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Title: Emergent geometry experienced by fermions in graphene in the presence of dislocations

Abstract

In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov–Bohm effect while the torsion singularity results in Stodolsky effect.

Authors:
 [1];  [2];  [3];  [2]
  1. Low Temperature Laboratory, School of Science and Technology, Aalto University, P.O. Box 15100, FI-00076 AALTO (Finland)
  2. (Russian Federation)
  3. The University of Western Ontario, Department of Applied Mathematics, 1151 Richmond St. N., London (ON), Canada N6A 5B7 (Canada)
Publication Date:
OSTI Identifier:
22451168
Resource Type:
Journal Article
Journal Name:
Annals of Physics
Additional Journal Information:
Journal Volume: 356; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DISLOCATIONS; ELASTICITY; FERMIONS; GRAPHENE; HAMILTONIANS; MAGNETIC FIELDS; QUASI PARTICLES; STRAINS

Citation Formats

Volovik, G.E., L. D. Landau Institute for Theoretical Physics, Kosygina 2, 119334 Moscow, Zubkov, M.A., E-mail: zubkov@itep.ru, and ITEP, B.Cheremushkinskaya 25, Moscow, 117259. Emergent geometry experienced by fermions in graphene in the presence of dislocations. United States: N. p., 2015. Web. doi:10.1016/J.AOP.2015.03.005.
Volovik, G.E., L. D. Landau Institute for Theoretical Physics, Kosygina 2, 119334 Moscow, Zubkov, M.A., E-mail: zubkov@itep.ru, & ITEP, B.Cheremushkinskaya 25, Moscow, 117259. Emergent geometry experienced by fermions in graphene in the presence of dislocations. United States. doi:10.1016/J.AOP.2015.03.005.
Volovik, G.E., L. D. Landau Institute for Theoretical Physics, Kosygina 2, 119334 Moscow, Zubkov, M.A., E-mail: zubkov@itep.ru, and ITEP, B.Cheremushkinskaya 25, Moscow, 117259. Fri . "Emergent geometry experienced by fermions in graphene in the presence of dislocations". United States. doi:10.1016/J.AOP.2015.03.005.
@article{osti_22451168,
title = {Emergent geometry experienced by fermions in graphene in the presence of dislocations},
author = {Volovik, G.E. and L. D. Landau Institute for Theoretical Physics, Kosygina 2, 119334 Moscow and Zubkov, M.A., E-mail: zubkov@itep.ru and ITEP, B.Cheremushkinskaya 25, Moscow, 117259},
abstractNote = {In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov–Bohm effect while the torsion singularity results in Stodolsky effect.},
doi = {10.1016/J.AOP.2015.03.005},
journal = {Annals of Physics},
issn = {0003-4916},
number = ,
volume = 356,
place = {United States},
year = {2015},
month = {5}
}