On localization of Dirac fermions by disorder

Medvedyeva, M.V. (2011)

Doctoral Thesis

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.

• Phase transition
• Dirac fermions
• Majorana bound states
• Nanomechanics
• Graphene
• P-, d- wave superconductor
• Disorder

• All authors: Medvedyeva, M.V.
• Supervisor: Beenakker, C.W.J.
• Co-supervisor: Blanter, Y.M.; Tworzydlo, J.
• Qualification: Doctor (dr.)
• Awarding Institution: Leiden University Medical Center (LUMC), Leiden University
• Date: 2011-05-03
• Title of host publication: Casimir PhD Series
• ISBN (print): 9789085930990
• Name: 2011-09
• Sponsorship: Foundation for Fundamental Research of Matter