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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.
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