Liubov Lokot

Creation of bielectron of Dirac cone: the tachyon solution in magnetic field, F1000Physics: Condens. Matter; F1000.com/Workspace

Blog Post created by Liubov Lokot on Jul 24, 2017

Schrödinger equation for pair of two massless Dirac particles when magnetic field is applied in Landau gauge is solved exactly. In this case the separation of center of mass and relative motion is obtained. Landau quantization $\epsilon=\pm\,B\sqrt{l}$ for pair of two Majorana fermions coupled via a Coulomb potential from massless chiral Dirac equation in cylindric coordinate is found. The root ambiguity in energy spectrum leads into Landau quantization for bielectron, when the states in which the one simultaneously exists are allowed. The tachyon solution with imaginary energy in Cooper problem ($\epsilon^{2}<0$) is found. The continuum symmetry of Dirac equation allows perfect pairing between electron Fermi spheres when magnetic field is applied in Landau gauge creating a Cooper pair.

 

Citation  (bibtex)   [Switch view]

 

@BOOK{Berestetskii:1989qr,

    title = {Quantum Electrodynamics},

    publisher = {Nauka, Moskow},

    author = {Berestetskii, V.~B. and Lifshitz, E.~M. and Pitaevskii, L.~P.},

    year = {1989},

    edition = {3th},

}

 

@ARTICLE{Novoselov:2005jd,

    author = {Novoselov, K.~S. and Geim, A.~K. and Morozov, S.~V. and Jiang, D. and Katsnelson, M.~I. and Grigorieva, I.~V. and Dubonos, S.~V. and

Firsov, A.~A.},

    title = {},

    journal = {Nature},

    year = {2005},

    volume = {438},

    pages = {197},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Wallace:1947jd,

    author = {Wallace, P.~R.},

    title = {},

    journal = {Phys. Rev.},

    year = {1947},

    volume = {71},

    pages = {622},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Gusynin3:2007jd,

    author = {Gusynin, V.~P. and Sharapov, S.~G. and Carbotte, J.~P.},

    title = {},

    journal = {International Journal of Modern Physics B},

    year = {2007},

    volume = {21},

    pages = {4611},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Malard:2008jd,

    author = {Malard, L~M. and Mafra, D.~L. and Guimaraes, M.~H.~D. and Mazzoni, M.~S.~C. and Jorio, A.},

    title = {},

    journal = {Phys. Rev. B, arXiv:0812.1293v1 [cond-mat.mes-hall]},

    year = {2009},

    volume = {79},

    pages = {125426},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Vasko:2008jd,

    author = {Vasko, F.~T. and Ryzhii, V.},

    title = {},

    journal = {Phys. Rev. B},

    year = {2008},

    volume = {77},

    pages = {195433},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

 

@ARTICLE{Stroucken1:2011jd,

    author = {Gr\"{o}nqvist, J.~H. and Stroucken, T. and Begh\"{a}user, G. and Koch, S.~W.},

    title = {},

    journal = {arXiv:1107.5653v1 [cond-mat.mtrl-sci] (2011)},

    year = {2011},

    volume = {},

    pages = {},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Alicea:2006jd,

    author = {Alicea, J. and Fisher, M.~P.~A.},

    title = {},

    journal = {Phys. Rev. B},

    year = {2006},

    volume = {74},

    pages = {075422},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Stroucken:2011jd,

    author = {Stroucken, T. and Gr\"{o}nqvist, J.~H. and Koch, S.~W.},

    title = {},

    journal = {Phys. Rev. B},

    year = {2011},

    volume = {84},

    pages = {205445},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Malic:2011jd,

    author = {Malic, Ermin and Winzer, Torben and Bobkin, Evgeny and Knorr, Andreas},

    title = {},

    journal = {Phys. Rev. B},

    year = {2011},

    volume = {84},

    pages = {205406},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Gamayun:2009jd,

    author = {Gamayun, O.~V. and Gorbar, E.~V. and Gusynin, V.~P.},

    title = {},

    journal = {Phys. Rev. B},

    year = {2009},

    volume = {80},

    pages = {165429},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Hartmann:2011jd,

