A few topics in Graphene physics Antonio H

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

Outline • Coulomb impurity in graphene Vitor M. Pereira, Johan Nilsson, Valeri Kotov Phys. Rev. Lett. 99, 166802 (2007); ar. Xiv: 0803. 4195 • Anderson impurity in graphene Bruno Uchoa, Chiung-Yuan Lin, Valeri Kotov, Nuno Peres Phys. Rev. B 77, 035420 (2008); ar. Xiv: 0802. 1711

(1/k ) NO 2 2 1 0 -40 -20 0 20 Vg (V) 40 6 (103 cm 2/Vs) Controlling scattering 4 2 0 0 Geim’s group Nim 1 (1012 cm-2) 2

12 conductivity (m. S) smin (e 2/h) 16 8 4 0 4 e 2/h 4 e 2/ph 0 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 1. 4 10 8 6 4 2 0 -50 Tail Mobility (m 2/V sec) 0 50 8 6 4 X 2 2 0 -50 0 Vg (V) 50 10 conductivity (m. S) Vg (V) 8 6 4 2 0 -50 0 50 Vg (V) Kim’s group 10 8 6 4 2 0 -50 0 Vg (V) 50

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

Coupling 3 D Schroedinger

Undercritical Supercritical

Andrei’s group

HIC Neutron stars

E N(E) Anderson’s Impurity Model

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

Mean-Field

U = 1 e. V n_up n_down V=1 e. V, e 0=0. 2 e. V The impurity moment can be switched on and off!

U = 40 me. V U = 0. 1 e. V

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.