Quantum Criticality and Minimal Conductivity in Graphene with Long-Range Disorder

2007/02/05 by P. M. Ostrovsky, I. V. Gornyi, A. D. Mirlin · 1 citation
Materials Science · Physics and Astronomy · #Graphene research and applications #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.dis-nn #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevlett.98.256801

published as Phys. Rev. Lett. 98, 256801 (2007) · 4 pages, 1 figure

arxiv created 2007/02/05 · openalex publication_date 2007/06/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We consider the conductivity sigma of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class sigma model including a topological term with theta=pi. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of e(2)/h. When the effective time-reversal symmetry is broken, the symmetry class becomes unitary, and sigma acquires the value characteristic for the quantum Hall transition.

Citations

• Quantum Transport of Massless Dirac Fermions
• Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene
• Molti passi avanti ma resta da fare una lunga strada
• Electric Field Effect in Atomically Thin Carbon Films
• Path integral for gauge theories with fermions

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