    author = {Hartmann, R.~R. and Shelykh, I.~A. and Portnoi, M.~E.},

    title = {},

    journal = {Phys. Rev. B, arXiv:1012.5517v2 [cond-mat.mes-hall] (2011)},

    year = {2011},

    volume = {84},

    pages = {035437},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Zhang:2005jd,

    author = {Zhang, Y. and Tan, Y.~W. and St\"{o}rmer, H.~L. and Kim, P.},

    title = {},

    journal = {Nature},

    year = {2005},

    volume = {438},

    pages = {201},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Semenoff:1984jd,

    author = {Semenoff, G.},

    title = {},

    journal = {Phys. Rev. Lett.},

    year = {1984},

    volume = {53},

    pages = {2449},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Zheng:2002jd,

    author = {Zheng, Y. and Ando, T.},

    title = {},

    journal = {Phys. Rev. B},

    year = {2002},

    volume = {65},

    pages = {245420},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Gusynin1:2005jd,

    author = {Gusynin, V.~P. and Sharapov, S.~G.},

    title = {},

    journal = {Phys. Rev. Lett.},

    year = {2005},

    volume = {95},

    pages = {146801},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Gusynin2:2006jd,

    author = {Gusynin, V.~P. and Sharapov, S.~G.},

    title = {},

    journal = {Phys. Rev. B},

    year = {2006},

    volume = {73},

    pages = {245411},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Peres:2006jd,

    author = {Peres, N.~M.~R. and Guinea, F. and Castro Neto, A.~H.},

    title = {},

    journal = {Phys. Rev. B},

    year = {2006},

    volume = {73},

    pages = {125411},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Berry:1984jd,

    author = {Berry, M.~V.},

    title = {},

    journal = {Proc. R. Soc. London A},

    year = {1984},

    volume = {392},

    pages = {45},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Carmier:2008jd,

    author = {Carmier, P. and Ullmo, D.},

    title = {},

    journal = {Phys. Rev. B},

    year = {2008},

    volume = {77},

    pages = {245413},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Novikov:2007jd,

    author = {Novikov, D.~S.},

    title = {},

    journal = {Phys. Rev. B, arXiv:0706.1391[cond-mat.mes-hall]},

    year = {2007},

    volume = {76},

    pages = {245435},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{lol:2015jd,

    author = {Lokot, Lyubov~E.},

    title = {},

    journal = {arXiv: 1409.0303v3 [cond-mat.mes-hall] (2015)},

    year = {2015},

    volume = {},

    pages = {},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@BOOK{Landau:1977qr,

    title = {Quantum Mechanics. Non-Relativistic Theory},

    publisher = {Pergamon, NewYork},

    author = {Landau, L.~D. and Lifshitz, E.~M.},

    year = {1977},

    edition = {},

}

 

@ARTICLE{McClure:1956jd,

    author = {McClure, J.~W.},

    title = {},

    journal = {Phys. Rev.},

    year = {1956},

    volume = {104},

    pages = {666},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Nandkishore:2012jd,

    author = {Nandkishore, R. and Levitov, L.~S. and Chubukov A.~V.},

    title = {},

    journal = {Nature Physics},

    year = {2012},

    volume = {1},

    pages = {1},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Rashba:1969jd,

    author = {Rashba, E.~I. and Edelshteyin, B.~M.},

    title = {},

    journal = {JETP Letters},

    year = {1969},

    volume = {9},

    pages = {475},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{Julian:2012jd,

    author = {Julian, S.},

    title = {},

    journal = {Physics},

    year = {2012},

    volume = {5},

    pages = {17},

    number = {},

    month = {},

    publisher = {Publisher}

}

 

@ARTICLE{lokot:2015jd,

    author = {Lokot, Lyubov~E.},

    title = {},

    journal = {SSRG International Journal Material Science and Engineering, arXiv: 1501.03696v2 [cond-mat.mes-hall] (2015)},

    year = {2015},

    volume = {1},

    pages = {1},

    number = {2},

    month = {},

    publisher = {Publisher}

}

Attachments

Outcomes