On localization of Dirac fermions by disorder

Leiden Repository

On localization of Dirac fermions by disorder

Type: Doctoral Thesis
Title: On localization of Dirac fermions by disorder
Author: Medvedyeva, Mariya Vyacheslavivna
Publisher: Instituut Lorentz for Theoretical Physics, Leiden Institute of Physics (LION), Faculty of Science, Leiden University
Issue Date: 2011-05-03
Keywords: Phase transition
Dirac fermions
Majorana bound states
Nanomechanics
Graphene
P-, d- wave superconductor
Disorder
Abstract: This thesis is devoted to the effects of disorder on two-dimensional systems of Dirac fermions. Disorder localizes the usual electron system governed by the Schroedinger equation. The influence of disorder on Dirac fermions is qualitevely different. We concentrate on a random mass term in the Dirac equation. We have discovered that Dirac fermions in graphene are localized by a random mass, without any transition into metallic state. The situation is entirely different for Dirac fermions in a p-wave superconductor. There electrostatic disorder appears in the Dirac equation as a random mass, which localizes the excitation, but only if the disorder is relatively weak. For large mass fluctuations a transition into metallic state appears. This qualitatively different response to disorder in graphene and in p-wave superconductors is explained by the appearance of Majorana bound states, which allow for resonant tunneling and metallic state. Electrostatic disorder in a d-wave superconductor represented as random vector potential in the Dirac equation. We look at the transmission of Dirac fermions for electrostatic potential with long- and short-range fluctuations. We study the interplay of electrical and mechanical properties of suspended graphene by calculating the correction to the conductivity due to its deformation by a gate electrode.
Description: Promotor: C.W.J. Beenakker, Co-promotores: Y.M. Blanter, J. Tworzydlo
With Summary in Dutch
Faculty: Faculteit der Wiskunde en Natuurwetenschappen
Citation: Medvedyeva, M.V., 2011, Doctoral Thesis, Leiden University
Series/Report no.: CasimirPhD Series
2011-09
ISBN: 9789085930990
Sponsor: Foundation for Fundamental Research of Matter
Handle: http://hdl.handle.net/1887/17606
 

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