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

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

V g (V)  (1/k  ) N im (10 12 cm -2 )  (10 3 cm 2 /Vs) NO 2 Controlling scattering Geim’s group

Tail Mobility (m 2 /V sec)  min (e 2 /h) V g (V) conductivity (mS) X V g (V) conductivity (mS) V g (V) conductivity (mS) V g (V) conductivity (mS) 4e 2 /h 4e 2 /  h Kim’s group

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

3D Schroedinger Coupling

Undercritical Supercritical

Andrei’s group

HIC Neutron stars

E N(E) Anderson’s Impurity Model

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

Mean-Field

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

U = 40 meV U = 0.1 eV

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.