Lectures 15-16

Graphene and

nanotubes

Graphene is atomically thin crystal of carbon which is stronger than steel but flexible, is transparent for light, and conducts electricity (gapless ). D.I.Y. Graphene Geim & Novoselov (Manchester) 2004 Graphene from a nanopensil Kim (Columbia Univ) 2005 Ultra-thin graphitic films mechanically exfoliated from bulk

Novoselov & Geim (Manchester) Science 306,,() 666 (2004)

Geim & Novoselov - Nature Materials 6, 183 (2007) Geim & MacDonald , Physics Today 60, 35-41 (2007) Geim & Kim, Scientific American 90-97 (April 2008)

10 nm Carbon has 4 in the outer s-p shell

2 sp hybridisation forms strong directed bonds which determine a honeycomb lattice structure.

C  - bonds

2  Strong sp hybridised bonds * empty make graphene mechanically strong.  It takes 48,000 kN·m·kg−1 (compare to best steel's 154 kN·m·kg−1). Also, it is chemically resilient. ?- conduction properties

strong covalent  full bonds hexagonal Bravais lattice uutcenit cell – can be R  n a  n a chosen differently n1n2 1 1 2 2 2full2 full sites

6x1/3sites6 x 1/3 sites Carbon has 4 electrons in the outer s-p shell

2 sp hybridisation forms strong directed bonds which determine a honeycomb lattice structure.

C  - bonds  0 ~ 3eV z p ( ) orbitals determine conduction properties of graphite   *

pz-bands ~ 10eV

 Bragg scattering conditions Reciprocal lattice      iGR n1n2 G  N G  N G e 1 N1N2 1 1 2 2   G  R  2M    2a1 n1n2 G1  a1; | G1 | Sunitcell

    2a2 G2  a2 ; | G2 | G2 Sunitcell

Hexagonal Bravais lattice determines a hexagonal reciprocal lattice, with   2a 4  | G || G |  1 2 2 G1 a 3 / 2 3a Reciprocal lattice        (k  G )   (k ) G  N G  N G N1N2 N1N2 1 1 2 2

Hexagonal reciprocal lattice corresponding to  the hexagonal G2 Bravais lattice

1st Brilloun zone

 G1 Fermi ‘point’ in graphene

  (k )  EF  G Valley

 G' Graphene (monolayer of graphite) is an atomically thin zero-gap two-dimensional semiconductor with linear dispersion of conduction and valence band electrons.

cond 2 2   vp  v px  py

Electronic dispersion in the vicinity of the corner of px p y the Brillouin zone: the same in both valleys.

val 2 2   vp  v px  py Simultaneous detection high-energy photon of the energy, E and ħω~100-1000eV propagation angl e θ of photo-electrons enables p||  2mE cos one  to restore    ( p|| )  A  E completely the band structure.

work function

AlAngle-resoldhlved photo-emissi on spectroscopy (ARPES) of heavily doped graphene synthesized on silicon carbide A. Bostwick et al – Nature Physics, 3, 36 (2007) Graphene: gapless semiconductor DoS

hlholes eltlectrons Wallace, Phys. Rev. 71, 622 (1947) ncarriers Vgate

Graphene-based field-effect transistor: GraFET

Geim and Novoselov, Nature Mat. 6, 183 (2007) Graphene-based pixels

When embedded in polymers, ggpraphene reinforces them , remains graphene conducting and, since it’s thin, it is highly transparent. Thus, it is an ideal material to make flexible liquid crystal screens

Blake (Graphene Industries Ltd), et al Nano Lett. 8, 1704, (2008) or to be used in conducting coating. Graphene: state of the art in applicaitons

G sublimated on G grown on copper and G exfoliated from bulk inch-size SiC is used transferred into various media ggpraphite into for manufacturing THz is used for flexible suspensions is used to circuits. IBM & HRL (USA) optoelectronics, enhance mechanical LCD displays, touch screens. properties of light-weight (Samsung) materials (for aerospace and medical implants ).

Carbon nanotubes

Iijima 1991 Smalley 1993

STM images of carbon nanotubes T.W. Odom, J.-L. Huang, P.Kim, C.Lieber, Nature 391 (1998) Nanotubes growth Nanotube types

armchair (n,n) metallic

zig-zag (0)(n,0) semidticonductor

chiral (n, m) small-gap with n-m=3 Metallic nanotubes (n,n)  (y  0)  (y  L )  ~ 1 ei2y / L L perimeter, 2πr 2 py  M L

2 2  cond 2 h M cond 2 2 n 1  n  v px  2   v px  py L

n  0  F p px n  0,1,2,3,.... y px

2 2 val 2 h M val 2 2  n  v px    v px  py 2 L Metallic nanotubes (m,m’) with m=m’  M 1 truly 1D conductors ditdensity of states M  0  v | p | M 1 x M 1 1 px DoS  v M  0 

Yao et al (TUDelft)1999 Semicondutor-type nanotubes (different n and m) DdihthbhtillditDepending on how the carbon sheet is rolled into a nanotube, the resulting nanotube may have a gap in the spectrum. A gap in the nanotube sppyectrum is determined by its radius r, which offers a direct root towards engineering semiconductor wires with a prescribed , for use in electronic and optoelectronic devices.  v r gap

px

tunnelling current T.W. Odom, J.-L. Huang, P. Kim, C. Lieber, Nature 391 (1998) Potential applications of carbon nanotubes:

In surface tunnelling microscopy – used as a tip.

Make excellent tips for field-effect electron guns for plasma. displays (SONY). equi-potent ia l lines Northwest Doctoral Training Centre in Nanoscience

Initial training designed to demonstrate the breadth and potential of nanoscience, before focusing on one specific area of the subject.

Research and training in fundamental nanoscience, practical nano-engineering, and in medicine.

Interdisciplinary PhD projects which span from development and studies (exp and th) of fundamental properties of new materials and structures to makinggpp devices for applications in electronics and medicine.

Development of skills in nanofabrication, low-temperature physics, materials science and data storage, synthetic chemistry, cell &tissue biology, biophysics, nanophotonics and materials science – this will be your choice!