Is graphene a strongly correlated electron system ? Antonio H. Castro Neto

1. Is graphene a strongly correlated electron system ?Antonio H. Castro Neto Buzios, August 2008

2. Andre Geim A brief history of graphene 2004 – Graphene is isolated by A. Geim and collaborators 1564 – Invention of the pencil

3. Au contacts SiO2 graphite Si Plus some nanotechnology… 2m • optical image • SEM image • design • contacts and mesa

4. Some electronic properties of graphene t’ ~ 0.1 eV A t ~ 2.7 eV A B Next Nearest neighbors Nearest neighbors Unit cell

5. In momentum space Dirac Cone Semi-Metal “Ultra relativistic” Solid State at low speed of light

6. Electron-electron interactions Controlling parameter: In QED: Gonzalez et al. PRL 77, 3589 (96)

7. Perturbative Renormalization group Marginally Irrelevant δμ/δVbg density [Vbg] Martin et al., Nat. Phys. 4, 144 (2008)

8. What about impurity atoms ? • Coulomb impurity in graphene Vitor M. Pereira, Johan Nilsson, AHCN Phys.Rev.Lett. 99, 166802 (2007); Vitor M. Pereira, Valeri Kotov, AHCN Phys. Rev. B 78, 085101 (2008). • Anderson impurity in graphene Bruno Uchoa, Valeri Kotov, Nuno Peres, AHCN Phys. Rev. Lett. 101, 026805 (2008)

10. Undercritical Supercritical

12. E N(E) Anderson’s Impurity Model

14. Non-interacting: U=0 V=0 Broadening Energy Energy

15. Mean-Field

17. U = 1 eV n_up n_down V=1eV, e0=0.2 eV The impurity moment can be switched on and off!

18. U = 40 meV U = 0.1 eV

19. Conclusions • Impurities in graphene behave in an unusual way when compared to normal metals and semiconductors. • One can test theories of nuclear matter under extreme conditions. • Control of the magnetic moment formation of transition metals using electric fields.