摘要Starting with the U(1)−gauge covariant four-dimensional Dirac equation, we derive the analytic solutions describing the chiral massless fermions evolving in static orthogonal magnetic and electric fields. Working in cylindric coordinates, we compute the electric current density essential component and the off-diagonal conductivities. By summing up the conductivities of the two distinct species of electrons connected to the orientation of spin, the well-known 4n-quantization law is restored.
Abstract：Starting with the U(1)−gauge covariant four-dimensional Dirac equation, we derive the analytic solutions describing the chiral massless fermions evolving in static orthogonal magnetic and electric fields. Working in cylindric coordinates, we compute the electric current density essential component and the off-diagonal conductivities. By summing up the conductivities of the two distinct species of electrons connected to the orientation of spin, the well-known 4n-quantization law is restored.
[1] Wellington da Cruz 2003 Chaos, Solitons and Fractals 17 975
Georgiev L S 2004 Phys. Rev. B 69 085305
Castro Neto A H et al 2009 Rev. Mod. Phys. 81 109
[2] Novoselov K S et al 2006 Nature Phys. 2 177
[3] Gusynin V P and Sharapov S G 2006 Phys. Rev. B 73 245411
[4] Beneventano C G and Santangelo E M 2008 J. Phys. A 41 164035
[5] Creutz M 2008 J. High Eerngy Phys. 0804 017
Mecklenburg M, Woo J and Regan B C 2010 Phys. Rev. B 81 245401
[6] Dariescu M A, Dariescu C and Murariu G 2006 Chaos, Solitons and Fractals 28 1
Dariescu M A and Dariescu C 2007 J. Phys.: Condens Matter 19 256203
[7] Novoselov K S et al 2005 Nature 438 197
[8] Jackiw R and Pi S Y Arxiv:0808.1562[cond-mat]
[9] Zhang Y et al 2005 Nature 438 201
[10] Romanovsky I, Yannouleas C and Landman U 2009 Phys. Rev. B 79 075311
[11] Jain J K 2007 Composite Fermions (Cambridge: Cambridge Univ Press)
Yannouleas C and Landman U 2007 Rep. Prog. Phys. 70 2067
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