1. A few topics in Graphene physics Antonio H. Castro Neto San Sebastian, May 2008

2. Coulomb impurity in graphene Vitor M. Pereira, Johan Nilsson, Valeri Kotov Phys.Rev.Lett. 99, 166802 (2007); arXiv:0803.4195 Anderson impurity in graphene Bruno Uchoa, Chiung-Yuan Lin, Valeri Kotov, Nuno Peres Phys.Rev.B 77, 035420 (2008)‏; arXiv:0802.1711 Outline

5. -40-2004020 V g (V)  (1/k  ) 0 1 2 N im (10 12 cm -2 )  (10 3 cm 2 /Vs) 0 2 4 6 012 NO 2 Controlling scattering Geim’s group

6. Tail Mobility (m 2 /V sec)  min (e 2 /h) 12 8 4 0 1.41.21.00.80.60.40.20 16 10 8 6 4 2 0 -50050 V g (V) conductivity (mS) X 2 10 8 6 4 2 0 -50050 V g (V) conductivity (mS) 10 8 6 4 2 0 -50050 V g (V) conductivity (mS) 10 8 6 4 2 0 -50050 V g (V) conductivity (mS) 4e 2 /h 4e 2 /  h Kim’s group

7. Pereira et al., Phys.Rev.Lett. 99, 166802 (2007);

8. 3D Schroedinger Coupling

9. Undercritical Supercritical

11. Andrei’s group

13. HIC Neutron stars

16. E N(E) Anderson’s Impurity Model

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

19. Mean-Field

21. The impurity moment can be switched on and off! U = 1 eV n_down V=1eV, e 0 =0.2 eV n_up

22. U = 40 meV U = 0.1 eV

23. 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.