Quantum critical scaling in magnetic field near the Dirac point in graphene

ORAL

Abstract

Graphene, a monolayer of graphite, exhibits some peculiar electronic properties which are consequences of the pseudo relativistic Dirac like excitations. The anomalous integer quantum Hall effect, i. e. platoues in Hall conductivity $\sigma_{xy}$ at filling factors $f=\pm(4 n+2)$, which can be understood within the framework of non-interacting Dirac like quasiparticles is one of such. On the other hand, the appearance of additional Hall states at filling factors $f=0$ and $f=\pm 1$ at higher magnetic fields calls for electron-electron interactions to be taken into account. Motivated by the recent measurement of the activation energy at the quantum Hall state at the filling factor $f =1$ in graphene, I will discuss the scaling of the interaction-induced gaps in the vicinity of the Dirac point with the magnetic field. The gap at $f =1$ is shown to be bounded from above by $E(1)/C$, where $E(n)={v_F}\sqrt{2nB}$ is the Landau-level energy and $C=5.985+O{1/N}$ is a universal number. The universal scaling functions computed exactly for a large number of Dirac fermions N will also be presented. The sublinear dependence of the gap at the laboratory fields of $10 T

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Authors

  • Bitan Roy

    Simon Fraser University

  • Anthony Colaprete

    Triumf, Texas A\&M University, Tel Aviv University, TRIUMF, Simon Fraser University, Dept. of Physics, SFU, BC, Canada, Department of Physics and Astronomy, University of British Columbia, Cavendish Laboratory, University of Cambridge, Department of Physics, Simon Fraser University, University of British Columbia, University of Wisconsin-Madison, Brookhaven National Laboratory, Los Alamos National Laboratory, Department of Molecular Science and Technology, Ajou University, Suwon 443-749, Korea, Department of Physics, Oregon State University, Corvallis, OR 97331-6507, Imago Scientific Instruments Corp., Department of Physics, Simon Fraser University, 8888 University Dr., Burnaby, BC, V5A 1S6 Canada, Linfield College, PNNL, University of Washington, University of Victoria, IUPUI1, Wabash, IUPUI2, Environmental Biotechnology Institute, University of Idaho, Moscow ID 83843, Physics Department, University of Idaho, Moscow ID 83843, Environmental Biotechnology Institute, University of Idaho, Moscow, ID 83844, Physics Department, University of Idaho, Moscow, Idaho 83844, TRIUMF / UBC, 5CSNSM-IN2P3-CNRS, Universit\'e Paris 11, University of Manitoba, Texas A\&M, U. Manitoba, Tel Aviv U., U. British Columbia, Universidad de Pa\'is Vasco, Department of Physics, University of Idaho, Moscow, Idaho 83844-0903, University of Idaho, Boise State University, Idaho State University, NASA Ames Research Center