Graphene: electrons in the flatland Antonio H. Castro Neto Seoul, September 2008

Disclaimer Graphene is discovered IQHE measured Andre Geim Kostya Novoselov Philip Kim AHCN, P. Guinea, N. Peres, K. Novoselov, A. Geim, Rev. Mod. Phys. (2008)

A brief history of graphene

5  m

Plus some nanotechnology… 2m2m SiO 2 Si Au contacts graphite  optical image  SEM image  design  contacts and mesa

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

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

Novoselov et al, Science 306, 666 (2004)

Outline Coulomb impurity in graphene Vitor M. Pereira, Johan Nilsson, AHCN Phys.Rev.Lett. 99, (2007); Vitor M. Pereira, Valeri Kotov, AHCN Phys. Rev. B 78, (2008). Anderson impurity in graphene Bruno Uchoa, Valeri Kotov, Nuno Peres, AHCN Phys. Rev. Lett. 101, (2008); Bruno Uchoa, Chiung-Yuan Lin, Nuno Peres, AHCN Phys.Rev.B 77, (2008)‏. Johan Nilsson Bruno UchoaVitor Pereira Valeri Kotov Nuno Peres

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

3D Schroedinger Coupling

Undercritical Supercritical

Andrei’s group

HIC Neutron stars

1 nm

E N(E) Anderson’s Impurity Model T>T K

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.