Localization and the Kosterlitz-Thouless Transition in Disordered Graphene

2008/10/11 by Yanyang Zhang, Yan-Yang Zhang, Jiangping Hu +7
Materials Science · Physics and Astronomy · #Graphene research and applications #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.dis-nn

paper · pdf · doi:10.1103/physrevlett.102.106401

published as Phys. Rev. Lett 102, 106401 (2009) · 5 pages, 4 figures

arxiv created 2008/10/11 · openalex publication_date 2009/03/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate disordered graphene with strong long-range impurities. Contrary to the common belief that delocalization should persist in such a system against any disorder, as the system is expected to be equivalent to a disordered two-dimensional Dirac fermionic system, we find that states near the Dirac points are localized for sufficiently strong disorder (therefore inevitable intervalley scattering) and the transition between the localized and delocalized states is of Kosterlitz-Thouless type. Our results show that the transition originates from bounding and unbounding of local current vortices.

Citations

• Berry's Phase and Absence of Back Scattering in Carbon Nanotubes
• Topological Delocalization of Two-Dimensional Massless Dirac Fermions
• Density Inhomogeneity Driven Percolation Metal-Insulator Transition and Dimensional Crossover in Graphene Nanoribbons
• Numerical studies of localization in disordered systems
• Spatial distribution of local currents of massless Dirac fermions in quantum transport through graphene nanoribbons
• Impurity Scattering in Carbon Nanotubes – Absence of Back Scattering –
• Ordering, metastability and phase transitions in two-dimensional systems
• Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions