K. Geim, S.V. Morozov et al., Electric field effect in atomically thin carbon films, Science 306, 666 (2004).
http://dx.doi.org/10.1126/science.1102896
V.P. Gusynin, S.G. Sharapov, and J.P. Carbotte, AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics, Int. J. Mod. Phys. B 21, 4661 (2007).
http://dx.doi.org/10.1142/S0217979207038022
A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, and A.K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
http://dx.doi.org/10.1103/RevModPhys.81.109
D.S.L. Abergel, V. Apalkov, J. Berashevich, K. Ziegler, and T. Chakraborty, Properties of graphene: A theoretical perspective, Adv. Phys. 59, 261 (2010).
http://dx.doi.org/10.1080/00018732.2010.487978
G. Giovanetti, P.A. Khomyakov et al., Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations, Phys. Rev. B 76, 073103 (2007).
http://dx.doi.org/10.1103/PhysRevB.76.073103
L.A. Ponomarenko et al., Nature 497, 594 (2013).
http://dx.doi.org/10.1038/nature12187
O.V. Gamayun, E.V. Gorbar, and V.P. Gusynin, Supercritical Coulomb center and excitonic instability in graphene, Phys. Rev. B 80, 165429 (2009).
http://dx.doi.org/10.1103/PhysRevB.80.165429
Y. Wang et al., Observing atomic collapse resonances in artificial nuclei on graphene, Science 340, 734 (2013).
http://dx.doi.org/10.1126/science.1234320
O.O. Sobol, E.V. Gorbar, and V.P. Gusynin, Supercritical instability in graphene with two charged impurities, Phys. Rev. B 88, 205116 (2013).
http://dx.doi.org/10.1103/PhysRevB.88.205116
O.O. Sobol, Variational method for the calculation of critical distance between two Coulomb centers in graphene, Ukr. J. Phys. 59, 531 (2014).
http://dx.doi.org/10.15407/ujpe59.05.0531
A. de Martino, D. Klopfer, D. Matrasulov, and R. Egger, Electric-dipole-induced universality for Dirac fermions in graphene Phys. Rev. Lett. 112, 186603 (2014).
http://dx.doi.org/10.1103/PhysRevLett.112.186603
E.V. Gorbar, V.P. Gusynin, and O.O. Sobol, Supercritical electric dipole and migration of electron wave function in graphene, Europhys. Lett. 111, 37003 (2015).
http://dx.doi.org/10.1209/0295-5075/111/37003
E.V. Gorbar, V.P. Gusynin, and O.O. Sobol, Supercriticality of novel type induced by electric dipole in gapped graphene, Phys. Rev. B 92, 235417 (2015).
http://dx.doi.org/10.1103/PhysRevB.92.235417
E. Fermi and E. Teller, The capture of negative mesotrons in matter, Phys. Rev. 72, 399 (1947).
http://dx.doi.org/10.1103/PhysRev.72.399
J.E. Turner, Minimum dipole moment required to bind an electron–molecular theorists rediscover phenomenon mentioned in Fermi–Teller paper twenty years earlier, Am. J. Phys. 45, 758 (1977).
http://dx.doi.org/10.1119/1.10767
D.I. Abramov and V.I. Komarov, Weakly bound states of a charged particle in a finite-dipole field, Theor. Math. Phys. 13, 1090 (1972).
http://dx.doi.org/10.1007/BF01035530
K. Connolly and D.J. Griffiths, Critical dipoles in one, two, and three dimensions, Am. J. Phys. 75, 524 (2007).
http://dx.doi.org/10.1119/1.2710485
V.I. Matveev, M.M. Musakhanov, and D.U. Matrasulov, Dirac electron in the electric dipole field, hep-th/9501027.
J. von Neumann and E.P. Wigner, Uber die analytischen eigenschaften von gruppen linearer transformationen und ihrer darstellungen, Z. Phys. 30, 467 (1929).
http://dx.doi.org/10.1007/bf01187749
L.D. Landau and E.M. Lifshitz, Quantum Mechanics. Non-Relativistic Theory (Pergamon Press, New York, 1977).
H.A. Bethe and E.E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer, Berlin, 1957).
http://dx.doi.org/10.1007/978-3-662-12869-5
P. Marmier and E. Sheldon, Physics of Nuclei and Particles, Vol. 1 (Academic Press, New York, 1969).
C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics, Vol. 2 (Hermann, Paris, 1977).
Downloads
Published
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
