1 / 25

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.

saima
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related