Eur. Phys. J. B (2016) 89: 213
https://doi.org/10.1140/epjb/e2016-70182-7

Regular Article

Landau levels in graphene in the presence of emergent gravity

¹ Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117259 Moscow, Russia
² Moscow Institute of Physics and Technology, 9, Institutskii per., Dolgoprudny, 141700 Moscow Region, Russia
³ Far Eastern Federal University, School of Biomedicine, 690950 Vladivostok, Russia
⁴ National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe highway 31, 115409 Moscow, Russia

^a e-mail: zubkov@itep.ru

Received: 22 March 2016
Received in final form: 2 July 2016
Published online: 3 October 2016

Abstract

We consider graphene in the presence of external magnetic field and elastic deformations that cause emergent magnetic field. The total magnetic field results in the appearance of Landau levels in the spectrum of quasiparticles. In addition, the quasiparticles in graphene experience the emergent gravity. We consider the particular choice of elastic deformation, which gives constant emergent magnetic field and vanishing torsion. Emergent gravity may be considered as perturbation. We demonstrate that the corresponding first order approximation affects the energies of the Landau levels only through the constant renormalization of Fermi velocity. The degeneracy of each Landau level receives correction, which depends essentially on the geometry of the sample. There is the limiting case of the considered elastic deformation, that corresponds to the uniformly stretched graphene. In this case in the presence of the external magnetic field the degeneracies of the Landau levels remain unchanged.