Electronic Multicriticality in Bllayer Graphene

ORAL

Abstract

We use renormalization group (RG) methods to investigate the symmetry-breaking phases of bilayer graphene. We derive the flow equations for different coupling constants that appear in a low-energy effective theory for the system, and show how they may be used to determine the different symmetry-breaking phases in the system. We are able to map out all of the possible phases that the system is unstable to. We also apply our methods to the special case of finite-range, monotonically-decreasing, density-density interactions. We map out which phase(s) that the system is unstable to as a function of the overall interaction strength and of the range. We find that the system is unstable to an antiferromagnetic state for short-range interactions and to a nematic state, in which the parabolic degeneracy of the low-energy modes splits into two Dirac-like cones, for long ranges. Finally, we investigate, within the framework of variational mean field theory, the behavior of the antiferromagnetic state in the presence of a magnetic field applied perpendicular to the sample. We show how to determine the energy gap in the system, and find a slight non-monotonic behavior at low fields and a quasi-linear behavior at high fields. We then compare this result to experimental findings.

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Authors

  • Robert Throckmorton

    Florida State University, National High Magnetic Field Laboratory

  • Chris Neu

    Florida State University, NHMFL, Institut Neel, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China, Florida State University, Department of Physics, Florida State University, Tallahassee, FL, Department of Chemistry and Biochemistry, Florida State University, Tallahassee, FL, Florida State University, National High Magnetic Field Laboratory, Institute of Physics, Chinese Academy of Sciences, China, Austin Peay State University, University of Pardubice, Davidson College, Covenant College, Lookout Mtn, GA 30750, Russian Academy of Sciences, Moscow, RU, University of Tennessee Space Institute, Tullahoma, TN, USA, Sandia National Laboratories,* Albuquerque, NM, Arkansas State University, Jonesboro, AK, None, Mississippi State University, Mississippi State University Department of Physics and Astronomy, Florida State University and the National High Magnetic Field Laboratory, Faculte des Sciences et Techniques and Universite Aix-Marseille, MIT Haystack Observatory, Departments of Chemistry and Physics, University of Tennessee of Chattanooga, Departments of Chemistry and Physics, University of Tennessee at Chattanooga, Western Kentucky University, Thomas Jefferson National Accelerator Facility, Newport News, VA, Fermilab, University of Virginia and Fermilab, Indiana University Bloomington, Indiana University Health Proton Therapy Center, University of North Florida, National Superconducting Cyclotron Laboratory, Michigan State University, Flordia State University, Louisiana State University, Washington University, Argonne National Laboratory, Lawrence Berkeley National Laboratory, Department of Physics, Florida State University., JINR, Tsinghua University, LBNL, LBNL/Vanderbilt University, Vanderbilt University, Florida A\&M University, Georgia Institute of Technology, Department of Physics, Virginia Tech, Gatton Academy, Exeter University, Florida International University, Office of Research, University of North Florida, Physics Department, University of North Florida, NSCL, Michigan State University, Physics Department, Florida State University, University of Tennessee-Knoxville, Neel Institut, Kazan Federal University, Bielefeld University, Ben Gurion University, LCIB - CEA, University of Georgia, Lawrence Livermore National Laboratory, Livermore, CA 94550, NHMFL, Tallahassee, USA, Department of Chemistry, University of Waterloo, Ontario, Canada, NHMFL, Tallahassee FL 32310 USA, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany, Wigner Research Center for Physics, Budapest, Hungary, Experimental physics II, University of Augsburg, Germany, Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, National High Magnetic Field Laboratory Florida State University, Tallahassee, Florida 32310, IM2NP-CNRS (UMR 7334) and Universite Aix-Marseille, National High Magnetic Field Laboratory Applied Superconductivity Center, Heifei National Lab for Physical Science at Microscale, USTC, Institute of Physics, Chinese Academy of Sciences, Department of Electrical Engineering, Rice University, National High Magnetic Field Laboratory, National High Magnetic Field Laboratory/FSU, University of Virginia

  • Oskar Vafek

    Florida State University, National High Magnetic Field Laboratory