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A new field dependence of Landau levels in a graphene-like structure

A new field dependence of Landau levels in a graphene-like structure. Petra Dietl , Ecole Polytechnique student Frédéric Piéchon, LPS G. M. PRL 100 , 146802 (2008) . www.lps.u-psud.fr/users/gilles. field dependence of Landau levels . Schrödinger electron gas.

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A new field dependence of Landau levels in a graphene-like structure

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  1. A new field dependence of Landau levels in a graphene-like structure Petra Dietl , Ecole Polytechnique student Frédéric Piéchon, LPS G. M. PRL 100, 146802 (2008) www.lps.u-psud.fr/users/gilles

  2. field dependence of Landau levels Schrödinger electron gas Graphene: Weyl (massless Dirac) electron gas other field dependencies for 2D gas ?

  3. new field dependence of Landau levels hybrid 2D electron gas : new dispersion relation

  4. tight-binding problem on honeycomb lattice Y. Hasegawa et al., 2006 hexagonal Bravais lattice+2 atoms basis B A Bloch theorem: Gap ?

  5. graphene: isotropic Dirac gas Dirac points energy bands isotropic Dirac gas

  6. Landau levels of graphene honeycomb lattice in a magnetic field low field Hofstadter-Rammal butterfly 5 3 5 3 1 1 -1 -1 -3 -5 -3 -5 Valley degeneracy 2-fold degeneracy of LL

  7. anisotropicDirac gas energy bands moving Dirac points

  8. Landau levels of anisotropicDirac gas low field 2 3 lifts 2-fold LL degeneracy 1 -1 -3 -2 Y. Hasegawa, M. Kohmoto, 2006

  9. anisotropicDirac gas moving Dirac points

  10. anisotropic hybrid Schrödinger-Dirac gas energy bands Merging of Dirac points

  11. “hybrid” gas 2 1 -1 -2

  12. hybrid Schrödinger-Dirac gas Density of states Onsager argument gap opening

  13. A simple problem of quantum mechanics Instead of for a linear spectrum

  14. Quartic oscillator Harmonic oscillator

  15. g and Berry’s phase Roth, 1966 Wilkinson

  16. Universal features for 2D lattices with two atoms basis oblique lattice model

  17. Phase diagram GAP GAP graphene Dirac spectrum “Hybrid” spectrum 1 GAP GAP

  18. Summary • tight binding Hamiltonian on honeycomb lattice • motion and merging of Dirac points • universal features of 2D Bravais lattices with 2 atoms basis experimental realization? A. Kobayashi, S. Katayama,Y. Suzumura, H. Fukuyama (2006) Massless Dirac fermions in organic conductor a-(BEDT-TTF)2I3‏ ‏ (J.N. Fuchs, M.O. Goerbig, F. Piéchon and G.M. arXiv:0803.0912 next nearest neighbor hopping  tilted cones Landau levels with renormalized velocity and Quantum Hall effect Realization of a graphene structure in atomic gases

  19. Dirac cones in organic conductors 4 atoms basis, 8 hopping integrals

  20. hybrid model transition line 2atoms basis 4 hopping integrals tilted Dirac cones I= conic II= conic, but metallic III= gap

  21. It is enough to consider… 4 atoms per cell, 8 hopping integrals 2 atoms per cell, 4 hopping integrals

  22. I = conic IV= gap

  23. Chocolate The Chocolate LEDERER Prize The NOBEL Prize Lederer FRANCAIS First recipient : Pascal Lederer FRANCAIS

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