"Grafeno : Prêmio Nobel em Física de 2010 e Perspectivas Tecnológicas“ 20/04/2011 "Grafeno : Prêmio Nobel em Física de 2010 e Perspectivas Tecnológicas“ Yakov Kopelevich Instituto de Física "Gleb Wataghin", UNICAMP

Nobel Prize in Physics 2010 – GRAPHENE (Andrei Geim & Konstantin Novoselov). According to the Oficial Web Site of the Nobel Prize (Nobelprize.org) this Prize has been awarded for “groundbreaking experiments regarding the two-dimensional material graphene”.

Carbon allotropes

Why graphene ? What are the “groundbreaking experiments” regarding this material ?

Has graphene been experimentally obtained first in 2004 ? Actually, prior observations of graphene date back to at least 1962. H. P. Boehm et al. Zeitschrift für Naturforschung B 17, 150 (1962). (TEM)

EXPERIMENTS on GRAPHENE: 1992 1997

2000 2001

HOPG = Highly Oriented Pyrolitic Graphite FLG c-axis With AFM tip: Xuekun Lu, Minfeng Yu, Hui Huang and Rodney S Ruoff Nanotechnology , 1999

The crystal structure of graphite: layers of honeycomb lattices of carbon atoms d = B A The single-atom thick graphitic plane is called "graphene" Dirac-like cone spectrum: E(p) =  vp; v ~ t||a/ћ, v  106 m/s F Band structure of one graphitic layer K - Fermi point

Quantum Hall Effect Klaus von Klitzing

Quantum oscillations and/or Quantum Hall Effect (QHE) originate from Landau quantization > kBT Lev Landau B = 0 c > 1 1908 - 1968 or c << 1 Energy spectra En = ћc(n + 1/2), c = eB/m*

Quantum Hall Array Resistance Standards

Quantum effects at room temperature !

?!  ~ 104 cm2/Vs <<  ~ 106 cm2/Vs (graphite)

Room-Temperature Quantum Oscillations in Bulk Graphite: More Experimental Evidence for Dirac-like Spectrum HOPG En = ±(2evF2|n|B)1/2  ~ 106 cm2/Vs ! Y. Kopelevich and P. Esquinazi, Advanced Materials 19, 4559 (2007)

Andre Geim, Nobel Lecture 2010

Finding of the Quantum Hall Effect in Graphite Y. Kopelevich et al., PRL 90, 156402 (2003); PRB 68, 165408 (2003). c/basal  105

The occurrence of QHE in graphite has been confirmed by others: QHE measured for 8 m thick HOPG sample at T = 0.3 K; K. S. Novoselov et al., cond-mat/0410631 QHE measured for a few-layer thick graphite sample at T = 3 K; K. S. Novoselov et al., Science’2004

Y. Kopelevich et al., PRL 2003 FLG Novoselov et al., 2004

Dirac fermions in graphene and bulk graphite

Bulk graphite

Massive electrons Quasi-2D Dirac holes o – max xx (n) I. A. Luk’yanchuk and Y. K. , PRL 93, 166402 (2004); ibid. 97, 256801 (2006) o – max xx (n) x - min xx (n + 1/2); shifted by 1/2 to the left Massive electrons Quasi-2D Dirac holes

Hence, before graphene has been measured, its fundamental properties have already been experimentally uncovered.

In graphite ! Phys. Rev. Lett. 103, 136403 (2009) Cyclotron resonance measurements on natural graphite

spintronics

One example: EPFL

“Future of graphene”: