Nobel Prize in Physics 2010: The rise of graphene

The Nobel Prize in Physics 2010The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics for 2010 to Andre Geim and Konstantin Novoselov, both at University of Manchester, UK “for groundbreaking experiments regarding the two-dimensional material graphene”.

Illustration: Science vol 324, 15 May 2009

Carbon AllotropesDimensionality

diamond

The Nobel Prize in Chemistry 1996

Graphene films Field effect in graphene

(September 2010)

Every day one new paper appears!

Interesting fact:Initially submitted toNature but rejected

What is so special about graphene?

Theory: thermal fluctuations should destroy long-range order, resulting in melting of a 2D lattice at any finite temperature. (Peierls 1934; Landau 1937; Mermin 1967)

Experiments: numerous experiments on thin films have been in accord with the theory, showing that below a certain thickness, typically of dozens of atomic layers, the films become thermodynamically unstable (segregate into islands or decompose) unless they constitute an inherent part of a three-dimensional crystal.

Perfect two-dimensional (2D) crystals cannot exist in the free state, according to both theory and experiments

”Friday’s evening experiments”

Gecko tape: Geim et al., Nature Materials 2, 461 - 463 (2003)

Gecko lizard Gecko’s foot the sole of the gecko foot is covered with millions of submicron hairs that apparently stick the animal to the substrate by way of intermolecular van der Waals forces.

An artificial gecko-tape exhibits an adhesive force per hair that is comparable to that of a gecko foot-hairGeim et al., Nature Materials 2, 461 - 463 (2003)

http://improbable.com/2010/10/05/geim-becomes-first-nobel-ig-nobel-winner/

http://www.youtube.com/watch?v=A1vyB-O5i6E

Earnshaw’s theorem (1842):No stationary object made of charges, magnets and masses in a fixed configuration can be held in stable equilibrium by any combination of static electric, magnetic or gravitational forces.

Abstract. … Earnshaw’s theorem does not apply to induced magnetism. …… General stability conditions are derived, and it is shown that stable zonesalways exist

H. A. M. S. ter Tisha = hamster ”Tisha”

History of the discovery:

Motivation: metal electronics: substituting semiconductors for metal. A few-layer (100) graphite as a candidate for metal electronics.

• Initially the task was assigned to a student whoused a sophisticate polishing machine to make films as thin as possible. It did not work out.

• Scotch-tape method worked!

”Friday’s evening experiments”

http://www.youtube.com/watch?v=rphiCdR68TE&feature=player_embedded#!

even Homer Simpson can make graphene

Why is graphene stable?

substrate (SiO2)gate

graphene

Stabilizing interaction with a substrate?

Freely suspended samples are also stable (Geim et al. Nature 2007)

Graphene sheets are not perfectly flat: they exhibit intrinsic microscopic roughening. This provide a reason for the stability of two-dimensional graphene crystals

1 nm

Graphene fabrication

Micromechanical cleavage of bulk graphite(exfoliation with the help of a Scotch tape)

Epitaxial graphene grown on SiC

Crystal structure of SiC showing the two faces of the crystal cut along the (0001) plane.

One monolayer of epitaxial graphene on SiC (on C-face)

mobilities:5000 cm2/(Vs)

Berger et al., Science 2006

suspended graphene

single graphene layer on a SiO substarteNovoselov, K. S. et al. Proc. Natl Acad. Sci. USA 102, 10453 (2005).

mobilities: 200,000 cm2 /(Vs)such high mobilities can not be achieved in semiconductors!

Du et al. Nature Nanotech. 2009

The direct synthesis of large-scale graphene films using chemical vapour deposition on thin nickel layers Kim et al., Nature 2010

Roll-to-roll production of 30-inch graphene films for transparent electrodes

Ahn et al., Nature Nanotech 2010

To be useful in post-silicon electronics, spintronics or quantum computing, graphene-based devices need to be scaled to nanodimensions, with nanoribbons as the fundamental building blocks of nanocircuits and/or individual devices.

Fabrication of nanoribbons:

Controlled formation of sharp zigzag and armchair edges

Jia et al.,Science 2009

Girit et al.,Science 2009

Chemical synthesis

Li et al. Science 2008

Bottom-up approach

Cai et al. Nature 2010

Graphene patterned structures (nanoconstrictions, quantum dots, quantum antidots)

Electron beam lithography and etching technique

nanoconstrictions (Molitor et al. PRB 2009)

quantum dots (T. Ihn. 2009)

(image: T. Ihn, ETH Zurich)

antidot array (Shen et al. APL 2008)

Unzipping of carbon nanotubes to form graphene nanoribbons

by oxidative process

Kosynkin et al., Nature 458, 872 (2009)

Basics of electronics properties of graphene

A hexagonal graphene lattice with the units vectors a1 and a2

• Full and open circles mark atoms belonging to lattices A and B

• An each unit cell contains two atoms (A and B)

Two atoms in the unit cell

The Brillion zone has three equivalent K points and K´ points

The reciprocal lattice:

Basics of the electronic structure of graphene

Carbon atom:

localized covalent σ-bonds

delocalized electrons in pz-orbitals

delocalized electrons in pz-orbitals are responsible for the electronic structure of graphene

Tight-binding Hamiltonian for p-electrons in graphene

Hamiltonian:

hopping integral 2.7eV A-lattice B-lattice

Why are graphene’s electron properties so different from properties ofconventional semiconductors and metals?

Classical description ofelectron motion:Newtons’ equation

Quantum-mechanical descriptionof electron motion:Schrödinger equation

F = ma

Conventional semiconductors and metals

wave function

Graphene:

Dirac equation: m = 0

Graphene as a mother of all graphitic forms. Graphene is a 2D building material for carbon materials of all other dimensionalities. It can be wrapped up into 0D buckyballs, rolledinto 1D nanotubes or stacked into 3D graphite.(Geim and Novoselov, Nature Materials, 2007)

Previous theoretical works:Graphene as a model for carbon-based systems

The Dirac equation

Bloch electrons:

Schrödinger equation H=E gives:

Using the Bloch form, Eigenvectors and eigenfunctionsof the Bloch electrons in graphene:

The Brillion zone

Graphene is semimetal(or, altenatively, zero-band semiconductor)

Expand f(k) and in the vicinity of K-points: Using the quantum momenta operators,the Hamiltonian transforms:

Klein tunneling in graphene: quantum electrodynamics enters the lab.

Klein tunneling in graphene

Katsnelson, Novoselov, Gaim, Nature physics 2, 620 (2006)

Electron penetrate a potential barrier without reflection

Transmission T = 1 for the normal incidence

“Minimum conductivity” in graphene (Novoselov et al, Nature 2005)

Absence of localization and of the metal-insulator transition in graphene: Klein tunneling in action

Missing problem: most theoretical studies predict min = 4e2/h

The unconventional Landau level quantization in graphene,

Recent observation of the fractional quantum Hall effect:indication of the exceptional high material quality

Du et al., Nature 2009Bolotin et al., Nature 2009

Integer quantum Hall effect:Unusual sequence of the ladder of steps in the Hall conductivity (shifted by ½):

Novoselov et al., Nature 438, 197 (2005).

Applications of graphene

Andre Geim (from an interview for ScienceWach.com, 2008):

“… When someone asks about applications in my talks, I usually tell a story about how I was on a boat one day watching dolphins, and they were jumping out of the water, allowing people to nearly touch them. Everyone was hypnotized by these magnificent creatures. It was an extraordinary romantic moment.

until a little boy shouted out, "Mom, can we eat them?"

.. It's a similar matter here, okay, we just found this extraordinary material, so we're enjoying this romantic moment, and now people are asking if we can eat it or not. Probably we can, but you have to step back and enjoy the moment first”.

The highest speed graphene transistors to date, with a cutoff frequency up to 300 GHz —comparable to the very best transistors from high-electron mobility materials such gallium arsenide or indium phosphide.

Liao et al., Nature October 2010:

• There has been little motivation for the chip-makers to introduce devices based on a fundamentally different physics or on a material other than silicon. Reasons: cost for semiconductor plants, complexity of integrated circuits.

• The situation is different for radiofrequency electronics, where circuits are much less complex than digital logic chips, and makers of radiofrequency chips being more open to new device concepts and different materials.

work at progress at IBM, Samsung, Nokia

Optical properties of graphene

Nair et al., Science 2008

Despite being only one atom thick, graphene absorbs a significant ( > 2%) fraction of incident radiation. Note that a layer of conventional optoelectronic material (e.g. GaAs) of comparable thickness is practically transparent for incoming radiation.

Optical absorbtion

In all conventional semiconductor structures the absorption is fixed by the semiconductor band-gap.

Eg

Graphene opens the possibility to cover the whole range, from visible to infrared.

Gate-induced changes in the optical transition strengths

Wang et al., Science 2008

Unlike conventional materials, the optical transitions in graphene can be dramatically modified through electrical gating

Sensing application:

graphene is superior to all know materials for sensing applications.

The graphene-based sensors have achieved sensitivity to individual molecules, - the resolution that has so far been beyond the reach of any detection technique

NO2

Schedin et al., Nature Mat. 2007

Indium tin oxide (ITO) is the most commonly utilized transparent conductor in touch-screens, displays, solar cells, etc.

It is commonly recognized that the replacement of ITO is badly and urgently needed as the sources of indium dwindle while the demand for transparent conductors increases.

Graphene as a transparent electrode

Graphene electrod is superior the ITO electrodes

Ahn et al., Nature Nanotech. 2010

Bilayer graphene intra-layer hopping

inter-layer hopping

Wave function: Expansion in the vicinity of the K-point:

Energy eigenvalues:Linear dispersion:

parabolic dispersion:

Controlling the electron transport in graphene: how to open up the band gap?

Opening of the band-gap under application of the transverse gate voltage McCan, Fal’ko PRL 2006

single layer

bilayer

Bilayer in a transverse electric field

Probing the bandgap by electrical means

Oostinga et al., Nature Materials, 2008

Probing the bandgap by optical means

Zhang et al., Nature, 2008

Graphene research at LiU:

http://www.liu.se/forskning/reportage/grafen?l=sv

Graphene at LiU

More challenges in the graphene research:

Fundamental physical properties• nonlinear optical properties; Optoelectronics & Plasmonics, THz Generation• graphene hybrids with other materials; substrate-graphene interaction • spin-orbit coupling and spin relaxation; electron interaction and correlation• nonequilibrium transport and relaxation mechanisms • physics at Dirac point, disorder, screening

Material challenges:• sub-10 nm nanoribbons; atomistic control of edges• epitaxial graphene

Device applications:• Transistors• Optoelectronic devices• Sensors• Transparent electronics• …?

Ideal graphene nanoribbons

N = 7

N = 8

armchair nanoribbons are metallic for N=3p+1 and semiconducting otherwise

Armchair edge

N

Zigzag edge

N

zigzag nanoribbons are metallic for all N

Ab initio calculations predict energy gaps in all nanoribbons (both zigzag and armchair) due to the exchange interaction (Son et al., PRL 2006)

Zigzag nanoribbons armchair nanoribbons

The gap Eg is however rapidly decreases as the width of the ribbon increases

Experimental results are strikingly different from the expectations based on ideal models

M. Han et al., Phys. Rev. Lett. 98, 206805 (2007)

• The conductance does not exhibit the metallic behavior expected for the ideal zigzag ribbons.

• The experiment did not show any difference between the armchair and zigzag nanoribbons.

• All nanoribbons show the conductance gap that depends on the ribbon’s width

nanoribbon

contacts

1 m

24 nm

49 nm

71 nm

Anderson-type localization with a strongly enhanced intensity near the defects at the ribbon edges.

Already very modest edge disorder is sufficient to induce the conduction gap and to lift any difference in the conductance between nanoribbons of different edge geometry. The formation of the conduction gap is due to the pronounced edge-disorder-induced Anderson-type localization which leads to blocking of conductive paths through the ribbons.