Conformal mapping and shot noise in graphene

Adam Rycerz, Patrik Recher, and Michael Wimmer
Phys. Rev. B 80, 125417 – Published 18 September 2009

Abstract

Ballistic transport through a collection of quantum billiards in undoped graphene is studied analytically within the conformal mapping technique. The billiards show pseudodiffusive behavior, with the conductance equal to that of a classical conductor characterized by the conductivity σ0=4e2/πh and the Fano factor F=1/3. By shrinking at least one of the billiard openings, we observe a tunneling behavior, where the conductance shows a power-law decay with the system size, and the shot noise is Poissonian (F=1). In the crossover region between tunneling and pseudodiffusive regimes, the conductance G(1F)×se2/h. The degeneracy s=8 for the Corbino disk, which preserves the full symmetry of the Dirac equation, s=4 for billiards bounded with smooth edges which break the symplectic symmetry, and s=2 when abrupt edges lead to strong intervalley scattering. An alternative, analytical, or numerical technique is utilized for each of the billiards to confirm the applicability of the conformal mapping for various boundary conditions.

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  • Received 12 June 2009

DOI:https://doi.org/10.1103/PhysRevB.80.125417

©2009 American Physical Society

Authors & Affiliations

Adam Rycerz1,2, Patrik Recher3, and Michael Wimmer2,*

  • 1Marian Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, PL-30059 Kraków, Poland
  • 2Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
  • 3Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany

  • *Present address: Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands.

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Issue

Vol. 80, Iss. 12 — 15 September 2009

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