Graphene- Electric Properties

Shpyrko Research Group. UCSDOct 15th 2010Jong Woo Kim

MotivationMotivation

• 2010 Nobel Prize for Physics

Physicists Konstantin Novoselov (left) and Andre Geim of University of Manchester

History History

Theory of GrapheneP. R. Wallace

Isolated atomic layer from graphite A. K. Geim, K. S. Novoseolv

Massless Dirac equation of Graphene G. W. Semenoff

[Fabrication techniques]CVD Epitaxial growth on SiCChemical method by reducing agent

1947 1984 2004 2005

Massless Dirac Fermion Proved A. K. Geim, K. S. Novoseolv Y. Zhang, P. Kim

Graphene?Graphene?

Fullerene(Bucky ball*)

Nanotube Graphene

* Nobel Prize in Chemistry 1996

0D 1D 2D

Graphene?Graphene?

• Thin, mechanically strong, transparent and flexible conductor • Can be used in touch screen, light panel, solar cells (ITO) and

flexible display

Electrical Properties Electrical Properties

• Verified Exotic Electrical Behaviors – Dirac Fermions with zero effective mass– Half-Integer Quantum Hall effect

• Novoselov, et al. Nature (2005), Zhang et al, Nature (2005)

– Klein Tunneling• A. F. Young and P. Kim, Nature (2009)

• Revisited topics – Quantum dot, p-n junction, nanoribbons, quantum point

contacts, magnetotransport near neutrality point

• Exceptional Band Structure

Dirac Point

Brillouin Zone

Dirac Cone

Electrical Properties Electrical Properties

• Unique Band Structure

Energy

Momentum

Energy

Momentum

Band GapElectrons in usual solids(Schrodinger equation)

Electrons in graphene(Dirac equation)

Electrical Properties Electrical Properties

• Hall Effect – Electric field developed across two faces of conductor in the direction j × H

when a current j flows across a magnetic field H

• Quantum Hall Effect– Discovered in 1980– σxy =νˑe2/h (ν is an integer)

– At low temperature and strong magnetic field

• Half-integer quantum Hall effect– σxy =4ˑ(N+ ½)e2/h (N is an integer)

– At room temperature (300K)

Novoselov et al, 2005

Electrical Properties Electrical Properties

• Klein tunneling– In 1929, Oscar Klein– A tunnel barrier can become fully transparent for normal incidence of

massless particles– Test in graphene was suggested by Katsnelson, Geim and Noveselov in

2006 and verified by Young and Kim in 2009

Electrical Properties Electrical Properties

• Novoselov et al. Nature. 438, 197-200 (2005)• Zhang et al. Phys. Lett. 86, 073104 (2005)• A. F. Young et al. Nature Phys. 5, 222 (2009)• A. K. Geim. Science Vol. 324. no. 5934, pp. 1530 – 1534(2009)

ReferenceReference