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

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

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

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

Perturbative Renormalization group Marginally Irrelevant δμ/δ V bg density [V bg ] Martin et al., Nat. Phys. 4, 144 (2008)

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) What about impurity atoms ?

Undercritical Supercritical

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.